Fuzzy Group Identification Problems

Abstract

We consider a class N = {1, . . . , n} of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function pi : N → [0, 1], indicating for each agent, including herself, the degree of membership to J. We consider the problem of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. While some results are analogous to those of the model with crisp preferences, the fuzzy version is able to overcome some of the main impossibility results found in the literature.