AN INTERVAL-VALUED PROGRAMMING APPROACH TO MATRIX GAMES WITH PAYOFFS OF TRIANGULAR INTUITIONISTIC FUZZY NUMBERS

The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payos are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payos of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies and the value of the matrix game with pay- os of TIFNs. Based on the cut sets and ranking order relations between TIFNs, the intuitionistic fuzzy programming models are transformed into lin- ear programming models, which are solved using the existing simplex method. Validity and applicability of the proposed methodology are illustrated with a numerical example of the market share problem.

[1]  Antonio González,et al.  On the use of the ranking function approach to solve fuzzy matrix games in a direct way , 1992 .

[2]  Lourdes Campos Fuzzy linear programming models to solve fuzzy matrix games , 1989 .

[3]  Suresh Chandra,et al.  Matrix Games with Fuzzy Goals and Fuzzy Linear Programming Duality , 2004, Fuzzy Optim. Decis. Mak..

[4]  C. R. Bector,et al.  Matrix games with fuzzy goals and fuzzy payoffs , 2005 .

[5]  Antonio González,et al.  Fuzzy matrix games considering the criteria of the players , 1991 .

[6]  Ichiro Nishizaki,et al.  Solutions based on fuzzy goals in fuzzy linear programming games , 2000, Fuzzy Sets Syst..

[7]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[8]  Suresh Chandra,et al.  Application of linear programming with I-fuzzy sets to matrix games with I-fuzzy goals , 2012, Fuzzy Optimization and Decision Making.

[9]  Pavel V. Sevastjanov,et al.  An interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect , 2010, Knowl. Based Syst..

[10]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[11]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..

[12]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[13]  Madhumangal Pal,et al.  Linear Programming Technique to Solve Two Person Matrix Games with Interval Pay-Offs , 2009, Asia Pac. J. Oper. Res..

[14]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[15]  C. R. Bector,et al.  Fuzzy Mathematical Programming and Fuzzy Matrix Games , 2005 .

[16]  Suresh Chandra,et al.  Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs , 2004, Fuzzy Sets Syst..

[17]  Sanat Kumar Mahato,et al.  Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization , 2006 .

[18]  Chiang Kao,et al.  Solution of fuzzy matrix games: An application of the extension principle , 2007, Int. J. Intell. Syst..

[19]  Ranjit Biswas,et al.  An application of intuitionistic fuzzy sets in medical diagnosis , 2001, Fuzzy Sets Syst..