Abstract The problem of fuzzy filters in residuated lattices is deeply studied by using the principle and method of fuzzy sets. Three new notions of fuzzy prelinear, divisible and Glivenko filters are introduced in residuated lattices. Some of their properties and characterizations are given. Relations among these new fuzzy filters, fuzzy positive implicative filter, fuzzy Boolean filter, fuzzy MV filter, and fuzzy regular filter are discussed systematically. It is proved that a fuzzy filter is a fuzzy MV filter if and only if it is both a fuzzy regular filter and a fuzzy divisible filter.
