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.
Highlights
Different types of uncertainty are common in many real-life decision-making problems, including matrix games
We propose a novel algorithm for solving fuzzy rough constrained matrix games
Since the fuzzy rough constrained matrix game has not been discussed in the literature, there are no numerical results in other works for the problem under study
Summary
Different types of uncertainty (such as fuzziness, randomness, ambiguity, roughness) are common in many real-life decision-making problems, including matrix games. Decision-makers might face hybrid uncertain scenarios where roughness and fuzziness exist simultaneously. In such scenarios, fuzzy rough numbers (FRNs) are used to model the decision-making problem. Rough programming and fuzzy programming have been proposed for decision-making problems under uncertainty. In these decision-making problems, fuzziness and roughness are considered separate aspects. Several researchers have studied the issue of combining roughness and fuzziness in a general framework for the study of fuzzy rough sets. The fuzzy rough set has been considered in several practical problems.
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