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Open AccessArticle

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

1
School of Mathematics and Statistics, Central South University, Changsha 410083, China
2
Department of Basic Science Faculty of Computers & Informatics. Suez Canal University, 41522 Ismailia, Egypt
3
Department of Mathematics, Faculty of Science, Tanta University, 31527 Tanta, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(5), 702; https://doi.org/10.3390/sym11050702
Received: 28 April 2019 / Revised: 17 May 2019 / Accepted: 20 May 2019 / Published: 22 May 2019
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
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. View Full-Text
Keywords: fuzzy rough number; rough interval arithmetic; constraint matrix games; fuzzy multi-objective programming; game theory fuzzy rough number; rough interval arithmetic; constraint matrix games; fuzzy multi-objective programming; game theory
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MDPI and ACS Style

Brikaa, M.G.; Zheng, Z.; Ammar, E.-S. Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers. Symmetry 2019, 11, 702.

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