On fuzzy topologies generated by fuzzy relations

Abstract

In this paper, we have introduced a fuzzy topology generated by a fuzzy relation as a generalization of the corresponding concept given by Smithson and obtained sufficient conditions under which this fuzzy topology becomes fuzzy T₀, fuzzy T₁ and fuzzy T₂. We have also introduced ‘finite intersection property (F.I.P.)’ for fuzzy topological spaces and shown that in a fuzzy topological space (X, τ ), this property is equivalent to the Lowen’s fuzzy compactness. We have also obtained a sufficient condition under which a fuzzy topology generated by a fuzzy relation becomes fuzzy compact.