A BI-OBJECTIVE PROGRAMMING APPROACH TO SOLVE MATRIX GAMES WITH PAYOFFS OF ATANASSOV’S TRIANGULAR INTUITIONISTIC FUZZY NUMBERS

Document Type : Research Paper

Authors

1 School of Management, Fuzhou University, No. 2, Xueyuan Road, Daxue New District, Fuzhou 350108, Fujian, China

2 School of Mathematics and Computing Sciences, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China

Abstract

The intuitionistic fuzzy set has been applied to game theory very
rarely since it was introduced by Atanassov in 1983. The aim of this paper is
to develop an effective methodology for solving matrix games with payoffs of
Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology,
the concepts and ranking order relations of Atanassov’s TIFNs are defined.
A pair of bi-objective linear programming models for matrix games with
payoffs of Atanassov’s TIFNs is derived from two auxiliary Atanassov’s intuitionistic
fuzzy programming models based on the ranking order relations of
Atanassov’s TIFNs defined in this paper. An effective methodology based on
the weighted average method is developed to determine optimal strategies for
two players. The proposed method in this paper is illustrated with a numerical
example of the market share competition problem.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 9, Issue 3 - Serial Number 3
May and June 2012
Pages 93-110

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