Abstract
In fuzzy set theory, similarity phenomenon is approached using so-called fuzzy equivalence relations. An important role in fuzzy modeling is played by similarity-based closure (called also the extensional hull). Intuitively, the degree to which an element x belongs to a similarity-based closure of a fuzzy set A is the degree to which it is true that there is an element y in A which is similar to x. In this paper, we show a basic relationship between similarity-based closure and metric closure, and provide an axiomatic characterization of the operation of a similarity-based closure.