Constructing possibility measures

Addresses some aspects of the extension problem for possibility measures: given the values that a (fuzzy) set mapping takes on a family of (fuzzy) sets, is it possible to extend this mapping to a possibility measure? This problem is shown to be equivalent to a special system of relational equations. When the family of sets considered is a (semi-)partition, two important solutions are identified. It is shown that these solutions, and their fuzzifications, play a central part in the treatment of the more general extension problem. This role is shown to be even more conspicuous when the family of fuzzy sets considered is a T- (semi-)partition, a notion introduced and studied for the first time in this paper