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

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...

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Vydáno v:Symmetry (Basel) Ročník 11; číslo 5; s. 702
Hlavní autoři: Brikaa, M. G., Zheng, Zhoushun, Ammar, El-Saeed
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.05.2019
Témata:
Algorithms
Constraints
Decision making
Fuzzy sets
Game theory
Games
Linear programming
Market shares
Mathematical programming
Upper bounds
ISSN:2073-8994, 2073-8994
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Shrnutí: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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ISSN:2073-8994
2073-8994
DOI:10.3390/sym11050702