A further discussion on fuzzy interval cooperative games

Article type: Research Article

Authors: Wang, Liming^{a; b} | Zhang, Qiang^{a; *}

Affiliations: [a] School of Management and Economics, Beijing Institute of Technology, Beijing, China | [b] School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot, China

Correspondence: [*] Corresponding author. Qiang Zhang, School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China. Tel.: +86 010 68912844; Fax: +86 010 68912483; E-mail: qiangzhang@bit.edu.cn.

Abstract: The F-core and the F-balancedness have been introduced for fuzzy interval cooperative games by Mallozzi et al. (2011). It was pointed out that the F-balancedness was a necessary but not sufficient condition for the non-emptiness of the F-core. In this paper, a numerical example is given to show that the F-balancedness can not guarantee the non-emptiness of the F-core. Furthermore, the F-cores of trapezoidal fuzzy interval games are discussed in detail. Some properties of the F-core are obtained and three sufficient conditions for the non-emptiness of the F-core are given. These conclusions are generalizations of the corresponding results in both interval cooperative game theory and classical cooperative game theory. Lastly, an application example is also provided.

Keywords: Fuzzy interval, cooperative games, convex games, core

DOI: 10.3233/IFS-162131

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 185-191, 2016