ALBERT

Description: 〈p〉Publication date: Available online 1 November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Michal Holčapek〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this article, we propose an axiomatic system for fuzzy “cardinality” measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by two appropriate homomorphisms between the reducts of residuated-dually residuated (rdr-)lattices. For linearly ordered rdr-lattices, we prove that each fuzzy c-measure is a product of a non-decreasing and a non-increasing fuzzy c-measure, which indicates that there is a close relation between fuzzy c-measures and FGCount, FLCount and FECount provided by L.A. Zadeh (1983) and generalized by M. Wygralak (2001). Finally, the relationship of fuzzy c-measures to graded equipollence introduced in the first part of this contribution is analyzed.〈/p〉〈/div〉

Description: This paper aims to investigate the implementation flexibility of multiperiod rail line design in a linear monocentric city. Three alternatives (fast-tracking, deferring, and do-nothing-alternative (DNA) of a candidate rail line project) are examined, based on an in-depth uncertainties analysis of the demand side for this candidate rail line project. Conditions for the three alternatives of fast-tracking, deferring, and DNA are analytically explored and an illustrative example is given to demonstrate the application of the proposed models. Insightful findings are reported on the interrelationship between the rail line length and spatial and temporal correlation of population distribution as well as the implication of the correlation in practice. Sensitivity analyses are carried out in several scenarios in another numerical example to show the proposed conditions of three alternatives.

Description: To reduce the inventory cost and ensure product quality while meeting the diverse demands of customers, manufacturers yield products in batches. However, the raw materials required for manufacturing need to be obtained from suppliers in advance, making it necessary to understand beforehand how to best structure the pickup routes so as to reduce the cost of picking up and stocking while also ensuring the supply of raw materials required for each batch of production. To reduce the transportation and inventory costs, therefore, this paper establishes a mixed integer programming model for the joint optimization of multibatch production and vehicle routing problems involving a pickup. Following this, a two-stage hybrid heuristic algorithm is proposed to solve this model. In the first stage, an integrated algorithm, combining the Clarke-Wright (CW) algorithm and the Record to Record (RTR) travel algorithm, was used to solve vehicle routing problem. In the second stage, the Particle Swarm Optimization (PSO) algorithm was used to allocate vehicles to each production batch. Multiple sets of numerical experiments were then performed to validate the effectiveness of the proposed model and the performance efficiency of the two-stage hybrid heuristic algorithm.

Description: Drivers consecutively direct their gaze to various areas to select relevant information from the traffic environment. The rate of crash risk increases with different off-road glance durations in different driving scenarios. This paper proposed an approach to identify current driving scenarios and predict driver’s eyes-off-road durations using Hidden Markov Model (HMM). A moving base driving simulator study with 26 participants driving in three driving scenarios (urban, rural, and motorway) was conducted. Three different fixed occlusion durations (0-s, 1-s, and 2-s) were applied to quantify eyes-off-road durations. Participants could initiate each occlusion for certain duration by pressing a microswitch on a finger. They were instructed to occlude their vision as often as possible while still driving safely. Drivers’ visual behavior and occlusion behavior were captured and analyzed based on manually frame by frame coding. Visual behaviors in terms of glance duration and glance location in time series were used as input to train HMMs. The results showed that current driving scenarios could be identified ideally using glance location sequences, the accuracy achieving up to 89.3%. And motorway was relatively distinguishable easily with over 90% accuracy. Moreover, HMM-based algorithms that fed up with both glance duration and glance location sequences resulted in a highest accuracy of 92.7% in driver’s eyes-off-road durations prediction. And higher accuracy achieved in longer eyes-off-road durations prediction. It indicates that time series of glance allocations could be used to predict driving behavior and indentify driving environment. The developed models in this study could contribute to the development of scenario sensitive visual inattention prewarning system.

Description: Sustainable supply chain network design has attracted great attention of academia and industry in recent years. Baijiu is one of the world’s oldest distilled alcoholic beverages and plays a significant role in Chinese culture and Chinese people’s daily life. As the production and consumption of Baijiu have a significant influence on the economic, environmental, and social performance of supply chain management, sustainable supply chain network design decisions are critical to the long-term success of the industry. In concert with the rapidly growing Chinese economy, there is a growing demand for a sustainable Baijiu industry. Therefore, this paper constructs and optimizes a network decision-support model for a sustainable Baijiu industry network design. To achieve this, the Baijiu supply chain is examined and a model is proposed for a design that encompasses economic (costs), environmental (carbon emissions), and social (local employment and regional per capita GDP) dimensions. R language programming is then applied to solve the model. A case example indicated that S1 was the optimal decision for reducing costs, S2 was the optimal solution for minimizing carbon emissions, and S3 was the best for maximizing the social impact. Considering the situation of the Baijiu industry and the focal enterprise, it was concluded that S1 would be the best solution for the case company. And the results verified the effectiveness of the framework. This paper develops a systematic and effective approach that decision-makers can use to conduct sustainable network design for Baijiu enterprises.

Description: 〈p〉Publication date: Available online 30 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Dragan Jočić, Paweł Drygaś, Ivana Štajner-Papuga〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The issue of distributivity is crucial for many different theoretical areas such as the utility theory and the integration theory. Also, this problem is of high interest for modelling some practical situations from, e.g., fields of economics and social sciences. Thus, recently, the distributivity equations have been studied for different classes of aggregation operators by a significant number of researchers. The focus of this paper in particular is on solving the left and the right distributivity equations between semi-t-operators.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Andrey G. Bronevich, Igor N. Rozenberg〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉It is an important feature of a monotone measure that it is not additive in general. In the paper we propose the mathematical tool, based on canonical sequences of monotone measures, for analyzing additivity of monotone measures on subalgebras and give a way of generating such monotone measures. It turns out that the generating rule can be considered as an effect of a linear operator defined on the set of monotone measures. We also investigate in what cases the sequence of such operators behaves commutatively and preserve continuity properties from the generating monotone measure.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Ľubomíra Horanská, Peter Sarkoci〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper answers the problem of copulas invariant with respect to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉-transformations recently proposed by Horanská and Kolesárová (2017) [8]. Using tools from ergodic theory and iterated function systems we prove that the conjecture formulated therein is not true in general and for every 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si127.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mo stretchy="true"〉]〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="true"〉[〈/mo〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉 we construct a one-parametric class of nontrivial copulas invariant with respect to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉a〈/mi〉〈mo〉,〈/mo〉〈mi〉b〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉-transformation.〈/p〉〈/div〉

Description: In this study the interaction energies for single-stranded DNA and double-stranded DNA molecules with a lipid bilayer are investigated. The 6-12 Lennard-Jones potential and continuous approximation are used to derive analytical expressions for these interaction energies. Assuming that there is a circular gap in the lipid bilayer, we determine the relationship of the molecular interaction energy, including the circular gap radius and the perpendicular distance of the single-stranded DNA and double-stranded DNA molecules from the gap. For both single-stranded and double-stranded DNA molecules, the relationship between the minimum energy location and the hole radius is calculated; in the case of the double-stranded DNA molecule, we assume that the helical phase angle is equal to . By minimizing the total interaction energies, the results demonstrate that the single-stranded DNA and double-stranded DNA molecules move through a lipid bilayer when the gap radius 10 Å and 13.8 Å, respectively. The results present in this project can be leveraged to understand the interactions between cell-penetrating peptides and biomembranes, which may improve gene and drug delivery.

