Generalized intuitionistic fuzzy filters on residuated lattices

Article type: Research Article

Authors: Liu, Lianzhen

Affiliations: School of Science, Jiangnan University, Wuxi, China

Note: [] Corresponding author. Lianzhen Liu, School of Science, Jiangnan University, 214122 Wuxi, China. Tel.: +86 18915328585; Fax: +86 051085910532; E-mail: zhen712000@126.com

Abstract: Filters play an important role in studying fuzzy logics. From logical point of view, filters correspond to sets of provable formulae. The aim of this paper is to solve two problems appeared in (α, β]-intuitionistic fuzzy filters of residuated lattices. Some characteristics of (α, β]-intuitionistic fuzzy filters ( (α, β]-intuitionistic fuzzy P-filters) are obtained. The relations among (α, β]-intuitionistic fuzzy filters, cut sets and s-upper cut sets are established. The “Extension property” and “Triple of equivalent characteristics” of (α, β]-intuitionistic fuzzy P-filters are also presented.

Keywords: Residuated lattice, intuitionistic fuzzy filter, P-filter, intuitionistic fuzzy P-filter

DOI: 10.3233/IFS-141437

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 4, pp. 1545-1552, 2015