Abstract
In this paper, we apply the standard element free mathematical definitions of equivalence relation and function as relations to the case of fuzzy relations. One of the surprising results of this approach is that fuzzy functions take their values from the complemented elements of a Brouwerian lattice. Thus, in the common case of the values being taken from the unit interval, the only fuzzy functions of this type are the ordinary functions. This might suggest that fuzzy set theory is more than just a generalization of ordinary set theory.
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