Parameterized bilinear programming methodology for solving triangular intuitionistic fuzzy number bimatrix games

The aim of this paper is to develop a new methodology for solving bimatrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs), which are called TIFN bimatrix games for short. In this methodology, we define the concepts of the value-index and ambiguity-index and hereby develop a difference-index based ranking method, which is proven to be a total order. The parameterized bilinear programming models are derived from a pair of auxiliary TIFN mathematical programming models, which are used to determine solutions of TIFN bimatrix games. Validity and applicability of the models and method proposed in this paper are illustrated with a practical example.

[1]  Jiang-Xia Nan,et al.  A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers , 2010, Int. J. Comput. Intell. Syst..

[2]  V. Lakshmana Gomathi Nayagam,et al.  Ranking of intuitionistic fuzzy numbers , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

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

[4]  Shu-Ping Wan,et al.  The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers , 2013, Knowl. Based Syst..

[5]  Dejian Yu,et al.  Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator , 2012, Int. J. Intell. Syst..

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

[7]  T. Maeda,et al.  Characterization of the Equilibrium Strategy of the Bimatrix Game with Fuzzy Payoff , 2000 .

[8]  Deng-Feng Li,et al.  Decision and Game Theory in Management With Intuitionistic Fuzzy Sets , 2013, Studies in Fuzziness and Soft Computing.

[9]  Deng-Feng Li,et al.  A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems , 2010, Comput. Math. Appl..

[10]  Suresh Chandra,et al.  Bi-matrix Games with Fuzzy Goals and Fuzzy , 2004, Fuzzy Optim. Decis. Mak..

[11]  Peide Liu,et al.  Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making , 2010 .

[12]  Moussa Larbani,et al.  Solving bimatrix games with fuzzy payoffs by introducing Nature as a third player , 2009, Fuzzy Sets Syst..

[13]  Dejian Yu,et al.  Researching the development of Atanassov intuitionistic fuzzy set: Using a citation network analysis , 2015, Appl. Soft Comput..

[14]  Shu-Ping Wan,et al.  Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute Group Decision Making with Incomplete Weight Information , 2014, Int. J. Comput. Intell. Syst..

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

[16]  Etienne E. Kerre,et al.  Reasonable properties for the ordering of fuzzy quantities (II) , 2001, Fuzzy Sets Syst..

[17]  Ehsan Jafarian,et al.  A valuation-based method for ranking the intuitionistic fuzzy numbers , 2013, J. Intell. Fuzzy Syst..

[18]  H. M. Nehi.  A New Ranking Method for Intuitionistic Fuzzy Numbers , 2010 .

[19]  Aparna Mehra,et al.  Linear programming with Triangular Intuitionistic Fuzzy Number , 2011, EUSFLAT Conf..

[20]  Dengfeng Li.  Representation theorem and extension principles for Atanassov’s intuitionistic fuzzy sets and algebraic operations , 2012 .