Cooperative Fuzzy Games with Convex Combination Form

Fanyong Meng and Xiaohong Chen
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Fanyong Meng: School of Business, Central South University, Changsha 410083, P. R. China
Xiaohong Chen: School of Business, Central South University, Changsha 410083, P. R. China†School of Accounting, Hunan University of Commerce, Changsha 410205, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2016, vol. 33, issue 01, 1-25

Abstract: In this paper, a new class of cooperative fuzzy games named fuzzy games with convex combination form is introduced. This kind of fuzzy games considers two aspects of information. One is the contribution of the players to the associated crisp coalitions; the other is their participation levels. The explicit expression of the Shapley function is given, which is equal to the production of the Shapley function on crisp games and the player participation levels. Meanwhile, the relationship between the fuzzy core and the Shapley function is studied. Surprisingly, the relationship between them does coincide as in crisp case. Furthermore, some desirable properties are researched. Finally, an example is provided to illustrate the difference in fuzzy coalition values and the player Shapley values for four types of fuzzy games.

Keywords: Fuzzy game; Shapley value; fuzzy core; convex combination (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S021759591650007X

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