Some types of generalized fuzzy filters of MTL-algebras

Article type: Research Article

Authors: Ma, X. | Zhan, J. | Xiang, D.

Affiliations: Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, P.R. China

Note: [] Corresponding author. E-mail: zjmhbmy@126.com; zhanjianming@hotmail.com (J. Zhan).

Abstract: 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.

Keywords: MTL-algebra, (∈, ∈, ∨q)-fuzzy Boolean filter, (∈, ∈, ∨q)-fuzzy G-filter, (∈, ∈, ∨q)-fuzzy MV-filter

DOI: 10.3233/IFS-2009-0425

Journal: Journal of Intelligent & Fuzzy Systems, vol. 20, no. 4, 5, pp. 169-174, 2009