A NONLINEAR PROGRAMMING APPROACH TO MATRIX GAMES WITH PAYOFFS OF ATANASSOV'S INTUITIONISTIC FUZZY SETS

被引：51

作者：

Li, Deng-Feng ^{[1
,2
]}

Nan, Jiang-Xia ^{[3
,4
]}

机构：

[1] Dalian Naval Acad, Dept 5, Dalian 116018, Liaoning, Peoples R China

[2] Shenyang Inst Aeronaut Engn, Dept Sci, Shenyang 110034, Liaoning, Peoples R China

[3] Dalian Univ Technol, Coll Appl Math, Dalian 116024, Liaoning, Peoples R China

[4] Dalian Univ, Coll Informat Engn, Dalian 116622, Liaoning, Peoples R China

来源：

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS | 2009年 / 17卷 / 04期

关键词：

Intuitionistic fuzzy set; matrix game; mathematical programming; uncertainty; TERMINOLOGICAL DIFFICULTIES; DUALITY; GOALS;

D O I：

10.1142/S0218488509006157

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The intuitionistic fuzzy set (IFS) introduced by Atanassov in 1986 is characterized by two functions and 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 payoffs of Atanassov's IFSs. In this methodology, the concepts of the solutions for matrix games with payoffs of Atanassov's IFSs are defined based on the degree of membership and the degree of non-membership. It is proven that matrix games with payoffs of Atanassov's IFSs have solutions, which can be obtained through solving a pair of nonlinear programming models derived from two auxiliary nonlinear bi-objective programming models. The proposed method is illustrated with a numerical example.

引用

页码：585 / 607

页数：23

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