Description: 〈p〉Publication date: Available online 29 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Do Wan Kim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper focuses on a fuzzy-model-based design problem for the hovering control of a class of nonlinear quadrotors. The concerned problem turns into an exponential stabilization of an augmented error system to incorporate the tracking of the desired three dimensional position and yaw angle and the stabilization of roll and pitch motions. The augmented error dynamics under the proposed control scheme can be viewed as an interconnected system. It is shown that the interconnected system is exponential stable if its subsystems systems are so. This property makes the separate design of the available control inputs possible. Then, sufficient linear matrix inequality (LMI) conditions for its local exponential stabilizability are derived in the sense of Lyapunov stability criterion. An example is given to illustrate the effectiveness of the proposed design methodology.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Nikolai Krivulin, Sergeĭ Sergeev〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise comparison data. In this framework, we first consider the minimax Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale. Recasting this approximation problem as a problem of tropical pseudo-quadratic programming, we then write out a closed-form solution to it. This solution might be either a unique score vector (up to a positive factor) or a set of different score vectors. To handle the problem when the solution is not unique, we develop tropical optimization techniques of maximizing and minimizing the Hilbert seminorm to find those vectors from the solution set that are the most and least differentiating between the alternatives with the highest and lowest scores, and thus are well representative of the entire solution set.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Daniel Jardón, Iván Sánchez, Manuel Sanchis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For a continuous function 〈em〉f〈/em〉 on a Hausdorff space 〈em〉X〈/em〉, we prove that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mo stretchy="false"〉[〈/mo〉〈mover accent="true"〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈mrow〉〈mo〉ˆ〈/mo〉〈/mrow〉〈/mover〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉]〈/mo〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈/mrow〉〈/msub〉〈mo〉=〈/mo〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 for each 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉u〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="script"〉F〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si239.gif" overflow="scroll"〉〈mi〉α〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉[〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉]〈/mo〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si110.gif" overflow="scroll"〉〈mover accent="true"〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈mrow〉〈mo〉ˆ〈/mo〉〈/mrow〉〈/mover〉〈/math〉 is the Zadeh's extension of 〈em〉f〈/em〉. By means of this result, some results on (locally) compact spaces and the Zadeh's extension are generalized. Given a metric space 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, we introduce Skorokhod's metric 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 on the set 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" overflow="scroll"〉〈mi mathvariant="script"〉F〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 of the family of all upper semicontinuous fuzzy sets 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.gif" overflow="scroll"〉〈mi〉u〈/mi〉〈mo〉:〈/mo〉〈mi〉X〈/mi〉〈mo stretchy="false"〉→〈/mo〉〈mo stretchy="false"〉[〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉]〈/mo〉〈/math〉 with compact support and such that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉u〈/mi〉〈/mrow〉〈mrow〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is non-empty. We show that if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" overflow="scroll"〉〈mi〉f〈/mi〉〈mo〉:〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉→〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is a continuous function, then its Zadeh's extension 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si110.gif" overflow="scroll"〉〈mover accent="true"〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈mrow〉〈mo〉ˆ〈/mo〉〈/mrow〉〈/mover〉〈/math〉 to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="script"〉F〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is also continuous and that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is separable if and only if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="script"〉F〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉X〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is separable. We also present a fuzzy version of the so-called Hutchinson operator, a valuable tool in fractal theory.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 13 November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): M. Rahimi, A. Shakouri〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In Rahimi and Riazi (2014) [22], a type of entropy of continuous maps on compact metric spaces is defined via integrating a local entropy map. This average entropy is represented in terms of the entropy in the sense of Dumitrescu, but the equality of these two types of entropy is left as an open problem in [22]. In this paper, we modify the problem stated in [22], by replacing the Dumitrescu entropy by the Hudetz entropy, since in our case, the two previous types of entropy take an infinite value and the problem stated in [22] reduces to a trivial equality. Then we conclude the paper by proving the equality of the modified average entropy and the Hudetz entropy. The key tool is a version of Jaccob's theorem for the Hudetz entropy.〈/p〉〈/div〉

Description: Short-term traffic flow forecasting is one of the key issues in the field of dynamic traffic control and management. Because of the uncertainty and nonlinearity, short-term traffic flow forecasting remains a challenging task. In order to improve the accuracy of short-term traffic flow forecasting, a short-term traffic flow forecasting method based on LSSVM model optimized by GA-PSO hybrid algorithm is put forward. Firstly, the LSSVM model is constructed with combined kernel function. Then the GA-PSO hybrid optimization algorithm is designed to optimize the kernel function parameters efficiently and effectively. Finally, case validation is carried out using inductive loop data collected from the north-south viaduct in Shanghai. The experimental results demonstrate that the proposed GA-PSO-LSSVM model is superior to comparative method.

Description: The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

Description: 〈p〉Publication date: Available online 11 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Hongxiang Tang, Zhaowen Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A fuzzy information system is an important mathematical model in the field of artificial intelligence and the notion of homomorphisms between fuzzy information systems is a kind of tool to study data compression in fuzzy information systems. This paper investigates invariant characterizations of fuzzy information systems under some homomorphisms based on data compression. Upper-reducts, lower-reducts and reducts in a fuzzy information system are first investigated. Then, fuzzy sets in a fuzzy information system are divided into three categories according to their importance. Next, measures of uncertainty for fuzzy information systems are investigated and in order to show the performance of the proposed measures, a numerical experimental example on the Ecoli data set that comes from UCI Repository of machine learning databases is given. Finally, invariant and inverse invariant characterizations of a fuzzy information system under some homomorphisms are obtained.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 11 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Peng Wang, Xiaobing Zhang, Jihong Zhu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Under a large deviation between the initial state and the desired trajectory, the traditional single-loop control method usually fails to solve the output tracking of SISO nonlinear systems due to the inherent uncertainties, input saturation, and unmeasurable states. In this work, a novel tracking control system is proposed in the framework of two-loop control system to achieve high-accurate tracking performance and reconcile the contradiction between the system's available regulating capacity and the required tracking capacity. Specifically, an observer and command-filtered-based adaptive fuzzy controller are synthesized in the inner loop to guarantee a satisfying tracking accuracy and remain robust to uncertainties. A simplified fuzzy approximator is utilized to estimate the uncertainties with a single adaptive parameter. Then, a replanned reference trajectory is generated in the outer loop by online optimization to minimize the transient performance over the predictive horizon. Moreover, a tracking governor of reference trajectory is proposed to obtain an adaptive convergence rate with respect to the desired trajectory while only satisfying relatively loose constraints. Simulation results prove that the proposed two-loop scheme can not only improve the tracking accuracy; but also has the adaptability to fulfill the particular engineering problems that have a large difference between the initial condition and the desired trajectory.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Antonio Di Nola, Anatolij Dvurečenskij, Giacomo Lenzi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An observable on an MV-algebra is any 〈em〉σ〈/em〉-homomorphism from the Borel 〈em〉σ〈/em〉-algebra 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉B〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="double-struck"〉R〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 into the MV-algebra which maps a sequence of disjoint Borel sets onto summable elements of the MV-algebra. We establish that there is a one-to-one correspondence between observables on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1153.gif" overflow="scroll"〉〈mi mathvariant="normal"〉Rad〈/mi〉〈/math〉-Dedekind 〈em〉σ〈/em〉-complete perfect MV-algebras with principal radicals and their spectral resolutions. It means that we show that our partial information on an observable known only on all intervals of the form 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mo〉−〈/mo〉〈mo〉∞〈/mo〉〈mo〉,〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is sufficient to determine the whole information about the observable. In addition, this correspondence allows us to define the Olson order which is a partial order on the set 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1025.gif" overflow="scroll"〉〈mi mathvariant="script"〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉M〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 of all observables on an MV-algebra 〈em〉M〈/em〉 as well as, we can define a sum of observables, so that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1025.gif" overflow="scroll"〉〈mi mathvariant="script"〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉M〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 becomes a lattice-ordered semigroup.〈/p〉〈/div〉

Description: The application of pest management involves two thresholds when the chemical control and biological control are adopted, respectively. Our purpose is to provide an appropriate balance between the chemical control and biological control. Therefore, a Smith predator-prey system for integrated pest management is established in this paper. In this model, the intensity of implementation of biological control and chemical control depends linearly on the selected control level (threshold). Firstly, the existence and uniqueness of the order-one periodic solution (i.e., OOPS) are proved by means of the subsequent function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the limit method of the successor points’ sequences and the analogue of the Poincaré criterion. Moreover, an optimization strategy is formulated to reduce the total cost and obtain the best level of pest control. Finally, the numerical simulation of a specific model is performed.

Description: The pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation method. At the end of this paper, some numerical experiments were adopted to compare the new pricing formula introduced in this paper with the classical Black-Scholes pricing formula. The result showed that the new pricing formula conformed to the actual financial market. In fact, the option value is positively correlated with the underlying asset price and the company’s asset price and the jump process has significant influence on the value of option.

Description: Direct chain enterprises (DCEs) face a decision-making issue as to how to allocate and supply their products to their stores for sales with the minimum losses and maximum profits for the manufacturers. This paper presents a single-cycle optimal allocation model for DCEs under the given total production amount and conditional value at risk loss. The optimal strategy for production allocation and supply is derived. Subsequently, an approximate algorithm for solving the optimal total production amount is presented. The optimal allocation and supply strategy, the minimum total production amount, the minimum allocation strategy, and the discount pricing strategy are obtained for the single cycle. Finally, with the sales data of a food DCE, numerical results corroborate that adopting different production and supply strategies reduces the risk of expected losses and increases the expected return. It is of an important theoretical significance in guiding the production and operation of direct chain enterprises.

