A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-22
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs), which are called TrIFN bimatrix games for short.
In this method, we define the value index and ambiguity index for a TrIFN and propose a new order relation of TrIFNs based on the difference index of value index to ambiguity index, which is proven to be a total order relation.
Hereby, we introduce the concepts of solutions of TrIFN bimatrix games and parametric bimatrix games.
It is proven that any TrIFN bimatrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bimatrix game.
The latter can be obtained through solving the auxiliary parametric bilinear programming model.
The method proposed in this paper is demonstrated with a real example of the commerce retailers’ strategy choice problem.
American Psychological Association (APA)
Li, Deng-Feng& Yang, Jie. 2013. A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-491427
Modern Language Association (MLA)
Li, Deng-Feng& Yang, Jie. A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers. Journal of Applied Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-491427
American Medical Association (AMA)
Li, Deng-Feng& Yang, Jie. A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-491427
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-491427