General types of $({\in,}\,{\in}\,{\vee}\,{\rm q})$-fuzzy filters in BL-algebras

Abstract

As a generalization of an $({\in,}\,{\in}\,{\vee}\, \hbox{q})$-fuzzy filter in a BL-algebra, the notion of an $({\in,}\,{\in}\,{\vee}\,\hbox{q}_k)$-fuzzy filter in a BL-algebra is introduced, and related properties are investigated. Characterizations of an $({\in,}\,{\in\,\vee}\,\hbox{q}_k)$-fuzzy filter are considered. The implication-based fuzzy filters of a BL-algebra are discussed.