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Zhenbin Du, Zhenzheng Yan, Zhen Zhao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper addresses an interval type-2 (IT2) fuzzy sampled-data tracking control problem of nonlinear systems subject to uncertain parameters. The controlled plant is modeled as Takagi–Sugeno (T–S) fuzzy structure, where the parameter uncertainties are captured effectively by the lower and upper membership functions. By means of the linear matrix inequalities (LMIs) and free-weighting matrices, an IT2 fuzzy sampled-data control scheme is developed such that the system states are driven to track those of the reference model. Finally, an inverted pendulum system and a mass–spring–damper mechanical system are used to show the efficiency of the suggested tracking control design.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Xuan Liu, Ding Zhai, Tieshan Li, Qingling Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the problem of adaptive fuzzy fault-tolerant control (FTC) is investigated for a class of nonlinear pure-feedback systems with unknown control directions and sensor failures. By utilizing the mean value theorem, the considered nonlinear pure-feedback system is transformed into a strict-feedback structure. The unavailability of state variables caused by sensor faults is dealt with by using parameter separation and regrouping technique. Based on cancelation and decoupled backstepping technique, an adaptive fuzzy fault-tolerant control method is developed. It is proved that the proposed adaptive FTC scheme can guarantee the exponential stabilization of the resulting closed-loop system. Furthermore, all the signals of the system remain semi-global uniformly ultimately bound (SGUUB). The simulation results are provided to illustrate the effectiveness of the proposed control scheme.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Yue Wu, Jiuxiang Dong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies the tracking control problem for the non-Gaussian stochastic distribution sampled-data fuzzy systems. First, by constructing an augmented system, an asynchronous proportional-integral (PI) controller is designed such that the probability density functions (PDFs) of the system output can track the target one. Second, by introducing two sets (the extension reachable set and the ellipsoid set), the state trajectories of the augmented system with persistent reference input signal can be restricted in a given local region, namely, the state constrained problem can be addressed. Furthermore, in some existing asynchronous controller strategies, it is required that the derivative of the membership function of the system not explicitly depends on the system input. However, in this paper, by restricting the state into a specified region, a new asynchronous scheme is proposed so as to the above-mentioned requirement is removed. Finally, an example is given to demonstrate the efficiency of the presented method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Hao Shen, Mengping Xing, Shicheng Huo, Zheng-Guang Wu, Ju H. Park〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is concerned with the problem of the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉H〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 asynchronous state estimation for fuzzy Markov jump neural networks (FMJNNs) with uncertain measurements over a finite-time interval. In terms of a Bernoulli distributed white sequence, the phenomenon of the randomly occurring uncertainties in the output equation is represented by exploiting a random variable with known occurrence probabilities. The main focus of this paper is to present a state estimator such that the resulting error system is finite-time bounded and satisfies an 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉H〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 performance requirement. Then, by employing the stochastic analysis technique, sufficient conditions are provided to ensure that the state estimator is designed by means of solving a convex optimization problem. An example is finally given to explain the effectiveness and potentiality of the proposed design method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Temoatzin González, Antonio Sala, Miguel Bernal〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This work generalises the line-integral Lyapunov function in (Rhee & Won, 2006) for stability analysis of continuous-time nonlinear models expressed as fuzzy systems. The referred result applied only to Takagi–Sugeno representations, and required memberships to be a tensor-product of functions of a single state; these are generalised here so that membership arguments can be arbitrary polynomials of the state variables; in this way, systems for which earlier results cannot be applied are now covered. Both the modelling and the integral terms appearing in the Lyapunov functions are generalised to a fuzzy polynomial case. Illustrative examples show the advantage of the proposed method against previous literature, even in the TS case.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Ali Reza Tavakoli, Ali Reza Seifi, Mohammad Mehdi Arefi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This study presents a self-constructing fuzzy neural network (SCFNN) based static synchronous series control (SSSC) to mitigate the inter-area oscillations in interconnected power systems. The proposed intelligent system includes an on-line trained fuzzy neural network (FNN) controller with adaptive learning rates (ALRs) and self-constructing mechanism. The Lyapunov scheme is employed to obtain the adaptive learning rates. Therefore, convergence of the suggested controller can be ensured. The proposed approach is such that, at first, originally, no neurons exist in the structure of FNN. In fact, they are automatically created and if it is required, they will be created. Therefore, the total time for training algorithm is significantly reduced and the speed of controller is considerably increased. In addition, the Prony technique is utilized to guesstimate the damping ratio of oscillations. The results confirm the usefulness of the suggested controller.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): Xiaozhan Yang, Hak-Keung Lam, Ligang Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema〈sup〉1〈/sup〉. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 356〈/p〉 〈p〉Author(s): 〈/p〉

Description: The aim of this report to solve the open problem suggested by Chen et al. We study the graph entropy with ABC edge weights and present bounds of it for connected graphs, regular graphs, complete bipartite graphs, chemical graphs, tree, unicyclic graphs, and star graphs. Moreover, we compute the graph entropy for some families of dendrimers.

Description: 〈p〉Publication date: Available online 14 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Fang Wang, Zhi Liu, Yun Zhang, C.L. Philip Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates a finite-time tracking control of stochastic nonlinear systems with actuator failures. As the nonlinearities and actuator failures are completely unknown, the existing control methods are unavailable. By applying an approximation property of fuzzy logic systems, an adaptive finite-time control strategy is presented. Since the existing finite time stability criterion can not deal with the finite time control under the effect of approximation error, Lemma 5 is first established. Under the proposed scheme, the actuator failures are compensated successfully, and the finite-time tracking performance and stability of stochastic nonlinear system are assured. Based on Lemma 5 and Jessen's inequality, the finite-time stability of stochastic nonlinear systems is proved.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 28 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): J. Recasens, M.S. Tomás〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉Two geometric characterizations of positive definite reflexive and symmetric fuzzy relations are provided based on the embeddability of their naturally associated pseudodistances with respect to the continuous Archimedean t-norms with additive generators 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉t〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈mi mathvariant="normal"〉arccos〈/mi〉〈mo〉⁡〈/mo〉〈mi〉x〈/mi〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉t〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈msqrt〉〈mrow〉〈mn〉1〈/mn〉〈mo〉−〈/mo〉〈mi〉x〈/mi〉〈/mrow〉〈/msqrt〉〈/math〉.〈/p〉 〈p〉Due to the important role of the t-norm 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉T〈/mi〉〈/mrow〉〈mrow〉〈mi mathvariant="normal"〉arccos〈/mi〉〈mo〉⁡〈/mo〉〈mi〉x〈/mi〉〈/mrow〉〈/msub〉〈/math〉 with additive generator 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉t〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉x〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈mi mathvariant="normal"〉arccos〈/mi〉〈mo〉⁡〈/mo〉〈mi〉x〈/mi〉〈/math〉 in these characterizations, different characterizations of it are given. In particular, a left-continuous t-norm 〈em〉T〈/em〉 is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉T〈/mi〉〈/mrow〉〈mrow〉〈mi mathvariant="normal"〉arccos〈/mi〉〈mo〉⁡〈/mo〉〈mi〉x〈/mi〉〈/mrow〉〈/msub〉〈/math〉 if and only if the rank of the matrices of all one-dimensional indistinguishability operators with respect to 〈em〉T〈/em〉 are less than or equal to 2.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 29 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Yang Liu, Xiaoping Liu, Yuanwei Jing〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The semi-globally practical finite-time stability (SGPFS) problem for a class of uncertain strict-feedback nonlinear systems is discussed in this paper. A novel performance function called finite-time performance function (FTPF) is first defined. Moreover, this paper is the first to solve an adaptive semi-globally practical finite-time control issue by combining with backstepping, prescribed performance control (PPC) and fuzzy logic systems. Furthermore, it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite-time, but also all the signals of the closed-loop systems are SGPF-stable. Simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 28 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Oihana Aristondo, Eneritz Onaindia〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For decomposable poverty measures in incidence, intensity and inequality among the poor, poverty changes between two periods can be expressed in terms of the three poverty components in the two periods. However, most of the poverty decompositions cannot be written in a linear form of the terms. We apply the Shapley decomposition approach in order to decompose the overall poverty change as the sum of the contributions of the three poverty components' changes. We provide a method to compute the contributions for any decomposable poverty index, and specifically, the contributions formulas for the Sen index and the Foster, Greer and Thorbecke index for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉α〈/mi〉〈mo〉=〈/mo〉〈mn〉2〈/mn〉〈/math〉 are shown. Using EU-SILC data for 2008 and 2015 for 28 European Countries, we analyze the change over time in the FGT〈sub〉2〈/sub〉 poverty index and the value of the marginal contributions of the three components.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Quentin Brabant, Miguel Couceiro, José Rui Figueira〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper deals with the problem of interpolating partial functions over finite distributive lattices by lattice polynomial functions. More precisely, this problem can be formulated as follows: Given a finite distributive lattice 〈em〉L〈/em〉 and a partial function 〈em〉f〈/em〉 from 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉D〈/mi〉〈mo〉⊆〈/mo〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msup〉〈/math〉 to 〈em〉L〈/em〉, find all the lattice polynomial functions that interpolate 〈em〉f〈/em〉 on 〈em〉D〈/em〉. If the set of lattice polynomials interpolating a function 〈em〉f〈/em〉 is not empty, then it has a unique upper bound and a unique lower bound. This paper presents a new description of these bounds and proposes an algorithm for computing them that runs in polynomial time, thus improving existing methods. Furthermore, we present an empirical study on randomly generated datasets that illustrates our theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 18 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Changjiang Xi, Jiuxiang Dong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates the problem of approximation-based adaptive reliable tracking control for a class of uncertain nonlinear strict-feedback systems. The considered system is with unknown time delays and abrupt non-affine nonlinear faults. To eliminate the effect of unknown time delays, the finite covering lemma and fuzzy logic systems are utilized, and the traditional Lyapunov–Krasovskii function is abandoned. With the help of mean-value theorem, the non-affine nonlinear faults are decoupled for the strictness of system. Based on the property of Nussbaum function, the problem of unknown control directions and control gains is solved. Finally, a novel adaptive fault-tolerant control scheme with the feedback information of not only the current states but also the past states is designed. It is guaranteed that all the signals in the closed-loop system are semi-global uniformly bounded and the tracking error converges to a small neighborhood of the origin. Simulation results from a practical example of isothermal continuous stirred tanks reactors are given to demonstrate the effectiveness of the proposed control scheme.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Chao Wang, Ravi P. Agarwal, Donal O'Regan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we establish an embedding theorem for the fuzzy multidimensional space and introduce the new types of multiplications of fuzzy vectors determined by the determinant algorithm. Then some fundamental results of calculus of fuzzy vector-valued functions on time scales are established. Based on these results, we introduce the concept of shift almost periodic fuzzy vector-valued functions and develop a theory of almost periodic fuzzy functions on time scales. This function theory can be used to study almost periodic fuzzy dynamic equations on time scales including a new type of fuzzy dynamic equations called fuzzy 〈em〉q〈/em〉-dynamic equation (i.e., quantum fuzzy dynamic equation).〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 17 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Wuxi Shi, Fanlei Yan, Baoquan Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates an adaptive fuzzy decentralized control approach for a class of nonlinear systems with unknown control direction and different performance constraints. In the control design, the different performance constraints, that are the prescribed performance error constraints for some subsystems and the asymmetric time-varying output constraints for the others, can be unified as one form by selecting proper performance functions. The fuzzy systems are employed to approximate the unknown nonlinear functions, and an adaptive fuzzy decentralized controller loaded with the Nussbaum-type function is developed to resolve the unknown control direction issues. It is proved that all the signals in the resulting closed-loop systems are bounded and that the different performance constraints for the subsystems can be achieved simultaneously. The performance of the proposed scheme is highlighted through the simulation example.〈/p〉〈/div〉

