On (∈, ∈ ∨ q)‐fuzzy filters of  R  0 ‐algebras | Zendy

Ma Xueling | Zendy; Zhan Jianming | Zendy; Jun Young B. | Zendy

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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)

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