Abstract: A basic question in fuzzy set theory was studied: what is a many-valued filter on a set X? A new answer was presented by interpreting the axioms (three logical formulas) for classical filter theory in the fuzzy setting, which made use of the intrinsic fuzzy partial order on the fuzzy power set of X. The many valued filter theory was applied to characterize one of the many-valued topological theory —strong Ω-topology.

Key words: Ω-filter , strong Ω-topology, commutative quantale