Fuzzy equivalence and the resulting topology (Q1187462)

This paper presents a construction for a topology on a set \(E\) on which a fuzzy equivalence is defined. A fuzzy equivalence relation is a generalization of the usual notion of equivalence relation where transitivity has been extended in a way consistent with the theory of fuzzy sets. The authors then use the equivalence relation to construct a Kuratowski closure operator on \(E\). If the triangle function that supports transitivity is dense, then the resulting topology corresponds in a natural way to the underlying equivalence relation. The authors then give a connection between this construction and Poincaré's conception of the physical continuum.