Interval-Valued Fuzzy Relations

Abstract

By using the notion of interval-valued fuzzy relations, we forms the poset (IVFR (X), <TEX>$\leq$</TEX>) of interval-valued fuzzy relations on a given set X. In particular, we forms the subposet (IVFE (X), <TEX>$\leq$</TEX>) of interval-valued fuzzy equivalence relations on a given set X and prove that the poset (IVFE(X), <TEX>$\leq$</TEX>) is a complete lattice with the least element and greatest element.