Fuzzy Sets Defined on a Hierarchical Domain

This paper presents a new type of fuzzy sets, called "hierarchical fuzzy sets", that apply when the considered domain of values is not "flat," but contains values that are more specific than others according to the "kind of" relation. We study the properties of such fuzzy sets, that can be defined in a short way on a part of the hierarchy, or exhaustively (by their "closure") on the whole hierarchy. We show that hierarchical fuzzy sets form equivalence classes in regard to their closures and that each class has a particular representative called "minimal fuzzy set". We propose a use of this minimal fuzzy set for query enlargement purposes and, thus, present a methodology for hierarchical fuzzy set generalization. We finally present an experimental evaluation of the theoretical results described in the paper, in a practical application