T-generable indistinguishability operators and their use for feature selection and classification

Abstract

T-generable indistinguishability operators are operators E that can be expressed in the form , where T is a t-norm and is the fuzzy relation generated by the fuzzy subset μ. In this paper we analyse their relation with powers with respect to the t-norm T and with quasi-arithmetic means. For non-strict continuous Archimedean t-norms they are completely characterised as generable by crisp equivalence relations. These fuzzy relations are used to define a method, called JADE, useful for feature selection and classification tasks. JADE is based on minimising the distance between two indistinguishability measures: the one given by weighting the attribute-values describing the domain objects and the other one given by the correct classification taken as an equivalence relation. The preliminary experiments we carried out with JADE are promising concerning the accuracy in solving classification tasks. We also report some issues of the method that could be improved in the future.