A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transfor...A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.展开更多
Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value j...Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.展开更多
The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective t...The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective two person zero-sum matrix games with I-fuzzy goals.In this article,a class of piecewise linear membership and non-membership functions for I-fuzzy goals is constructed.These functions are more effective in real games because marginal rate of increase(decrease)of such membership functions(non-membership functions)is different in different intervals of tolerance errors.Finally,one numerical example is given to examine the effectiveness and advantages of the proposed results.展开更多
To accelerate the selection process of feature subsets in the rough set theory （RST）, an ensemble elitist roles based quantum game （EERQG） algorithm is proposed for feature selec- tion. Firstly, the multilevel eli...To accelerate the selection process of feature subsets in the rough set theory （RST）, an ensemble elitist roles based quantum game （EERQG） algorithm is proposed for feature selec- tion. Firstly, the multilevel elitist roles based dynamics equilibrium strategy is established, and both immigration and emigration of elitists are able to be self-adaptive to balance between exploration and exploitation for feature selection. Secondly, the utility matrix of trust margins is introduced to the model of multilevel elitist roles to enhance various elitist roles＇ performance of searching the optimal feature subsets, and the win-win utility solutions for feature selec- tion can be attained. Meanwhile, a novel ensemble quantum game strategy is designed as an intriguing exhibiting structure to perfect the dynamics equilibrium of multilevel elitist roles. Finally, the en- semble manner of multilevel elitist roles is employed to achieve the global minimal feature subset, which will greatly improve the fea- sibility and effectiveness. Experiment results show the proposed EERQG algorithm has superiority compared to the existing feature selection algorithms.展开更多
In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of ...In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of von Neumann and Morgenstern to change ordinal values into cardinal values using the analytical hierarchy process. We suggest using Saaty’s pairwise comparison with combined strategies as criteria for players involved in a repetitive game. We present and illustrate a methodology for moving from ordinal payoffs to cardinal payoffs. We summarize the impact on how the solutions are achieved.展开更多
Inspired by the first lustrum of the Club Positioning Matrix (CPM) for professional Dutch soccer teams, we model the interaction between soccer teams and their potential fans as a cooperative cost game based on the an...Inspired by the first lustrum of the Club Positioning Matrix (CPM) for professional Dutch soccer teams, we model the interaction between soccer teams and their potential fans as a cooperative cost game based on the annual voluntary sponsorships of fans in order to validate their fan registration in a central database. We introduce a natural cost allocation to the soccer teams, based in a natural manner on the sponsorships of fans. The game theoretic approach is twofold. On the one hand, an appropriate cost game called “fan data cost game” is developed and on the other, it is shown that the former natural cost allocation agrees with the solution concept called “nucleolus” of the fan data cost game.展开更多
基金Sponsored by the National Natural Science Foundation of China(70471063,70771010)
文摘A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.
文摘Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
文摘The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective two person zero-sum matrix games with I-fuzzy goals.In this article,a class of piecewise linear membership and non-membership functions for I-fuzzy goals is constructed.These functions are more effective in real games because marginal rate of increase(decrease)of such membership functions(non-membership functions)is different in different intervals of tolerance errors.Finally,one numerical example is given to examine the effectiveness and advantages of the proposed results.
基金supported by the National Natural Science Foundation of China(6113900261171132+4 种基金61300167)the Natural Science Foundation of Jiangsu Education Department(12KJB520013)the Open Project Program of Jiangsu Provincial Key Laboratory of Computer Information Processing Technologythe Qing Lan Project of Jiangsu Provincethe Starting Foundation for Doctoral Scientific Research,Nantong University(14B20)
文摘To accelerate the selection process of feature subsets in the rough set theory （RST）, an ensemble elitist roles based quantum game （EERQG） algorithm is proposed for feature selec- tion. Firstly, the multilevel elitist roles based dynamics equilibrium strategy is established, and both immigration and emigration of elitists are able to be self-adaptive to balance between exploration and exploitation for feature selection. Secondly, the utility matrix of trust margins is introduced to the model of multilevel elitist roles to enhance various elitist roles＇ performance of searching the optimal feature subsets, and the win-win utility solutions for feature selec- tion can be attained. Meanwhile, a novel ensemble quantum game strategy is designed as an intriguing exhibiting structure to perfect the dynamics equilibrium of multilevel elitist roles. Finally, the en- semble manner of multilevel elitist roles is employed to achieve the global minimal feature subset, which will greatly improve the fea- sibility and effectiveness. Experiment results show the proposed EERQG algorithm has superiority compared to the existing feature selection algorithms.
文摘In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of von Neumann and Morgenstern to change ordinal values into cardinal values using the analytical hierarchy process. We suggest using Saaty’s pairwise comparison with combined strategies as criteria for players involved in a repetitive game. We present and illustrate a methodology for moving from ordinal payoffs to cardinal payoffs. We summarize the impact on how the solutions are achieved.
文摘Inspired by the first lustrum of the Club Positioning Matrix (CPM) for professional Dutch soccer teams, we model the interaction between soccer teams and their potential fans as a cooperative cost game based on the annual voluntary sponsorships of fans in order to validate their fan registration in a central database. We introduce a natural cost allocation to the soccer teams, based in a natural manner on the sponsorships of fans. The game theoretic approach is twofold. On the one hand, an appropriate cost game called “fan data cost game” is developed and on the other, it is shown that the former natural cost allocation agrees with the solution concept called “nucleolus” of the fan data cost game.
