A Matrix Norm-Based Solution for Zero Sum Fuzzy Matrix Games: Fuzzy Matrix Norm Method

İzgi B., Köçken H., Özkaya M.

12. International Conference on Applied Analysis and Mathematical Modeling, İstanbul, Turkey, 19 - 23 July 2024, pp.186

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.186
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

This paper introduces novel methodology for addressing two-person zero-sum matrix games with fuzzy payoffs of triangular fuzzy numbers. Apart from traditional approaches, the proposed method aims to directly solve the game by utilizing the norms of the payoff matrix comprehensively, without the need for solving linear programming problems or dealing with sub-games created by considering the components of a fuzzy number individually. Initially, we introduce fuzzy versions of the 1-norm and ∞-norm using a ranking function and then develop the fuzzy matrix norm method to obtain approximate solutions for zero-sum fuzzy matrix games based on the matrix norm (MN) method for matrix games with real values. To demonstrate the effectiveness of the fuzzy matrix norm method, we provide illustrative examples.