∈γ∈γ∨qδintuitionistic FuzzySoft Filter of BLalgebras.pdf

Chin. Quart. J. of Math.
2014, 29 (1): 65—75
(∈γ, ∈γ∨qδ)-intuitionistic Fuzzy(Soft) Filter
of BL-algebras
YANG Yong-wei, XIN Xiao-long, HE Peng-fei
(Department of Mathematics, Northwest University, Xi’an 710127, China )
Abstract: In the paper, in order to further study the properties of filters of BL-algebras,
we propose the concepts of the (∈γ, ∈γ∨qδ)-intuitionistic fuzzy filters and (∈γ, ∈γ∨qδ)-
intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we
discuss the properties of images and inverse images of (∈γ, ∈γ∨qδ)-intuitionistic fuzzy soft
filters of BL-algebras.
Key words: BL-algebras; intuitionistic fuzzy sets; (∈γ, ∈γ∨qδ)-intuitionistic fuzzy filters;
soft sets
2000 MR Subject Classification: 03E72, 08A72
CLC number: O159 Document code: A
Article ID: 1002–0462 (2014) 01–0065–11
§1. Introduction
Since filter theory plays an important role in studying logic algebras, many researchers
combine it with mathematical approaches to discuss its generalized properties. Liu and Li[1]
applied the concept of fuzzy sets to filter theory and proposed the notions of fuzzy filters and
fuzzy prime filters in BL-algebras. Using the notions of membership and quasicoincidence of
fuzzy points related with fuzzy sets, Ma and Zhan[2] presented (∈, ∈∨q)-fuzzy filters in BL-
algebras. Farther more, Yin and Zhan[3] introduced (α, β)-fuzzy filters in BL-algebras where
[4]
α, β∈(∈γ, qδ, ∈γ∧qδ, ∈γ∨qδ) and α 6=∈γ∧qδ. Zhan and Jun applied the notion of soft sets
Received date: 2012-09-11
Foundation item: Supported by the Graduate Independent Innovation Foundation of Northwest Univer-
sity(YZZ12061)
Biographies: YANG Yong-wei(1984-), male, native of Shangqiu, Henan, a . candidate of Northwest
University, engages in fuzzy algebras, logic algebras; XIN Xiao-long(1955-), male, native of Xi’an, Shaanxi, a
professor of Northwest University, ., engages in logic algebras; HE Peng-fei(1986-), male, native of Xi’an,