A novel method for solving constrained matrix games with fuzzy payoffs

Article type: Research Article

Authors: Verma, Tina^{; *}

Affiliations: Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India

Correspondence: [*] Corresponding author. Tina Verma, Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India. E-mail: verma.tina21@gmail.com.

Abstract: In last few years, lots of researchers have proposed different methods to solve the constrained matrix games with fuzzy payoffs. In this paper, it has been shown that the mathematical programming problem of constrained matrix games with fuzzy payoffs, considered by researchers, is mathematically invalid and hence the method, proposed by researchers to obtain the complete solution (minimum expected gain of Player I, maximum expected loss of Player II and their corresponding optimal strategies) of constrained matrix games with fuzzy payoffs by solving the mathematical programming problem with fuzzy payoffs, are also invalid. Further, in the present paper, a new method has been proposed to find the complete solution of matrix games with fuzzy payoffs. To illustrate the proposed method, some existing numerical problems of constrained matrix games with fuzzy payoffs have been solved by the proposed method.

Keywords: Matrix games, fuzzy payoffs, mathematical programming problem

DOI: 10.3233/JIFS-191192

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 1, pp. 191-204, 2021