ALBERT

Description: Symmetry, Vol. 10, Pages 429: New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making Symmetry doi: 10.3390/sym10100429 Authors: Ke Song Quan The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

Description: Symmetry, Vol. 10, Pages 428: Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor Symmetry doi: 10.3390/sym10100428 Authors: Muhammad Gulistan Hafiz Abdul Wahab Florentin Smarandache Salma Khan Sayed Inayat Ali Shah In this paper, we combined entropy with linguisti neutrosophic cubic numbers and used it in daily life problems related to a corporation that is going to choose an area supervisor, which is the main target of our proposed model. For this, we first develop the theory of linguistic neutrosophic cubic numbers, which explains the indeterminate and incomplete information by truth, indeterminacy and falsity linguistic variables (LVs) for the past, present, as well as for the future time very effectively. After giving the definitions, we initiate some basic operations and properties of linguistic neutrosophic cubic numbers. We also define the linguistic neutrosophic cubic Hamy mean operator and weighted linguistic neutrosophic cubic Hamy mean (WLNCHM) operator with some properties, which can handle multi-input agents with respect to the different time frame. Finally, as an application, we give a numerical example in order to test the applicability of our proposed model.

Description: Symmetry, Vol. 10, Pages 427: On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras) Symmetry doi: 10.3390/sym10100427 Authors: Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéọlá Emmanuel Ilojide Memudu Olaposi Olatinwo Florentin Smarandache In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves’ identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves’ quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A ‘Cycle of Algebraic Structures’ which portrays this fact is provided.

Description: Symmetry, Vol. 10, Pages 426: General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons Symmetry doi: 10.3390/sym10100426 Authors: Haiying Wang The general ( α , t ) -path sum-connectivity index of a molecular graph originates from many practical problems, such as the three-dimensional quantitative structure–activity relationships (3D QSAR) and molecular chirality. For arbitrary nonzero real number α and arbitrary positive integer t, it is defined as t χ α ( G ) = ∑ P t = v i 1 v i 2 ⋯ v i t + 1 ⊆ G [ d G ( v i 1 ) d G ( v i 2 ) ⋯ d G ( v i t + 1 ) ] α , where we take the sum over all possible paths of length t of G and two paths v i 1 v i 2 ⋯ v i t + 1 and v i t + 1 ⋯ v i 2 v i 1 are considered to be one path. In this work, one important class of polycyclic aromatic hydrocarbons and their structures are firstly considered, which play a role in organic materials and medical sciences. We try to compute the exact general ( α , 2 ) -path sum-connectivity indices of these hydrocarbon systems. Furthermore, we exactly derive the monotonicity and the extremal values of these polycyclic aromatic hydrocarbons for any real number α . These valuable results could produce strong guiding significance to these applied sciences.

Description: Symmetry, Vol. 10, Pages 425: Astrape: An Efficient Concurrent Cloud Attestation with Ciphertext-Policy Attribute-Based Encryption Symmetry doi: 10.3390/sym10100425 Authors: Haihe Ba Huaizhe Zhou Songzhu Mei Huidong Qiao Tie Hong Zhiying Wang Jiangchun Ren Cloud computing emerges as a change in the business paradigm that offers pay-as-you-go computing capability and brings enormous benefits, but there are numerous organizations showing hesitation for the adoption of cloud computing due to security concerns. Remote attestation has been proven to boost confidence in clouds to guarantee hosted cloud applications’ integrity. However, the state-of-the-art attestation schemes do not fit that multiple requesters raise their challenges simultaneously, thereby leading to larger performance overheads on the attester side. To address that, we propose an efficient and trustworthy concurrent attestation architecture under multi-requester scenarios, Astrape, to improve efficiency in the integrity and confidentiality protection aspects to generate an unforgeable and encrypted attestation report. Specifically, we propose two key techniques in this paper. The first one—aggregated attestation signature—reliably protects the attestation content from being compromised even in the presence of adversaries who have full control of the network, therefore successfully providing attestation integrity. The second one—delegation-based controlled report—introduces a third-party service to distribute the attestation report to requesters in order to save computation and communication overload on the attested party. The report is encrypted with an access policy by using attribute-based encryption and accessed by a limited number of qualified requesters, hence supporting attestation confidentiality. The experimental results show that Astrape can take no more than 0.4 s to generate an unforgeable and encrypted report for 1000 requesters and deliver a throughput speedup of approximately 30 × in comparison to the existing attestation systems.

Description: Symmetry, Vol. 10, Pages 424: (Gravitational) Vacuum Cherenkov Radiation Symmetry doi: 10.3390/sym10100424 Authors: Marco Schreck This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, the most important findings for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After doing so, special emphasis is put on gravitational Cherenkov radiation. For a better understanding, the essential properties of the gravitational SME are recalled in this context. The common grounds and differences of vacuum Cherenkov radiation in Minkowski spacetime and in the gravity sector are emphasized.

Description: Symmetry, Vol. 10, Pages 423: Tunable Control of Mie Resonances Based on Hybrid VO2 and Dielectric Metamaterial Symmetry doi: 10.3390/sym10100423 Authors: Ju Gao Kuang Zhang Guohui Yang Sungtek Kahng Qun Wu In this paper, a tunable dielectric metamaterial absorber with temperature-based vanadium dioxide (VO2) is proposed. In contrast to previous studies, both the metal phase of VO2 and the semiconductor phase are applied to manipulate the Mie resonant modes in the dielectric cubes. By embedding VO2 in the main resonant structure, the control over Mie resonant modes in dielectric metamaterials is realized. Each resonant mode is analyzed through field distribution and explains why the phase switch of VO2 could affect the absorbance spectrum. This use of tunable materials could create another new methodology for the manipulation of the Mie resonance-based dielectric cubes and make them closer in essence to isotropic metamaterials.

Description: Symmetry, Vol. 10, Pages 422: A Vertex-Based 3D Authentication Algorithm Based on Spatial Subdivision Symmetry doi: 10.3390/sym10100422 Authors: Yuan-Yu Tsai Yu-Shiou Tsai I-Ting Chi Chi-Shiang Chan The study proposed a vertex-based authentication algorithm based on spatial subdivision. A binary space partitioning tree was employed to subdivide the bounding volume of the input model into voxels. Each vertex could then be encoded into a series of binary digits, denoted as its authentication code, by traversing the constructed tree. Finally, the above authentication code was embedded into the corresponding reference vertex by modulating its position within the located subspace. Extensive experimental results demonstrated that the proposed algorithm provided high embedding capacity and high robustness. Furthermore, the proposed algorithm supported controllable distortion and self-recovery.

Description: Symmetry, Vol. 10, Pages 421: A Class of Coupled Causal Differential Equations Symmetry doi: 10.3390/sym10100421 Authors: Wen-Li Wang Jing-Feng Tian Wing-Sum Cheung In this thesis, we consider the existence of extreme solutions to a class of coupled causal differential equations. By utilizing two comparison theorems and a monotone iterative technique, we have obtained sufficient conditions under which the equations have extreme solutions. One practical example is presented.

Description: Symmetry, Vol. 10, Pages 419: Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making Symmetry doi: 10.3390/sym10090419 Authors: Songtao Shao Xiaohong Zhang Yu Li Chunxin Bo The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated.