Three constructive methods for the definition of interval-valued fuzzy equivalencies

In this paper, we introduce the concept of an interval-valued fuzzy equivalence as an interval extension of the fuzzy equivalence. The partial orders between fuzzy equivalencies are studied. Three ways of constructing interval-valued fuzzy equivalencies from given fuzzy equivalencies and aggregation functions are provided. Some examples of interval-valued fuzzy equivalencies built by the proposed constructive methods are shown. The properties and structures of interval-valued fuzzy equivalencies are also studied.