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  • 1
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    Mathematics, Vol. 7, Pages 242: AHP-Group Decision Making Based on Consistency (2019)
    MDPI
    Details
    Publication Date: 2019
    Description: The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.
    Electronic ISSN: 2227-7390
    Topics: Mathematics
    Published by MDPI
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  • 2
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    Mathematics, Vol. 7, Pages 294: Homogeneous Groups of Actors in an AHP-Local Decision Making Context: A Bayesian Analysis (2019)
    MDPI
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    Publication Date: 2019
    Description: The two procedures traditionally followed for group decision making with the Analytical Hierarchical Process (AHP) are the Aggregation of Individual Judgments (AIJ) and the Aggregation of Individual Priorities (AIP). In both cases, the geometric mean is used to synthesise judgments and individual priorities into a collective position. Unfortunately, positional measures (means) are only representative if dispersion is reduced. It is therefore necessary to develop decision tools that allow: (i) the identification of groups of actors that present homogeneous and differentiated behaviours; and, (ii) the aggregation of the priorities of the near groups to reach collective positions with the greatest possible consensus. Following a Bayesian approach to AHP in a local context (a single criterion), this work proposes a methodology to solve these problems when the number of actors is not high. The method is based on Bayesian comparison and selection of model tools which identify the number and composition of the groups as well as their priorities. This information can be very useful to identify agreement paths among the decision makers that can culminate in a more representative decision-making process. The proposal is illustrated by a real-life case study.
    Electronic ISSN: 2227-7390
    Topics: Mathematics
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  • 3
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    Symmetry, Vol. 11, Pages 143: Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation (2019)
    MDPI
    In: Symmetry
    Details
    Publication Date: 2019
    Description: The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.
    Electronic ISSN: 2073-8994
    Topics: Mathematics
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  • 4
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    Mathematics, Vol. 6, Pages 262: Random Best Proximity Points for α-Admissible Mappings via Simulation Functions (2018)
    MDPI
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    Publication Date: 2018
    Description: In this paper, we introduce a new concept of random α -proximal admissible and random α - Z -contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces.
    Electronic ISSN: 2227-7390
    Topics: Mathematics
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  • 5
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    Mathematics, Vol. 7, Pages 441: Algorithms and Data Structures for Sparse Polynomial Arithmetic (2019)
    MDPI
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    Publication Date: 2019
    Description: We provide a comprehensive presentation of algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers as implemented in the freely available Basic Polynomial Algebra Subprograms (BPAS) library. We report on an algorithm for sparse pseudo-division, based on the algorithms for division with remainder, multiplication, and addition, which are also examined herein. The pseudo-division and division with remainder operations are extended to multi-divisor pseudo-division and normal form algorithms, respectively, where the divisor set is assumed to form a triangular set. Our operations make use of two data structures for sparse distributed polynomials and sparse recursively viewed polynomials, with a keen focus on locality and memory usage for optimized performance on modern memory hierarchies. Experimentation shows that these new implementations compare favorably against competing implementations, performing between a factor of 3 better (for multiplication over the integers) to more than 4 orders of magnitude better (for pseudo-division with respect to a triangular set).
    Electronic ISSN: 2227-7390
    Topics: Mathematics
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  • 6
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    Mathematics, Vol. 7, Pages 409: Anxiety about Mathematics among Economics Students in Mexico (2019)
    MDPI
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    Publication Date: 2019
    Description: Anxiety about mathematics is a phenomenon that occurs regardless of age, gender, or area of professional study. This research provides an overview of this phenomenon in Mexico, as experienced by undergraduate students in economics, a science that requires significant use of mathematics. The study is cross-sectional and not experimental and makes use of the ANOVA technique. The results obtained from the application of the Abbreviated Version of the Mathematics Anxiety Rating Scale (AMARS) to 381 students nationwide provide evidence of the existence of this phenomenon in more than 50% of the sample and indicate differences in terms of gender, region of origin, and type of university.
    Electronic ISSN: 2227-7390
    Topics: Mathematics
    Published by MDPI
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