Matching fuzzy quantities

A characteristic approach of approximate reasoning is the partial matching of observations to prototypes. The formal basis of partial matching has been investigated in the literature through different derivations of similarity measures for a particular model of uncertainty. The paper is cast in the framework of fuzzy set theory and brings another dimension to the fuzzy matching criterion; this dimension is the measure of uncertainty through the concept of subjective entropy. While a similarity measure, in the matching process, activates relevant prototypes, the entropy formalism derived here provides a measure of uncertainty in the partial matching to each prototype. The novel approach of this paper formalizes an entropy weights activation of prototypes for fuzzy partial matching. In addition to that we develop a new methodology of matching of observation to a set of prototypes making use of a suitable aggregation done with a framework of fuzzy integrals. A method of dealing with compound hypothesis (namely being a predicate over Boolean combination of individual prototypes) is also developed.