Solidarity Value and Solidarity Share Functions for TU Fuzzy Games

Abstract

TU games under both crisp and fuzzy environments describe situations where players make full (crisp) or partial (fuzzy) binding agreements and generate worth in return. The challenge is then to decide how to distribute the profit among them in a rational manner: we call this a solution. In this paper, we introduce the notion of solidarity value and the solidarity share function as a suitable solution to TU fuzzy games. Two special classes of TU fuzzy games, namely, TU fuzzy games in Choquet integral form and in multilinear extension form, are studied and the corresponding solidarity value and the solidarity share functions are characterized.