A Nonlinear Programming Model to Solve Matrix Games with Pay-offs of Single-valued Neutrosophic Numbers

Abstract

Single-valued neutrosophic number (SVNN) is an appropriate extension of the ordinary fuzzy number. The key feature of the SVNN is that it can capture indeterminacy in the imprecise information. In real-life problems, there are many situations where players of a matrix game can not assess their payoffs in terms of ordinary fuzzy or intuitionistic fuzzy numbers. The SVNN is used as an excellent tool to handle such situations. This paper explores matrix games with SVNN payoffs and investigates a non-linear programming approach to solve such a game. First, two auxiliary non-linear multi-objective programming problems have been formulated. Then, each of the two multi-objective programming problems is converted into two non-linear bi-objective programming problems. Finally, the lexicographic method is used to solve the reduced bi-objective programming problems. It is worth mentioning that the values of the game for both the players are obtained in SVNN forms, which is desirable. The applicability of the proposed approach is illustrated with a market share problem and results are compared and analyzed with an existing method.

Keywords

• matrix game
• single-valued neutrosophic number
• multi-objective optimization
• lexicographic method