Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables
This paper deals with bimatrix games in uncertainty environment based on several types of ordering, which Maeda proposed. But Maeda’s models was just made based on symmetrical triangle fuzzy variable. In this paper, we generalized Maeda’s model to the non-symmetrical environment. In other words, we...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/824790 |
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| author | Cun-lin Li |
| author_facet | Cun-lin Li |
| author_sort | Cun-lin Li |
| collection | DOAJ |
| description | This paper deals with bimatrix games in uncertainty environment based on several types of ordering, which Maeda proposed. But Maeda’s models was just made based on symmetrical triangle fuzzy
variable. In this paper, we generalized Maeda’s model to the non-symmetrical environment. In other words, we investigated the fuzzy bimatrix games based on nonsymmetrical L-R fuzzy variables. Then the pseudoinverse of a nonconstant monotone function was given and the concept of crisp parametric bimatrix games was introduced. At last, the existence condition of Nash equilibrium strategies of the fuzzy bimatrix games is proposed and (weak) Pareto equilibrium of the fuzzy bimatrix games was obtained through the Nash equilibrium of the crisp parametric bimatrix. |
| format | Article |
| id | doaj-art-4a3a24fcdd4947a8a3528cf99656f821 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4a3a24fcdd4947a8a3528cf99656f8212025-02-03T01:03:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/824790824790Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy VariablesCun-lin Li0School of Management, Beifang University of Nationalities, Yinchuan 750021, ChinaThis paper deals with bimatrix games in uncertainty environment based on several types of ordering, which Maeda proposed. But Maeda’s models was just made based on symmetrical triangle fuzzy variable. In this paper, we generalized Maeda’s model to the non-symmetrical environment. In other words, we investigated the fuzzy bimatrix games based on nonsymmetrical L-R fuzzy variables. Then the pseudoinverse of a nonconstant monotone function was given and the concept of crisp parametric bimatrix games was introduced. At last, the existence condition of Nash equilibrium strategies of the fuzzy bimatrix games is proposed and (weak) Pareto equilibrium of the fuzzy bimatrix games was obtained through the Nash equilibrium of the crisp parametric bimatrix.http://dx.doi.org/10.1155/2012/824790 |
| spellingShingle | Cun-lin Li Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables Journal of Applied Mathematics |
| title | Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables |
| title_full | Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables |
| title_fullStr | Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables |
| title_full_unstemmed | Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables |
| title_short | Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on L-R Fuzzy Variables |
| title_sort | characterization of the equilibrium strategy of fuzzy bimatrix games based on l r fuzzy variables |
| url | http://dx.doi.org/10.1155/2012/824790 |
| work_keys_str_mv | AT cunlinli characterizationoftheequilibriumstrategyoffuzzybimatrixgamesbasedonlrfuzzyvariables |