Generalized fuzzy filters of R0-algebras

Abstract

In R0-algebras, the notions of (α, β)-fuzzy (implicative, positive implicative, fantastic) filters where (α, β) are any two of {∈, q,∈ ∨q,∈ ∧q} with α ≠∈ ∧q are introduced and related properties are discussed. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set is an (∈, ∈)-fuzzy (implicative, positive implicative, fantastic) filter if and only if it is a fuzzy (implicative, positive implicative, fantastic) filter. Moreover, we also give the conditions for an (∈,∈ ∨q)-fuzzy (implicative, positive implicative, fantastic) filter to be an (∈, ∈)-fuzzy (implicative, positive implicative, fantastic) filter, and the conditions for a fuzzy set to be a (q,∈ ∨q)-fuzzy (implicative, positive implicative, fantastic) filter.