Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers
Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a...
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doaj-b4fb5a9650904ea49b8668248c7744e22021-06-28T01:51:26ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/5594623Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic NumbersMohamed Gaber0Majed G. Alharbi1Abd Alwahed Dagestani2El-Saeed Ammar3School of Mathematics and StatisticsDepartment of MathematicsSchool of BusinessDepartment of Mathematics Faculty of ScienceSingle-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work.http://dx.doi.org/10.1155/2021/5594623 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mohamed Gaber Majed G. Alharbi Abd Alwahed Dagestani El-Saeed Ammar |
spellingShingle |
Mohamed Gaber Majed G. Alharbi Abd Alwahed Dagestani El-Saeed Ammar Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers Journal of Mathematics |
author_facet |
Mohamed Gaber Majed G. Alharbi Abd Alwahed Dagestani El-Saeed Ammar |
author_sort |
Mohamed Gaber |
title |
Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers |
title_short |
Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers |
title_full |
Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers |
title_fullStr |
Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers |
title_full_unstemmed |
Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers |
title_sort |
optimal solutions for constrained bimatrix games with payoffs represented by single-valued trapezoidal neutrosophic numbers |
publisher |
Hindawi Limited |
series |
Journal of Mathematics |
issn |
2314-4785 |
publishDate |
2021-01-01 |
description |
Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work. |
url |
http://dx.doi.org/10.1155/2021/5594623 |
work_keys_str_mv |
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1721357221042847744 |