Abstract
Abstract Adding an additional degree of non-membership, K. T. Atanassov introduced the concept of the intuitionistic fuzzy (IF) set (IF-set), which has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs are expressed with real numbers rather than IF-sets. In this methodology, the concepts of IF-set goals and the solutions of matrix games with IF-set goals are proposed. It is proven that solutions of matrix games with IF-set goals can be obtained through solving the developed auxiliary linear programming models, which are the generalization of matrix games with fuzzy goals. The proposed methodology is illustrated with a numerical example. Furthermore, comparison analysis of the proposed methodology is conducted to show its advantages over matrix games with fuzzy goals.
Highlights
Game theory has been used as a powerful analytical tool for decision making problems in the organizations or competitive systems
We formulate the matrix games with intuitionistic fuzzy (IF)-set goals and hereby develop the linear programming method, which is different from those proposed by Li and Nan[27] and Li28
The matrix games discussed in this paper are ones in which uncertainty only appears in goals of players, i.e., the goals of players are expressed with the IF-sets whereas payoffs of players are real numbers rather than the IFsets
Summary
Game theory has been used as a powerful analytical tool for decision making problems in the organizations or competitive systems. Li and Nan[27] studied the matrix games in which payoffs of players are expressed with the IF-set and goals of players are not taken into consideration. The concepts of the solutions for matrix games with payoffs of IF-sets were defined and hereby a method was developed on the basis of a pair of auxiliary nonlinear/linear programming models, which were derived from the constructed bi-objective programming models. The discussed matrix games[27, 28] only taken into consideration uncertainty in payoffs of players, which was expressed with IF-sets. We study matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs of players are real numbers rather than IF-sets. A numerical example and conclusion are given in Sections 4 and 5, respectively
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