(s,t]-fuzzy filters of BCK-algebras

The definitions of (∈,∈∨q)-fuzzy filter and (β̄,ᾱ)-fuzzy filter, and four new (β̄,ᾱ)-fuzzy filters are acquired. As a generalization of fuzzy BCK-filter, (∈,∈∨q) -fuzzy filter and (∈,∈̄∨q) -fuzzy filter, we give the definition of (s,t]-fuzzy filter with thresholds. The relations between these fuzzy filters and their level filters are discussed, some proposed are studed, and their equivalent descriptions are given. How to deal with the homomorphic image and inverse image of (s,t]-fuzzy filters are investigated.