A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
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...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/697261 |
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| author | Deng-Feng Li Jie Yang |
| author_facet | Deng-Feng Li Jie Yang |
| author_sort | Deng-Feng Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-33da06618de240c5a715a7c2b76000e7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-33da06618de240c5a715a7c2b76000e72025-02-03T05:59:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/697261697261A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy NumbersDeng-Feng Li0Jie Yang1School of Management, Fuzhou University, Fuzhou, Fujian 350108, ChinaSchool of Management, Fuzhou University, Fuzhou, Fujian 350108, ChinaThe 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.http://dx.doi.org/10.1155/2013/697261 |
| spellingShingle | Deng-Feng Li Jie Yang A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers Journal of Applied Mathematics |
| title | A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers |
| title_full | A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers |
| title_fullStr | A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers |
| title_full_unstemmed | A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers |
| title_short | A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers |
| title_sort | difference index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers |
| url | http://dx.doi.org/10.1155/2013/697261 |
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