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On (∈, ∈ ∨ q)‐fuzzy filters of R 0 ‐algebras
Author(s) -
Ma Xueling,
Zhan Jianming,
Jun Young B.
Publication year - 2009
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200810022
Subject(s) - mathematics , fuzzy logic , filter (signal processing) , characterization (materials science) , fuzzy set , discrete mathematics , algebra over a field , boolean algebra , pure mathematics , computer science , artificial intelligence , materials science , computer vision , nanotechnology
In this paper, we introduce the notions of (∈, ∈ ∨ q)‐fuzzy filters and (∈, ∈ ∨ q)‐fuzzy Boolean (implicative) filters in R 0 ‐algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R 0 ‐algebras is an (∈, ∈ ∨ q)‐fuzzy Boolean filter if and only if it is an (∈, ∈ ∨ q)‐fuzzy implicative filter. Finally, we consider the concepts of implication‐based fuzzy Boolean (implicative) filters of R 0 ‐algebras (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)