A Similarity Measure with Uncertainty for Incompletely Known Fuzzy Sets

This paper is devoted to the problem of measuring similarity between pieces of uncertain (incomplete) information in the framework of I-fuzzy set theory (Atanassov's intuitionistic fuzzy sets and interval-valued fuzzy sets). We propose a way of determining an interval-valued similarity measure of I-fuzzy sets that preserves information about the operands' uncertainty by approximating lower and upper bounds of similarity degrees. We discuss some of the desirable properties of this measure and illustrate it with an example application in recommender systems.