Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

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.

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application

“…Charnes and Cooper [ 7 ] presented a survey on recent development of goal programming and multiple objective optimization problems that incudes goal and interval programming with some definitions and examples of goal functionals. Recently, various computational algorithms have been developed based on various types of optimization techniques, for example Cheng [ 8 ], Tarabia [ 34 ], Brikaa [ 6 ], Wu [ 39 ], Uddin [ 36 ] and Yang [ 42 ]. Shih et al [ 32 ] presented a method to find optimal solution of multiobjective programming in interval-valued fuzzy environment where crisp multiobjective programming was converted into an interval-valued fuzzy programming using interval-valued fuzzy membership functions for each crisp inequalities.…”

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

“…). By solving the above mathematical programming models, we obtain the following tabulated optimal solutions, given in Tables [13][14][15][16][17][18]. From the results shown in Tables 1-18, the optimal strategies obtained by different ranking approaches are the same as those of the proposed approach.…”

“…Ammar et al [13] studied bimatrix games with rough interval payoffs. Brikaa et al [14] developed fuzzy multiobjective programming technique to solve fuzzy rough constrained matrix games. Bhaumik et al [15] introduced multiobjective linguistic-neutrosophic matrix game with applications to tourism management.…”

Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

“…Utilizing the defined I-fuzzy inequality relations, resolving indeterminacy function, and Inuiguchi et al [42] algorithms, the multi criteria matrix game with I-fuzzy goals is transformed into a crisp multi-objective linear programming model which can be solved by GAMS software [43]. Brikaa et al [44] developed an effective fuzzy multi-objective programming approach to solve constraint matrix games with payoffs of fuzzy rough numbers through using Zimmermann's fuzzy programming algorithm. However, the multi-criteria matrix game studied under the I-fuzzy set environment in this article is entirely different from that of Brikaa et al [44].…”

“…Brikaa et al [44] developed an effective fuzzy multi-objective programming approach to solve constraint matrix games with payoffs of fuzzy rough numbers through using Zimmermann's fuzzy programming algorithm. However, the multi-criteria matrix game studied under the I-fuzzy set environment in this article is entirely different from that of Brikaa et al [44].…”