An activation detection based similarity measure for intuitionistic fuzzy sets

Abstract

Intuitionistic fuzzy sets (IF-sets), with mechanisms to represent both the degree of membership and hesitancy of a given entity with respect to a concept under consideration, have been proven to be a useful extension to Zadeh's fuzzy set theory. Noteworthy efforts by various researchers have been devoted to defining a robust similarity measure for a given pair of IF-sets, as we often need to quantify the similarity between given entities in application domains ranging from medical diagnosis to multiple criteria decision making. These efforts have shown that it is highly non-trivial to construct a truly robust IF-set similarity measure with easy-to-understand interpretations. In this article, grounded on native concepts from activation detection in medical image analysis, a model for determining the degree of similarity between IF-sets is proposed. An IF-set similarity measure (termed the activation detection based similarity measure) is then systematically built from this model. We show that the proposed measure produces results that are intuitively appealing, easy to understand, and can be robustly interpreted. Moreover, we demonstrate that the proposed measure obeys standard conventions regarding set definition in the classical setting, and is equivalent to the Jaccard's similarity measure as we transition from the intuitionistic fuzzy setting to the classical setting. The source code of the numerical implementation of the proposed measure is available from the author upon request.