Description: Using the panel data of 29 provinces and regions in China, this paper analyzes the temporal and spatial characteristics of PM2.5 concentration. The spatial Durbin model is used to empirically examine the impact of energy development and technological innovation on PM2.5. The results show that the interprovincial PM2.5 in China showed an inverted “N” trend. There is a spatial agglomeration of interprovincial PM2.5, and the spatial autocorrelation is significant. The spatial autoregression coefficients of adjacent weights and distance weights are significantly positive, and PM2.5 pollution in adjacent areas has a positive effect on the region. From the view of energy development, the increase in energy intensity will significantly increase the concentration of PM2.5 in adjacent areas, which will increase the global PM2.5 concentration. The increase in the proportion of coal consumption increases the concentration of PM2.5 in the region and globally. The increase in energy consumption prices will reduce the PM2.5 concentration in the region and globally. From the view of technological innovation, the increase in sales revenue of new products of industrial enterprises above the scale will reduce the concentration of PM2.5 in the region by 0.1285 percentage points and the concentration of PM2.5 in adjacent areas by 0.3058 percentage points, which will reduce the global PM2.5 concentration by 0.4343 percentage points. The increase in the number of granted patent applications will reduce the PM2.5 concentration of the adjacent regions and globally. The increasing level of infrastructure for technological innovation in the region will reduce the concentration of PM2.5 in adjacent areas. The increase in technical market turnover will reduce the concentration of PM2.5 in the region and the concentration of PM2.5 in adjacent areas, which will reduce the global PM2.5 concentration. In order to reduce the concentration of PM2.5 in China, we should continue to promote PM2.5 regional collaborative governance. In terms of energy development, it is necessary to reduce energy intensity, optimize energy structure, implement energy substitution, and rationalize energy prices. In terms of technological innovation, it is essential to increase sales revenue of new products of industrial enterprises, raise number of granted patent applications, vigorously improve level of infrastructure for technological innovation, and enhance technical market turnover.

Description: 〈p〉Publication date: Available online 14 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Yue Wu, Jiuxiang Dong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper focuses on a local stabilization problem for discrete-time T–S fuzzy time-delay systems with sensor fault and external disturbances. The main purpose is to synthesize a controller such that the state can be restricted into a pre-specified region even when the system is subject to sensor fault and external disturbance. First, by restricting the reachable set into an ellipsoid set which is contained in the objective domain, the system state is restricted into the objective area such that the local stabilization can be achieved. Second, the differential mean value theorem is used to determine the bound of the deviation between the membership function of the system and that of the controller. Then, the information of the deviation is employed for designing the controller. Different from some existing methods, in the proposed method, the influence of the sensor fault on the membership function of the controller has been fully considered and the information of aforementioned deviation is made full use of such that a less conservative stability criterion can be derived. Meanwhile, due to the use of the differential mean value theorem, the deviation bound can be calculated. Then, the requirement, where the deviation bound of is assumed to be previously known, is removed. Finally, an example is presented to verify the effectiveness of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Fei Xia, Hongxiang Tang, Sichun Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A knowledge base is a basic concept in rough set theory. Uncertainty measures are critical evaluation tools in machine learning fields. This article investigates relationships between knowledge bases and their uncertainty measures. Firstly, dependence and independence between knowledge bases are proposed, and are characterized by the inclusion degree. Secondly, knowledge distance between knowledge bases is studied. Thirdly, invariant and inverse invariant characteristics of knowledge bases under homomorphisms based on data compression are obtained. Fourthly, measuring uncertainty of knowledge bases is investigated, and an example is provided to illustrate the fact that knowledge granulation, rough entropy, knowledge entropy, and knowledge distance are neither invariant nor inverse invariant under homomorphisms based on data compression. Finally, a numerical experiment is provided to show features of the proposed measures for uncertainty of knowledge bases, and effectiveness analysis is conducted from the two aspects of dispersion and correlation. These results will be helpful for the establishment of a framework of granular computing in knowledge bases.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): H. Akrout, J.-F. Crouzet, O. Strauss〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Signal and image processing make intensive use of positive, bounded and centered functions that are called kernels. Kernels are used for defining the interplay between discrete and continuous domains, filtering, modeling a system through a point spread function, etc. The possible analogy between kernels and fuzzy sets has led to a wide use of fuzzy set theory for signal and image processing [1]. The possibilistic interpretation of fuzzy sets has recently been exploited to extend signal processing with the aim of accounting for poor knowledge of the appropriate kernel to be used. These 〈em〉imprecise kernels〈/em〉 are called maxitive kernels. A maxitive kernel can be seen as a convex set of conventional kernels. Within this framework, the triangular kernel with mode 0 and spread Δ has a specific role since it can be used to represent a convex set of all bounded centered bell-shaped kernels of spread 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉δ〈/mi〉〈mo〉≤〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈/math〉, i.e. the way kernels are usually imprecisely known (shape unknown, spread imprecise). However, this principle has yet to be extended to more than one dimension despite the fact that it is needed for image processing. An extension to higher dimensions is proposed in this paper.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Hongliang Lai, Dexue Zhang, Gao Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents a comparative study of three kinds of ideals in quantale-valued order theory: forward Cauchy ideals (generated by forward Cauchy nets), flat ideals and irreducible ideals. Main results include necessary and sufficient conditions for forward Cauchy ideals to be flat or irreducible for integral quantales.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): František Včelař, Zuzana Pátíková〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The paper deals mainly with a fuzzification of the classical Tarski's theorem for commutative sets of isotone maps (the so-called generalized theorem) in a sufficiently rich fuzzy setting on general structures called 〈strong〉L〈/strong〉-complete propelattices. Our concept enables a consistent analysis of the validity of single statements of the generalized Tarski's theorem in dependence on assumptions of relevant versions of transitivity (weak or strong). The notion of the 〈strong〉L〈/strong〉-complete propelattice was introduced in connection with the fuzzified more famous variant of Tarski's theorem for a single 〈strong〉L〈/strong〉-fuzzy isotone map, whose main part holds even without the assumption of any version of transitivity. These results are here extended also to the concept of the so-called 〈strong〉L〈/strong〉-fuzzy relatively isotone maps and then additionally compared to the results, which are achieved for the generalized theorem and which always need a relevant version of transitivity. Wherever it is possible, facts and differences between both the theorems are demonstrated by appropriate examples or counterexamples.〈/p〉〈/div〉

Description: This paper deals with stochastic dynamic facility layout problem under demand uncertainty in terms of material flow between facilities. A robust approach suggests a robust layout in each period as the most frequent one falling within a prespecified percentage of the optimal solution for multiple scenarios. Mont Carlo simulation method is used to randomly generate different scenarios. A mathematical model is established to describe the dynamic facility layout problem with the consideration of transport device assignment. As a solution procedure for the proposed model, an improved adaptive genetic algorithm with population initialization strategy is developed to reduce the search space and improve the solving efficiency. Different sized instances are compared with Particle Swarm Optimization (PSO) algorithm to verify the effectiveness of the proposed genetic algorithm. The experiments calculating the cost deviation ratio under different fluctuation level show the good performance of the robust layout compared to the expected layout.

Description: With the rapid development of modern automotive logistics industry, vehicle logistics has drawn more and more attention. Since the vehicle transporters mainly are the severe-polluting heavy-duty vehicles and their exhaust emissions vary under different traffic conditions, it is necessary to improve the planning of road motor-transporting services by taking into account road traffic condition, especially for urban areas. This study aims at minimizing the composite cost, including both the economic cost related to the driver cost and fuel consumption, and the social cost related to the vehicle emissions. The dynamic road traffic condition is imitated dynamically with a discretization technique. A metaheuristic is applied with data collected from a dense district in a huge city. Experimental results show that the proposed approach can always converge quickly to the best solution and the solution with minimal composite cost can always dominate the other solutions with classic route optimization goals.

Description: This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor’s measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results.

Description: In this paper we study the semigroup of all tropical matrices under multiplication. We give a description of the tropical matrix groups containing a diagonal block idempotent matrix in which the main diagonal blocks are real matrices and other blocks are zero matrices. We show that each nonsingular symmetric idempotent matrix is equivalent to this type of block diagonal matrix. Based upon this result, we give some decompositions of the maximal subgroups of which contain symmetric idempotents.

