Some kinds of (∈¯,∈¯∨q¯)-fuzzy filters of BLBL-algebras

The concepts of (∈¯,∈¯∨q¯)-fuzzy (implicative, positive implicative and fantastic) filters of BLBL-algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, (∈,∈∨q)-fuzzy (implicative, positive implicative and fantastic) filters and (∈¯,∈¯∨q¯)-fuzzy (implicative, positive implicative and fantastic) filters of BLBL-algebras. Finally, we prove that a fuzzy set FF of a BLBL-algebra LL is an (∈¯,∈¯∨q¯)-fuzzy implicative filter of LL if and only if it is both an (∈¯,∈¯∨q¯)-fuzzy positive implicative filter and an (∈¯,∈¯∨q¯)-fuzzy fantastic filter.