Foldnessof(∈,∈∨q)-fuzzyimplicativefiltersinBL-algebars

By using the concept of quasi-coincidence of a fuzzy point with a fuzzy set, the notion of(∈,∈∨q)-fuzzy n-fold implicative filters in BL-algebras which is a generalization of ordinary fuzzy n-fold implicative filters, is defined, and several characterizations of(∈,∈∨q)-fuzzy n-fold implicative filters are given. The relation between(∈,∈∨q)-fuzzy filters and(∈,∈∨q)-fuzzy n-fold implicative filters and the relation between(∈,∈∨q)-fuzzy n-fold implicative filters and(∈,∈∨q)-fuzzy(n+1)-fold implicative filters are investigated. The concept of a fuzzy n-fold implicative filters with thresholds in BL-algebras is proposed. The acceptable nontrivial concepts obtained in this manner were the ordinary fuzzy n-fold implicative filters and(∈,∈∨q)-fuzzy n-fold implicative filters. The extension properties for fuzzy n-fold implicative filters with thresholds and(∈,∈∨q)-fuzzy n-fold implicative filters are established.