Existence of Fuzzy Zhou Bargaining Sets in TU Fuzzy Games

Wenbo Yang, Jiuqiang Liu and Xiaodong Liu
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Wenbo Yang: Department of Trace Examination, National Police University of China, Shengyang, China
Jiuqiang Liu: Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, USA
Xiaodong Liu: School of Management Engineering, Xi'an University of Finance and Economics, Xi'an, China

International Journal of Fuzzy System Applications (IJFSA), 2018, vol. 7, issue 1, 46-55

Abstract: This article contends that cooperative games have been studied extensively in the literature. A central question in cooperative games is to study solution concepts and their relationships, those well-known solution concepts include cores, stable sets, Shapley values, bargaining sets, and so on. In 1981, Aubin introduced cooperative fuzzy games with fuzzy coalitions which reflect the situations where agents have the possibility to cooperate with different participation level with values between $0$ and $1$), varying from non-cooperation (participation level $0$) to full cooperation (participation level $1$). Since then, cooperative fuzzy games have been studied extensively in the literature. In this article, the authors extend the concept of Zhou bargaining sets - one of three major bargaining sets in cooperative games - to its fuzzy version and prove the existence of fuzzy Zhou bargaining sets which extends the existence theorem for Zhou bargaining sets by Zhou.

Date: 2018
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