On the core, nucleolus and bargaining sets of cooperative games with fuzzy payoffs

Article type: Research Article

Authors: Zhang, Xia | Sun, Hao^{; *} | Xu, Genjiu | Hou, Dongshuang

Affiliations: Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P.R.China

Correspondence: [*] Corresponding author. Hao Sun, Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P.R.China. Tel.: +86 29 88495957; Fax: +86 29 88430033; E-mail: [email protected].

Abstract:  Depended on the expected values of fuzzy numbers, a total order relation of fuzzy numbers is proposed. We show that three concepts of the indifference fuzzy core, nucleolus and bargaining sets of cooperative games with fuzzy payoffs are well-defined following from this total order relation, whereas it is impossible to define by any partial order relation of fuzzy numbers for these concepts. Moreover, we raise a necessary and sufficient condition for non-emptiness of the indifference fuzzy core. It is further shown that there is at least one fuzzy payoff vector in the indifference fuzzy nucleolus. For convex or superadditive cooperative games with fuzzy payoffs, the indifference fuzzy bargaining sets coincide with the indifference fuzzy core.

Keywords: Cooperative games, fuzzy payoffs, core, nucleolus, bargaining sets

DOI: 10.3233/JIFS-181982

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6129-6142, 2019