The G-nucleolus for fuzzy cooperative games

Article type: Research Article

Authors: Lin, Jian^; | Zhang, Qiang

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

Note: [] Corresponding author. Jian Lin, Tel.: +86 13763861300; E-mail: linjian36@163.com

Abstract: In this study, the G-nucleolus of fuzzy cooperative games is proposed based on the G-excess of fuzzy coalitions. The G-nucleolus considers not only the constructive and the blocking powers, but also the size of fuzzy coalitions. Moreover, we show that the G-nucleolus is reasonable, and coincides with the SM-nucleolus when the function f is equal to 1 for each fuzzy coalition. The G-nucleolus can be obtained by calculating the f-nucleolus of a constant-sum fuzzy cooperative game. We prove that G-nucleolus belong to the non-empty precore of the corresponding constant-sum fuzzy cooperative game. Finally, some linear programming models are employed to generate the G-nucleolus effectively.

Keywords: Nucleolus, cooperative games, dual game, fuzzy coalition

DOI: 10.3233/IFS-130962

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 6, pp. 2963-2971, 2014