Description: 〈p〉Publication date: Available online 26 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Bin Pang, Fu-Gui Shi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For fuzzy counterparts of hull operators and interval operators, two types of fuzzy hull operators and one type of fuzzy interval operators are proposed. Firstly, the concept of 〈em〉L〈/em〉-hull operators is introduced and the resulting category is shown to be isomorphic to that of 〈em〉L〈/em〉-convex spaces. Secondly, considering the graded inclusions of 〈em〉L〈/em〉-subsets, the notion of 〈em〉L〈/em〉-ordered hull operators is presented, which is shown to be categorically isomorphic to strong 〈em〉L〈/em〉-convex structures. Finally, the concept of 〈em〉L〈/em〉-interval operators is introduced and it is shown that there is a Galois correspondence between the category of 〈em〉L〈/em〉-interval spaces and that of 〈em〉L〈/em〉-convex spaces. In particular, the category of arity 2 〈em〉L〈/em〉-convex spaces can be reflectively embedded into that of 〈em〉L〈/em〉-interval spaces.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 353〈/p〉 〈p〉Author(s): Hsien-Chung Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Three types of binary operation between any two fuzzy sets are proposed in this paper. The concept of 0-level set of fuzzy set plays an important role for defining the binary operations between two fuzzy sets. According to the decomposition theorem of fuzzy sets, the consistency between the membership functions and 〈em〉α〈/em〉-level sets should be rigorously verified when the binary operation between two fuzzy sets is defined by using their 〈em〉α〈/em〉-level sets. The consistency is investigated thoroughly in this paper for the purpose of guaranteeing the existence of such binary operations. Moreover, we also propose the so-called Hausdorff difference between any two fuzzy sets to define the difference of any two fuzzy numbers.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): S. Mashchenko〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We investigate intersections and unions of sets with fuzzy sets of operands. These are natural generalizations of the corresponding operations which involve crisp sets of operands. It is shown that the resulting set is a fuzzy set of type-2 (T2FS). We prove several results which enable us to simplify constructing the type-2 membership functions for intersections and unions of fuzzy sets of operands. We check that de Morgan's laws hold for these two operations with fuzzy sets of operands. As far as the two operations on crisp sets are concerned, the resulting T2FS can be represented as two standard fuzzy sets of its sections. We provide some insight into how these sections are related.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 18 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Meng Zhang, Peng Shi, Longhua Ma, Jianping Cai, Hongye Su〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper focuses on the issue of network-based fuzzy control for nonlinear Markov jump systems with unreliable communication links. The nonlinear system under consideration is described by a Takagi–Sugeno (T–S) fuzzy model through corresponding fuzzy rules. The control signals are quantized by a logarithmic quantizer before they are transmitted to the network, and in case quantized control signals lose intermittently when being passed to the actuator, a compensation strategy is implemented to deal with the packet dropout. Based on a novel Lyapunov function which is both fuzzy-basis-dependent and mode-dependent, the existence criterion for the desired controller is established to ensure the stochastic stability as well as a predefined 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 performance index of the resulting closed-loop system. A bench mark example of robot arm is presented to demonstrate the validity of the proposed design technique.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Chun Yong Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Although Qiao and Hu intended to propose granular variable precision 〈em〉L〈/em〉-fuzzy rough sets based on residuated lattices, 〈em〉L〈/em〉 actually denotes a doubly residuated lattice with an involutive negation. However, there exist doubly residuated lattices without involutive negations. This paper presents a comparative study of variable precision fuzzy rough sets based on residuated lattices, in which we compare variable precision 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉-fuzzy rough sets with the preexisting models. A variable precision upper 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉-fuzzy rough approximation operator is proposed with 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉-fuzzy granules based on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉-fuzzy implication on a residuated lattice 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉 instead of a doubly residuated lattice. The variable precision upper 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉-fuzzy rough approximation operator is investigated with respect to different 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉L〈/mi〉〈/math〉-fuzzy relations regardless of proposing an involutive negation on a residuated lattice.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 14 June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Lyall Reid, Gary Richardson〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The concept of a ⊤-Convergence space has recently been introduced and studied. These spaces are related to the top level space of a lattice-valued convergence space. In order to consider completions, ⊤-Cauchy spaces are defined and investigated in the present work. Each ⊤-Cauchy space possesses a completion and, moreover, each topological ⊤-Cauchy space has a topological completion. Completions of ⊤-uniform limit spaces are also introduced.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Lingqiang Li, Qiu Jin, Kai Hu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, in the context of meet continuous quantale, we present a notion of conical topological lattice-valued convergence space, which provides the theory of lattice-valued convergence associated with such conical neighborhood spaces.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 11 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Dominik Hose, Michael Hanss〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The stochastic approach to regression, e.g. the least-squares method, is a commonly used technique in a wide range of disciplines as it offers an intuitive and well-founded solution to the problem of fitting a set of parameters to existing data. Specifically, in the case where the parameters of meta models are identified, the linear least-squares formulation receives wide appreciation among engineers due to its simple yet powerful formulation and solution. Usually, this approach provides a reasonable fit, depending largely on the quality of the model that is employed. However, it has two main drawbacks. From a statistical point of view, the premises justifying its use cannot always be assumed in good faith, and most importantly, the resulting model will almost certainly fail at correctly predicting the output without falling victim to the effect of over-fitting.〈/p〉 〈p〉The presented fuzzy regression algorithm originates from a set of different axioms. For the solution of the linear least-squares problem, it is able to provide the worst-case optimal parameter variation necessary to cover all of the crisp data points while encoding meaningful information in the membership function. This is accomplished by means of a sensible fuzzification procedure of the crisp data points and the application of an exact inverse fuzzy arithmetic for estimating the fuzzy-valued parameters of the model in question.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 354〈/p〉 〈p〉Author(s): Martynas Manstavičius, Gediminas Bagdonas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We provide necessary and sufficient conditions on a function 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉f〈/mi〉〈mo〉:〈/mo〉〈mo stretchy="false"〉[〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉]〈/mo〉〈mo stretchy="false"〉→〈/mo〉〈msub〉〈mrow〉〈mi mathvariant="double-struck"〉R〈/mi〉〈/mrow〉〈mrow〉〈mo〉+〈/mo〉〈/mrow〉〈/msub〉〈/math〉 so that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo〉,〈/mo〉〈mi〉v〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈mi〉C〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo〉,〈/mo〉〈mi〉v〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉−〈/mo〉〈mi〉u〈/mi〉〈mo〉−〈/mo〉〈mi〉v〈/mi〉〈mo〉+〈/mo〉〈mi〉C〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo〉,〈/mo〉〈mi〉v〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉u〈/mi〉〈mo〉,〈/mo〉〈mi〉v〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mo stretchy="false"〉[〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉]〈/mo〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉 is a copula for any bivariate copula 〈em〉C〈/em〉. Then we discuss several important bivariate copula properties preserved or not by the mapping 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si261.gif" overflow="scroll"〉〈mi〉C〈/mi〉〈mo stretchy="false"〉↦〈/mo〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉C〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. The considered bivariate copula construction unifies many examples found in the literature and opens a qualitatively new way of obtaining new copulas by simply using a function 〈em〉f〈/em〉 which has to satisfy a few easily verifiable properties.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Jiaojiao Ren, Xinzhi Liu, Hong Zhu, Shouming Zhong, Cong Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies the problem of exponential 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 synchronization of switching fuzzy systems with time-varying delay and impulses via maximum, minimum dwell time. The switching fuzzy model has locally Takagi and Sugeno (T–S) fuzzy models and switches them according to states, external variables and/or time. By introducing the concept of maximum, minimum dwell time and a modified two-side direction relation between the number of switchings and the maximum, minimum dwell time, a normal 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉 norm bound constraint is derived. By using the matrix decomposition method and reciprocal convex combination, and combining with the Wirtinger-based inequality, which gives a sharper upper bound than the Jensen's inequality, some new sufficient criteria are obtained to guarantee that the error system without impulses and with impulses is globally exponentially stable with an 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 performance index 〈em〉γ〈/em〉, respectively. Three illustrative examples are provided to show the effectiveness of the results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 31 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Dingwei Zheng, Pei Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we propose the concept of fuzzy Meir–Keeler contractive mappings in fuzzy metric spaces, which covers fuzzy 〈em〉ψ〈/em〉-contractive mappings and fuzzy 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉H〈/mi〉〈/math〉-contractive mappings as special cases. With the aid of the proposed concept, we obtain some Meir–Keeler type fixed point theorems. The derived theorems improve and extend the corresponding ones developed by D. Mihet, D. Wardowski and V. Gregori, et al. And an example in the end of the paper illustrates the validity of our results.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): Sarah Greenfield, Francisco Chiclana〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the Type-Reduced Set (TRS) of the continuous type-2 fuzzy set is considered as an object in its own right. The structures of the TRSs of both the interval and generalised forms of the type-2 fuzzy set are investigated. In each case the respective TRS structure is approached by first examining the TRS of the discretised set. The TRS of a continuous interval type-2 fuzzy set is demonstrated to be a continuous horizontal straight line, and that of a generalised type-2 fuzzy set, a continuous, convex curve. This analysis leads on to the concept of truncation, and the definition of the 〈em〉truncation grade〈/em〉. The 〈em〉truncated type-2 fuzzy set〈/em〉 is then defined, whose TRS (and hence defuzzified value) is identical to that of the non-truncated type-2 fuzzy set. This result is termed the 〈em〉Type-2 Truncation Theorem〈/em〉, an immediate corollary of which is the 〈em〉Type-2 Equivalence Theorem〈/em〉 which states that the defuzzified values of type-2 fuzzy sets that are equivalent under truncation are equal. Experimental corroboration of the equivalence of the non-truncated and truncated generalised type-2 fuzzy set is provided. The implications of these theorems for uncertainty quantification are explored. The theorem's repercussions for type-2 defuzzification employing the 〈em〉α〈/em〉-Planes Representation are examined; it is shown that the known inaccuracies of the 〈em〉α〈/em〉-Planes Method are deeply entrenched.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 353〈/p〉 〈p〉Author(s): J.J. Font, D. Sanchis, M. Sanchis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Fuzzy-number-valued functions, that is, functions defined on a topological space taking values in the space of fuzzy numbers, play a central role in the development of Fuzzy Analysis. In this paper we study completeness, metrizability and compactness of spaces of continuous fuzzy-number-valued functions.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 24 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Mikel Sesma-Sara, Julio Lafuente, Antonio Roldán, Radko Mesiar, Humberto Bustince〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we propose a new notion of monotonicity: 〈em〉strengthened ordered directional monotonicity〈/em〉. This generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity, two recent weaker forms of monotonicity. We discuss the relation between those different notions of monotonicity from a theoretical point of view. Additionally, along with the introduction of two families of functions and a study of their connection to the considered monotonicity notions, we define an operation between functions that generalizes the Choquet integral and the Łukasiewicz implication.