New types of fuzzy filters of BL-algebras

Yunqiang Yin, Jianming Zhan

Abstract: This paper introduces the concepts of (α,β)-fuzzy (implicative, positive implicative, fantastic) filters and (β¯,α¯)-fuzzy (implicative, positive implicative, fantastic) filters of BL-algebras, where α,β∈{∈γ,qδ,∈γ∧qδ,∈γ∨qδ}, α¯,β¯∈{∈γ¯,qδ¯,∈γ¯∧qδ¯,∈γ¯∨qδ¯}, α≠∈γ∧qδ and β¯≠∈γ¯∧qδ¯, and some related properties are investigated. Special attention is paid to (∈γ¯,∈γ¯∨qδ¯)-fuzzy (implicative, positive implicative, fantastic) filters and (∈γ¯,∈γ¯∨qδ¯)-fuzzy (implicative, positive implicative, fantastic) filters which are generalizations of (∈,∈∨q)-fuzzy (implicative, positive implicative, fantastic) filters and (∈¯,∈¯∨q¯)-fuzzy (implicative, positive implicative, fantastic) filters studied in Ma et al. (2008, 2009) [34], [35]. It also points out that Examples 3.1.2, 3.1.9, 3.2.2, 3.2.9 and 3.3.9 in Ma et al. (2009) [35] are incorrect.