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

M. G. Brikaa, Zhoushun Zheng and El-Saeed Ammar
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M. G. Brikaa: School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
Zhoushun Zheng: School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
El-Saeed Ammar: Department of Mathematics Faculty of Science, Tanta University, Tanta 31527, Egypt

Mathematics, 2020, vol. 8, issue 3, 1-30

Abstract: The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

Keywords: intuitionistic fuzzy set; multi-criteria matrix games; intuitionistic fuzzy goals; game theory; multi-objective programming; indeterminacy resolving approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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