The problem of collective identity in a fuzzy environment

We define the problem of group identification in a fuzzy environment. We concentrate on the case where the society is required to self-determine the belongingness of each member to a specific group, characterized by a single attribute. In general terms, this case consists of a collective identity issue that can be regarded as an aggregation problem of individual assessments within a group. Here we introduce the possibility that both the original assessments and the resulting output attach partial memberships to the collectivity, for each potential member. We propose relevant classes of rules, and some are axiomatically characterized. Our new approach provides a way to circumvent classical impossibility results like Kasher and Rubinstein's.