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 17 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Bonifacio Llamazares〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Choquet integrals (mainly weighted means and OWA operators) are a well-known family of functions widely used in several scientific fields. Because of this, it is very important to know the behavior of these functions in order to choose the best-suited operators in practical applications. In this sense, the analysis of the conjunctive/disjunctive character is very interesting given that allow understand the behavior of functions in relation to order statistics. In this paper we focus on some classes of SUOWA operators, which are Choquet integrals that simultaneously generalize weighted means and OWA operators, and provide conditions under which the 〈em〉k〈/em〉-conjunctive or 〈em〉k〈/em〉-disjunctive character of an OWA operator is retained by the SUOWA operators associated with it. Of particular interest is the case where the OWA operator is located between two order statistics, given that we can obtain SUOWA operators also located between the same order statistics. Likewise, we show closed-form expressions of 〈em〉k〈/em〉-conjunctiveness and 〈em〉k〈/em〉-disjunctiveness indices for some specific cases of SUOWA operators.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 353〈/p〉 〈p〉Author(s): Antonio Francisco Roldán López de Hierro, Concepción Roldán, Francisco Herrera〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Ranking fuzzy numbers plays an important role in the decision process. Several strategies can be found in the abundant literature existing on this topic, which can be basically classified into two main groups: approaches based on the so-called ranking indices and based on fuzzy binary relations. Ranking indices are functions from fuzzy numbers to real values. These defuzzification methods are critiqued by its implicit information loss which leads to results that might not be consistent with human intuition in certain cases. In a fuzzy context, approaches based on binary relations can be considered more suitable solutions. Following this strategy, this paper introduces a new technique for ranking fuzzy numbers which is applicable to the whole set of fuzzy numbers. It is proved that many desired properties (in particular, we give several new properties) are satisfied and numerical examples show reasonable results. The developed technique is very easy to compute and interpret in practice, and it overcomes certain shortcomings that appear when applying other more complex algorithms. In the case of triangular or trapezoidal fuzzy numbers, the procedure is particularly simple and intuitive. Finally, a real-life example involving data of Chinese Economy is also carried out.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Ngo Van Hoa, Ho Vu, Tran Minh Duc〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, an initial value problem of Caputo–Katugampola (CK) fractional differential equations in fuzzy setting is considered and an idea of successive approximations under generalized Lipschitz condition is used to prove the existence and uniqueness results of the solution to the given problem. In order to obtain the above results, some necessary comparison theorems in real-valued differential equation under CK fractional derivative are established. Finally, a new technique to find analytical solutions of CK fuzzy fractional differential equations by using the solutions of fuzzy integer order differential equations is proposed. Some examples illustrating the applications of our results are presented.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 24 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Carmen Puerta, Ana Urrutia〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For certain purposes it would be of interest to find aggregation functions for which the aggregate value of the shortfalls coincides with the shortfall of the aggregate value of the original attainments, i.e. self-dual aggregation functions. It is crucial to know the scale type in which attainments are measured and how to reverse that scale to measure the corresponding shortfalls properly. In this paper we consider alternative definitions of shortfalls depending on the scale type and extend some characterisation results to this new framework.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): Javier Gutiérrez García, Hongliang Lai, Lili Shen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the readership of fuzzy set theorists, with particular attention paid to fuzzy Galois connections between preordered fuzzy sets.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 12 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Nguyen Dinh Phu, Nguyen Nhut Hung〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we give a new concept that is the minimum stability control problems for fuzzy linear control systems and our observations revolve around this object. At the same time, study the existence of solutions for some kinds of this problem by generalized Hukuhara derivative. In addition, we present the time-optimal fuzzy control problem for this problems. An algorithm to find the time-optimal is described and illustrated by a basic example.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 14 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Radim Belohlavek, Marketa Trneckova〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present new results regarding the problem of factorization of matrices with grades, or, equivalently, decomposition of fuzzy relations. In particular, we examine geometry of factorizations and the role of fuzzy concept lattices in factorizations of matrices with grades. The results make it possible to reduce input data and enable a more focused search for factors in the search space, and are intended to guide the design of greedy and other approximation algorithms for the decomposition problem, which itself is NP-hard. To demonstrate usefulness of these results, we propose a new factorization algorithm based on these results. Our experiments demonstrate improvements in the quality of factorizations due to the new approach. We conclude by presenting further research topics implied by our findings.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 354〈/p〉 〈p〉Author(s): B. De Baets, H. De Meyer, T. Jwaid〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The geometrical interpretation of symmetry of a function on the unit square is that it takes the same value in mirror images w.r.t. the main diagonal. Here, this concept is generalized by considering the reflection w.r.t. a curve representing the graph of an automorphism of the unit interval. A function on the unit square that takes the same value in mirror images w.r.t. such a curve is called symmetric w.r.t. that curve. Moreover, a measure is proposed for quantifying to what extent a (quasi-)copula can be regarded as being asymmetric w.r.t. a given curve. The major part of the paper is concerned with establishing lower and upper bounds on this degree of asymmetry. Finally, it is shown that these bounds are sharp within the class of copulas.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Yueli Yue, Jinming Fang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we give a kind of Cauchy completeness in probabilistic quasi-uniform space by using pair ⊤-filters, and prove that this kind of Cauchy completeness is equivalent to the ⊤-completeness of induced probabilistic uniform space introduced by Höhle. We also give a characterization of Cauchy completeness by Lawvere completeness. Then, we study the completion of probabilistic (quasi-)uniform space and show that each 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉T〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 separated probabilistic quasi-uniform space has a 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉T〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈/math〉 Cauchy completion. Finally, in probabilistic quasi-metric space, we study the relationship between the completeness of induced quasi-uniform space and the completeness of probabilistic quasi-metric space.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 14 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Shiju Yang, Chuandong Li, Tingwen Huang, Wanli Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the fixed-time consensus problem for complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties is discussed. Different from most existing publications, the controller is designed as a fuzzy logic system, which is applicable for complex dynamical networks with system uncertainties and unknown topology to ensure the fixed-time consensus. Furthermore, compared with the initial-condition based finite-time consensus, the settling time is bounded by a constant within fixed-time regardless of the initial condition. Based on the Lyapunov stability theory and inequality techniques, some sufficient criteria for fixed-time consensus are obtained. Finally, two numerical examples are granted to display the performance of the obtained results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 2 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): LeSheng Jin, Radko Mesiar, Martin Kalina, Jana Špirková, Surajit Borkotokey〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we present a new method of construction of aggregation functions based on the so-called bijective chains, that generalizes the standard isomorphic 〈em〉ϕ〈/em〉-transforms of aggregation functions. It covers, among others, several known construction methods, such as the construction of copulas based on ultramodular copulas, or particular ordinal sums of aggregation functions, e.g., of t-norms, copulas, t-conorms. Several properties of the proposed construction method are discussed and exemplified.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Lemnaouar Zedam, Hassane Bouremel, Bernard De Baets〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In a recent paper, De Baets et al. have studied the compatibility of a(n) (strict) order relation with a fuzzy relation, and have characterized the fuzzy tolerance (and, in particular, fuzzy equivalence) relations that a given strict order relation is compatible with. We extend this study by considering the left- and right-compatibility of a(n) (strict) order relation with a fuzzy tolerance relation and vice versa. We characterize the fuzzy tolerance relations that are compatible with a given (strict) order relation. Conversely, we provide a representation of the fuzzy tolerance relations that a given strict order relation is left- or right-compatible with. Specific attention is paid to the case of fuzzy equivalence relations. We conclude by pointing out that the representation theorems in the above-mentioned paper need some minor rectification.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 15 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Shokrollah Ziari〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An iterative numerical method based on the three-point quadrature formula is applied to solve nonlinear fuzzy Hammerstein–Fredholm integral equations of the second kind and provides more accurate results than the trapezoidal quadrature iterative method. Also, we obtain the error estimation of the iterative method in terms of the uniform and partial modulus of continuity. Moreover, we investigate the concept of numerical stability of the iterative method with respect to the choice of the initial approximation. Illustrative examples are included to demonstrate the accuracy and efficiency of the iterative method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 355〈/p〉 〈p〉Author(s): Aoi Honda, Yoshiaki Okazaki〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We generalize the inclusion–exclusion integral for nondiscrete monotone measure spaces. The inclusion–exclusion integral for a monotone measure space on a finite space is discussed in previous papers. This is an integral with respect to a nonadditive monotone measure, which includes the Lebesgue and Choquet integrals. We are concerned with the monotonicity of the integral, and a sufficient condition for the monotonicity of the t-norm based inclusion–exclusion integral is given by introducing the complete monotonicity of the t-norm based interaction operator. Moreover concrete examples of the interaction operators that satisfy the complete monotonicity are shown.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): Sunil Mathew, Anjali N, J.N. Mordeson〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In any network, the problem of reduction of flow is more important and frequent than the disconnection of the network. Problems related with maximum bandwidth paths and maximal flows are also very significant. In this article, the authors discuss connectivity concepts related with paths and flows in interconnection networks in a fuzzy framework. Some of the properties and applications of a stable structure called transitive block are discussed. Blocks in fuzzy graphs generalize the concept of blocks in graphs. The existence of a strongest strong cycle in any fuzzy block having at least three vertices is established. Four characterizations previously proposed for a class of blocks in fuzzy graphs are found to be true for a larger class. Two subclasses of 〈em〉θ〈/em〉-fuzzy graphs, namely, connectivity-transitive and cyclically-transitive fuzzy graphs are introduced to get a better understanding of blocks in fuzzy graphs. An application of transitive blocks in interconnection networks is also proposed.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Bin Pang, Zhen-Yu Xiu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Considering a continuous lattice 〈em〉L〈/em〉 as the lattice background, an axiomatic approach to bases and subbases in the framework of 〈em〉L〈/em〉-convex spaces is provided. Firstly, the concepts of bases and subbases in 〈em〉L〈/em〉-convex spaces are introduced and then 〈em〉L〈/em〉-convexity base axioms and 〈em〉L〈/em〉-convexity subbase axioms are proposed by abstracting the properties of bases and subbases, respectively. Secondly, some applications of 〈em〉L〈/em〉-convexity base axioms and 〈em〉L〈/em〉-convexity subbase axioms are investigated. It is shown that 〈em〉L〈/em〉-convexity base axioms can be used to demonstrate some relationship between spatial structures with respect to 〈em〉L〈/em〉-convex structures and 〈em〉L〈/em〉-convexity subbase axioms can be applied to define the join space and the product space of 〈em〉L〈/em〉-convex spaces.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 14 June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Wenhai Qi, Ju H. Park, Jun Cheng, Xiaoming Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper treats the issues of stochastic stability and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/math〉-gain analysis for continuous-time positive fuzzy semi-Markov jump systems (PFSMJSs) with time-varying delay. The system under consideration involves semi-Markov stochastic process related to Weibull distribution. The practical systems such as Lotka–Volterra population model described by PFSMJSs always need to consider the sudden change in the operating process. To deal with these problems, a sufficient condition for stochastic stability of PFSMJSs is established, which is dependent of the bound of time-varying delay. Then, based on the obtained results, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/math〉-gain performance is analyzed in standard linear programming (LP). Finally, Lotka–Volterra population model shows the validity of the conclusions.