Some types of generalized fuzzy filters of MTL-algebras

摘要

The aim of this paper is to introduce the concepts of (∈, ∈ ∨q)-fuzzy Boolean filters and (∈, ∈ ∨q)-fuzzy MV-filters in MTL-algebras. Some characterizations of these kinds of generalized fuzzy filters are derived. Finally, the concept of (∈, ∈ ∨q)-fuzzy G-filters in MTL-algebras is introduced. It is proved that an (∈, ∈ ∨q)-fuzzy filter of MTL-algebras is Boolean if and only if it is both an (∈, ∈ ∨q)-fuzzy G-filter and an (∈, ∈ ∨q)-fuzzy MV-filter.