Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers

İzgi B., KÖÇKEN H., Özkaya M.

Applied Mathematics and Computation, cilt.479, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 479
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.amc.2024.128874
  • Dergi Adı: Applied Mathematics and Computation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Fuzzy matrix game, Game theory, Matrix norm method, Triangular fuzzy number, Zero-sum game
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we mainly consider the solution of two-person zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers. Contrary to the literature, we focus on developing the methods to solve the game directly based on only the norms of the payoff matrix holistically, without solving a linear programming problem or handling sub-games created by taking the components of fuzzy numbers separately. For this purpose, we first present fuzzy versions of 1-norm and ∞-norm with the help of a ranking function and develop the fuzzy matrix norm method to obtain an approximate solution of the zero-sum fuzzy matrix game. In addition to this approach, we provide the fuzzy extended matrix norm method as an enhanced version of the method, which involves the use of newly defined fuzzy matrix norms. Thus, we managed to avoid the complexity of the optimization process of the linear programming problem via the proposed matrix norm-based methods. Finally, we illustrate the implementation of the methods by considering several benchmark examples and a 3 × 3 fuzzy matrix game.