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 24 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Shengwei Han, Rongrong Wang, Xiaoting Xu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Quantum B-algebras as implicational subreducts of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantics for non-commutative algebraic logic. Due to the adjunction between multiplication and its residuals, they can be regarded as the implicational counterpart of partially ordered semigroups. By means of the injective hulls (envelopes) of quantum B-algebras, Rump gave the injective hulls of partially ordered semigroups. In this paper, one part of our work is to give new examples of quantum B-algebras where the lower sets do not form a quantale. Another part of our work is to consider the inverse problem of Rump's way, that is, we can also give the injective hulls of quantum B-algebras in terms of the injective hulls of partially ordered semigroups.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Gang Li, Hua-Wen Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉It is well known that under some conditions, a convex combination of the drastic product 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉T〈/mi〉〈/mrow〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈/msub〉〈/math〉 and the strict triangular norm is still a triangular norm. Uninorms, as a special kind of generalization of both triangular norms and triangular conorms, have been widely used in fuzzy set theory. In this paper, the convex combination of uninorms is studied. Some properties of the class of uninorms with the underlying triangular norm 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉T〈/mi〉〈/mrow〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈/msub〉〈/math〉 are presented firstly. Then the convex combination of this class of uninorms is discussed and it is shown that only in some trivial cases, the convex combination is still a uninorm.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 8 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Tao Li, Zhuxiang Dai, Gongfei Song, Lihua Wang, Haiping Du〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a fault tolerant attitude tracking control scheme is proposed for Mars entry vehicles (MEVs) with disturbances and actuator failures. The original attitude dynamics of MEVs is divided into two subsystems, named as slow subsystem and fast subsystem, respectively. For slow subsystem, the control-like angular velocity command is generated. For fast subsystem, the Takagi–Sugeno (T-S) fuzzy models are used to describe it at first. Based on these, the partial loss of actuator effectiveness with the generated angular velocity problem is transformed into solving the tracking problem with uncertain parameters. Then, a fault tolerant tracking control scheme is proposed by combining fuzzy line-integral Lyapunov function method with robust 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msub〉〈/math〉 control approach. The proposed controller design is simple and can guarantee the faulty closed-loop system to be stable with acceptable attenuation level. Finally, the effectiveness of the proposed design method is demonstrated in a MEVs attitude control system subject to loss of actuator effectiveness.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 14 June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Olivier Pivert, Olfa Slama, Virginie Thion〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper deals with 〈em〉fuzzy quantified queries〈/em〉 in a graph database context. We study a particular type of structural quantified query and show how it can be expressed in an extension of the Neo4j Cypher query language. A processing strategy based on a compilation mechanism that derives regular (nonfuzzy) queries for accessing the relevant data is also described. Then, some experiments are performed that show the tractability of this approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Jinling Wang, Jinling Liang, Abdullah M. Dobaie〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This article focuses on stability analysis and controller synthesis of a class of Roesser-type switched Takagi–Sugeno fuzzy systems with delays. First, sufficient conditions derived by use of the co-positive Lyapunov function and the average dwell time method are presented to guarantee the proposed system is positive and exponentially stable. Then via a state feedback fuzzy controller, criteria are also given under which not only the resulting closed-loop system is positive and exponentially stable but also the desired controller gain matrices can be designed by solving a set of coupled matrix inequalities. Finally, two illustrative examples are provided to show the effectiveness of the approach outlined in this article.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Bernhard Schmelzer〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The aim of this paper is to study the relation between multivariate capacity functionals and capacity functionals on product spaces (also called joint capacity functionals). Multivariate capacity functionals characterize the joint distribution of finitely many random sets whereas joint capacity functionals characterize the distribution of a random set in a product space and as such provide an upper bound on a set of (joint) probability measures. It is demonstrated how to define a multivariate capacity functional from a given joint capacity functional, and how to extend a multivariate capacity functional to a joint capacity functional. In addition, it is shown how to construct a joint capacity functional from marginal maxitive capacity functionals when a copula is used for modelling stochastic dependence.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Changzhong Wang, Yang Huang, Mingwen Shao, Degang Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Relation is one of the important concepts in rough set models. Some uncertainty measures for relations were proposed in recent years by generalizing information entropy. However, the existing theories considered only special relations and do not address mixed-type data well. They always transformed each attribute into a binary relation with the same structure regardless of attribute types. As a result, the structure information can be lost for other types of attributes. In this paper, a new theory about uncertainty measures for general fuzzy relations is proposed. The proposed theory can overcome the weakness of the existing theories. We first introduce a novel entropy to compute the uncertainty information of fuzzy binary relations and then present the concepts of joint fuzzy entropy, conditional fuzzy entropy and fuzzy mutual information. The basic properties of these uncertainty measures are studied. Finally, we apply the proposed theory to perform attribute reduction of heterogeneous data sets. The experimental results show that our proposed method is feasible and effective in some cases. The proposed theory can provide a fundamental framework that integrates all kinds of methods for the uncertainty information of special relations.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 26 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Jan Andres, Miroslav Rypka〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper deals mainly with new very general fuzzy fixed point theorems in metric spaces and their application to fuzzy fractals. It is a natural continuation of our paper (2018) [1] which significantly generalizes and improves the results by Diamond, Kloeden and Pokrovskii (1997) [2], where no application was given. Moreover, besides the existence, some further important properties of fixed point sets (in particular, fractals) like their weak local stability, called none-ejectivity in the sense of Browder (1965) [3], will be established.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Bin Yang, Bao Qing Hu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Fuzzy coverings are natural extensions of the coverings by replacing crisp sets with fuzzy sets. Recently, some fuzzy neighborhood operators based on a fuzzy covering were defined and their properties were investigated by D'eer et al. In this paper, we propose four types of fuzzy neighborhood operators by introducing the notions such as 〈em〉β〈/em〉-neighborhood system, fuzzy 〈em〉β〈/em〉-minimal description and fuzzy 〈em〉β〈/em〉-maximal description. First, we propose these notions and investigate their properties. Then we construct four types of fuzzy neighborhood operators based on the fuzzy 〈em〉β〈/em〉-coverings. Properties and relationship among these four types of fuzzy neighborhood operators are studied. Finally, six types of fuzzy 〈em〉β〈/em〉-coverings were derived by using these four types of fuzzy neighborhood operators and their properties are considered.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 355〈/p〉 〈p〉Author(s): Mirjana Štrboja, Endre Pap, Biljana Mihailović〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper a transformation of the pseudo-integral into another pseudo-integral is considered. Using the transformed pseudo-integral, monotone convergence theorems for the pseudo-integral are obtained. Based on the reverse Fatou's lemma for the pseudo-integral, the dominated convergence-type theorem is proven.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 353〈/p〉 〈p〉Author(s): Biljana Mihailović, Vera Miler Jerković, Branko Malešević〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present an efficient method for solving a singular, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉n〈/mi〉〈mo〉×〈/mo〉〈mi〉n〈/mi〉〈/math〉 fuzzy linear system (FLS), 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉A〈/mi〉〈mover accent="true"〉〈mrow〉〈mi〉X〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉˜〈/mo〉〈/mrow〉〈/mover〉〈mo〉=〈/mo〉〈mover accent="true"〉〈mrow〉〈mi〉Y〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉˜〈/mo〉〈/mrow〉〈/mover〉〈/math〉, where the coefficient matrix 〈em〉A〈/em〉 is a real matrix, singular or non-singular, using the block structure of the group inverse or any {1}-inverse. A characterization of the block structure of {1}-inverses, in particular, the group inverse, but also the Drazin inverse of the matrix associated to a square FLS is given. Based on the presented necessary and sufficient condition for the existence of a solution, the general solution of a square FLS is obtained. Finally, infinitely many solutions of a singular FLS are presented through many interesting examples.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Laura De Miguel, Daniel Gómez, J. Tinguaro Rodríguez, Javier Montero, Humberto Bustince, Graçaliz P. Dimuro, José Antonio Sanz〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉As a generalization of bivariate overlap functions, which measure the degree of overlapping (intersection for non-crisp sets) of 〈em〉n〈/em〉 different classes, in this paper we introduce the concept of general overlap functions. We characterize the class of general overlap functions and include some construction methods by means of different aggregation and bivariate overlap functions. Finally, we apply general overlap functions to define a new matching degree in a classification problem. We deduce that the global behaviour of these functions is slightly better than some other methods in the literature.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Radim Belohlavek, Jan Konecny〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a reduction theorem which relates sets of fixpoints of fuzzy closure operators to sets of fixpoints of ordinary closure operators. As a result we obtain a method to compute sets of fixpoints of fuzzy closure operators by algorithms available for ordinary operators. We also provide explicit descriptions of selected algorithms which result from the presented approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 30 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Yexing Dan, Bao Qing Hu, Junsheng Qiao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we investigate the degree of the symmetry of fuzzy relations on a set 〈em〉X〈/em〉. Based on the fuzzy 〈em〉e〈/em〉-equality derived from uninorms with unit element 〈em〉e〈/em〉, the degree of the symmetry of fuzzy relations are defined by two different approaches, the type-I degree of symmetry and the type-II degree of symmetry. The main work of this paper include: first, we discuss some basic properties of those two degrees, especially for the relationship between them. In particular, for continuous t-norms, we give a necessary and sufficient condition such that the type-I degree of symmetry and the type-II degree of symmetry are equal. And then, we obtain that the type-II degree of symmetry is more appropriate to character the degree of the symmetry of fuzzy relations than the type-I degree of symmetry with respect to whether they preserve the fuzzy 〈em〉e〈/em〉-equalities or not. In the meantime, for a special case with continuous t-norms, we provide a necessary and sufficient condition such that the type-I degree of symmetry preserves the fuzzy equalities. Finally, for conjunctive left-continuous idempotent uninorms with neutral element 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉e〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉]〈/mo〉〈/math〉, we find out a symmetric fuzzy relation 〈em〉S〈/em〉 which is close enough to the given fuzzy relation 〈em〉R〈/em〉 with respect to fuzzy 〈em〉e〈/em〉-equality such that the degree of fuzzy 〈em〉e〈/em〉-equality of 〈em〉S〈/em〉 and 〈em〉R〈/em〉 is the type-II degree of symmetry of 〈em〉R〈/em〉. In particular, we obtain analogous results for continuous t-norms and one class of left-continuous t-norms.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): Aifang Xie〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, by applying Zadeh's extension principle, we extend type-1 proper nullnorms and proper uninorms to fuzzy truth values. The definitions of type-2 nullnorms and uninorms are introduced. We mainly discuss in which subalgebras of fuzzy truth values extended proper nullnorms and proper uninorms are type-2 nullnorms and uninorms, respectively.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): Jinming Fang, Qingling Zhang, Qian Yu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In the paper, the implication and tensor operations of strong 〈em〉L〈/em〉-nested systems are found, and further we show that the family of all strong 〈em〉L〈/em〉-nested systems on a universal set forms a complete Girard residuated lattice provided the underlying complete residuated lattice is Girard. Finally, an isomorphism of complete Girard residuated lattices between the family of all strong 〈em〉L〈/em〉-nested systems and the 〈em〉L〈/em〉-power set for any fixed universal set is established, and thus a new representation theorem of 〈em〉L〈/em〉-subsets is obtained.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 352〈/p〉 〈p〉Author(s): 〈/p〉

