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A solution algorithm for finding the best and the worst fuzzy compromise solutions of fuzzy rough linear programming problem with triangular fuzzy rough number coefficients. GRANULAR COMPUTING 2022. [DOI: 10.1007/s41066-022-00341-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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Brikaa MG, Zheng Z, Ammar ES. Mehar approach for solving matrix games with triangular dual hesitant fuzzy payoffs. GRANULAR COMPUTING 2021. [DOI: 10.1007/s41066-021-00292-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Seikh MR, Dutta S, Li D. Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem. INT J INTELL SYST 2021. [DOI: 10.1002/int.22542] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
| | - Shibaji Dutta
- Department of Mathematics Kazi Nazrul University Asansol India
| | - Deng‐Feng Li
- School of Management and Economics University of Electronic Science and Technology of China Chengdu China
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Gaber M, Alharbi MG, Dagestani AA, Ammar ES. Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers. JOURNAL OF MATHEMATICS 2021; 2021:1-13. [DOI: 10.1155/2021/5594623] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
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.
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Affiliation(s)
- Mohamed Gaber
- School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
| | - Majed G. Alharbi
- Department of Mathematics, College of Arts and Sciences, Methnab, Qassim University, Buridah, Saudi Arabia
| | | | - El-Saeed Ammar
- Department of Mathematics Faculty of Science, Tanta University, Tanta, Egypt
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Naqvi D, Aggarwal A, Sachdev G, Khan I. Solving I-fuzzy two person zero-sum matrix games: Tanaka and Asai approach. GRANULAR COMPUTING 2019. [DOI: 10.1007/s41066-019-00200-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Bhaumik A, Roy SK. Intuitionistic interval-valued hesitant fuzzy matrix games with a new aggregation operator for solving management problem. GRANULAR COMPUTING 2019. [DOI: 10.1007/s41066-019-00191-5] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers. Symmetry (Basel) 2019. [DOI: 10.3390/sym11050702] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible.
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A novel equilibrium solution concept for intuitionistic fuzzy bi-matrix games considering proportion mix of possibility and necessity expectations. GRANULAR COMPUTING 2019. [DOI: 10.1007/s41066-019-00170-w] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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