The least square B-nucleolus for fuzzy cooperative games

Article type: Research Article

Authors: Lin, Jian^{a; b; *} | Zhang, Qiang^b

Affiliations: [a] College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou, China | [b] School of Management and Economics, Beijing Institute of Technology, China

Correspondence: [*] Corresponding author. Jian Lin, College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou, Fujian, P.R. China. Tel.: +86 13763861300; E-mail: linjian36@163.com.

Abstract: The least square B-nucleolus for fuzzy cooperative games is proposed based on the bi-excess of fuzzy coalitions. The proposed solutions consider not only the size of fuzzy coalitions, but also the blocking and constructive powers. The uniqueness of the least square B-prenucleolus for fuzzy cooperative games is proved detailedly. Some quadratic programming models for generating the least square B-nucleolus of complete and incomplete fuzzy cooperative games are presented, respectively. The least square B-prenucleolus is extended to the multiplicative setting, and the logarithmic least square B-prenucleolus for multiplicative fuzzy cooperative games is derived.

Keywords: Least square nucleolus, cooperative game, quadratic programming, fuzzy coalition

DOI: 10.3233/IFS-151754

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 279-289, 2016