Fuzzy filters of MTL-algebras

Characterizations of fuzzy filters in MTL-algebras are given. The fuzzy filter generated by a fuzzy set is considered. The notion of Boolean fuzzy filters and MV-fuzzy filters are introduced and related properties are investigated. A condition for a fuzzy filter to be Boolean is provided. A characterization of a Boolean fuzzy filter is given. A congruence relation on a MTL-algebra induced by a fuzzy filter is established, and we show that the set of all congruence relations induced by a fuzzy filter is a completely distributive lattice.