Similarity vs. Possibility in Measuring Fuzzy Sets Distinguishability

Two measures that quantify distinguishability of fuzzy sets are addressed in this paper: similarity, which exhibits sound theoretical properties but it is usually computationally intensive, and possibility, whose calculation can be very efficient but does not exhibit the same properties of similarity. It is shown that under mild conditions – usually met in interpretable fuzzy modelling – possibility can be used as a valid measure for assessing distinguishability, thus overcoming the computational inefficiencies caused by the use of similarity measures. Moreover, those procedures aimed to minimize possibility also minimize similarity and, consequently, improve distinguishability. In this sense, the use of possibility is fully justified in interpretable fuzzy modelling.