Uniform fuzzy relations and fuzzy functions

In this paper we introduce and study the concepts of a uniform fuzzy relation and a (partially) uniform F-function. We give various characterizations and constructions of uniform fuzzy relations and uniform F-functions, we show that the usual composition of fuzzy relations is not convenient for F-functions, so we introduce another kind of composition, and we establish a mutual correspondence between uniform F-functions and fuzzy equivalences. We also give some applications of uniform fuzzy relations in approximate reasoning, especially in fuzzy control, and we show that uniform fuzzy relations are closely related to the defuzzification problem.