Fuzzy group identification problems

Abstract

The Group Identification Problem (“Who is a J?”) introduced by Kasher and Rubinstein (1997) assumes a finite class of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function that indicates for each agent, including herself, the degree of membership to J. The problem is that of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. The literature has already considered fuzzy versions of this problem. In this paper we consider alternative fuzzy presentations of the axiomatic of the original problem. While some results are analogous to those of the original crisp model, we show that our fuzzy version is able to overcome some of the main impossibility results of Kasher and Rubinstein.