Description: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 355〈/p〉 〈p〉Author(s): E.A. Sánchez Pérez, R. Szwedek〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Integration with respect to vector-valued fuzzy measures is used to define and study information measuring tools. Motivated by some current developments in Information Science, we apply the integration of scalar functions with respect to vector-valued fuzzy measures, also called vector capacities. Bartle–Dunford–Schwartz integration (for the additive case) and Choquet type integration (for the non-additive case) are considered, showing that these formalisms can be used to define and develop vector-valued impact measures. Examples related to existing bibliometric tools as well as to new measuring indices are given.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 6 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): D. Boixader, J. Recasens〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Fuzzy subgroups are revisited considering their close relationship with indistinguishability operators (fuzzy equivalences) invariant under translations. Different ways to obtain new fuzzy subgroups from a given one are provided and different ways to characterize normal fuzzy subgroups are obtained. The idea of double coset of two (crisp) subgroups allows us to relate them via their equivalence classes. This is generalized to the fuzzy framework. The conditions in which a fuzzy relation 〈em〉R〈/em〉 on a group 〈em〉G〈/em〉 can be considered a fuzzy subgroup of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉G〈/mi〉〈mo〉×〈/mo〉〈mi〉G〈/mi〉〈/math〉 are obtained.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 3 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems〈/p〉 〈p〉Author(s): Yali Wu, Jing Wang, Yichuan Yang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉It is known that many logical algebras can be considered as L-algebras. In this paper, we first construct an effect algebra 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉E〈/mi〉〈mo〉,〈/mo〉〈mo〉⊕〈/mo〉〈mo〉,〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 that cannot be converted into an L-algebra 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈mi〉E〈/mi〉〈mo〉,〈/mo〉〈mo stretchy="false"〉→〈/mo〉〈mo〉,〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 with negation such that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si116.gif" overflow="scroll"〉〈mi〉x〈/mi〉〈mo stretchy="false"〉→〈/mo〉〈mn〉0〈/mn〉〈/math〉 is the orthosupplement. Then we prove that every lattice-ordered effect algebra gives rise to an L-algebra with the same orthosupplement. Finally, we characterize LE-L-algebras as lattice-ordered effect algebras. As an application, we extend those results obtained in some recent references for orthomodular lattices and MV-algebras.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Fuzzy Sets and Systems, Volume 353〈/p〉 〈p〉Author(s): Biljana Mihailović, Vera Miler Jerković, Branko Malešević〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we present a new method for solving an 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉m〈/mi〉〈mo〉×〈/mo〉〈mi〉n〈/mi〉〈/math〉 fuzzy linear system (FLS), 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉A〈/mi〉〈mover accent="true"〉〈mrow〉〈mi〉X〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉˜〈/mo〉〈/mrow〉〈/mover〉〈mo〉=〈/mo〉〈mover accent="true"〉〈mrow〉〈mi〉Y〈/mi〉〈/mrow〉〈mrow〉〈mo stretchy="false"〉˜〈/mo〉〈/mrow〉〈/mover〉〈/math〉, where the coefficient matrix 〈em〉A〈/em〉 is real, using the block representation of generalized inverses. A necessary and sufficient condition for a block matrix to be the Moore–Penrose inverse of the full rank matrix associated to a FLS is given. We obtain a necessary and sufficient condition for the existence of solutions of a FLS, with arbitrary real coefficient matrix. The exact algebraic form, with respect to the Moore–Penrose inverse, of any solution of FLS of this type is established. A general, efficient and universal method for obtaining the exact solutions is introduced. Some numerical examples are presented to illustrate the proposed method.〈/p〉〈/div〉