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Article type: Research Article
Authors: Meng, Fanyong | Zhao, Jinxian | Zhang, Qiang
Affiliations: School of Management, Qingdao Technological University, Qingdao, China | School of Management and Economics, Beijing Institute of Technology, Beijing, China
Note: [] Corresponding author. Fanyong Meng, School of Management, Qingdao Technological University, Qingdao 266033, China. Tel.: +86 18254298903; E-mail: mengfanyongtjie@163.com (Fanyong Meng).
Abstract: In this paper, we research fuzzy games with fuzzy characteristic functions, where the player participation levels are real numbers in [0, 1], and their payoffs are fuzzy numbers. Based on the Hukuhara difference between fuzzy numbers and the calculating formula of the Shapley function, we discuss a general form of fuzzy games with fuzzy characteristic functions, and study the Shapley function for this kind of fuzzy games. When the given fuzzy game is convex, we research some properties of fuzzy games with fuzzy characteristic functions. Furthermore, we research a special kind of fuzzy games with fuzzy characteristic functions, which is can be seen as an extension of fuzzy games with multilinear extension form. Finally, a numerical example is given.
Keywords: Cooperative fuzzy game, Shapley function, Hukuhara difference, fuzzy number
DOI: 10.3233/IFS-2012-0611
Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 1, pp. 23-35, 2013
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