The fuzzy bargaining set of cooperative game with fuzzy coalition

Article type: Research Article

Authors: Yu, Xiaohui^{a; *} | Zhou, Hong^b | Zhang, Xufeng^a | Zhang, Qiang^c | Liu, Yan^a | Pang, Jinhui^d

Affiliations: [a] School of Logistics Beijing Wuzi University, Beijing, P.R. China | [b] School of Information Beijing Wuzi University, Beijing, P.R. China | [c] School of Management and Economics, Beijing Institute of Technology, Beijing, P.R. China | [d] Library, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Xiaohui Yu, School of Logistics Beijing Wuzi University, Beijing 101149, P.R. China. Tel.: +86 13146060603; E-mail: yuxiaohui@bwu.edu.cn.

Abstract: In this paper, the fuzzy bargaining set of cooperative game with fuzzy coalition is proposed, which can be regarded as the generalization of crisp bargaining set. The fuzzy bargaining set is based on the assumption that the total worth of a fuzzy coalition will be allocated to the players whose participation rate is larger than zero. Because fuzzy core had been proposed as a kind of solution for the fuzzy games, the relationship between fuzzy bargaining set and fuzzy core is also showed. Surprisingly, the relationship between fuzzy bargaining set and fuzzy core does coincide as in the classical case. The property of fuzzy bargaining set is also analyzed, such as the existence condition of counter-objection.

Keywords: Cooperative game, fuzzy, coalition, bargaining set, core

DOI: 10.3233/JIFS-162417

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1757-1765, 2017