Abstract
The classical matrix theory is deficient to express the vagueness of the real life. The fuzzy set theory has been successfully applied to bridge this gap. Much work has already been done on a two-person zero sum matrix game with fuzzy goals. In continuation, this paper is dedicated to define and study a multi-criteria two-person zero sum game with intuitionistic fuzzy goals. It is shown that solving such games is equivalent to solving two crisp multi object linear programming problems. Our work generalizes the previous study on a multi-criteria game with fuzzy goals by adopting the approach of linear programming with intuitionistic fuzzy sets. Finally, an illustrative numerical example is provided to elaborate the proposed approach.
Highlights
Solving the two-person zero sum matrix game is proved to be equivalent to solving two linear programming models
The main result of this paper is presented which states that solving such an I-fuzzy game is equivalent to solving a pair of multi-criteria linear programming problems
A new game with I-fuzzy goals named MOIFG has been constructed for solving multi-criteria programming problems, which is different from MOFG that was studied by Aggarwal and Khan [33]
Summary
Solving the two-person zero sum matrix game is proved to be equivalent to solving two linear programming models. In the 1970s, Bellman and Zadeh [23] defined the notions of fuzzy constraints, fuzzy decisions and fuzzy goals, which lead to the development of mathematical programs with fuzzy objective functions, with fuzzy constraints (see Tanaka et al [24]) These fuzzy modeling tools are successfully applied in making and solving a two-person zero sum matrix game in different perspectives. The main result of this paper is presented which states that solving such an I-fuzzy game is equivalent to solving a pair of (crisp) multi-criteria linear programming problems.
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