International Journal of Computational Intelligence Systems

Volume 6, Issue 6, November 2013, Pages 1002 - 1011

IFI-ideals of lattice implication algebras

Authors
Hua Zhu, Jianbin Zhao, Yang Xu
Corresponding Author
Hua Zhu
Received 23 November 2012, Accepted 28 February 2013, Available Online 1 November 2013.
DOI
10.1080/18756891.2013.816024How to use a DOI?
Keywords
lattice implication algebra, ideals, –ideals, –ideals
Abstract

The notion of –ideal is introduced in lattice implication algebras. Firstly, the equivalent conditions of –ideals and –ideals are given in lattice implication algebras. Then the proposition of –ideal is investigated in lattice implication algebras. Next, the relations between –ideal and –ideal, between –ideal and –filter, between –ideal and fuzzy impilcative ideals, between –ideal and implicative ideals are discussed in lattice implication algebras. Moreover, the extension theorem of –ideals is obtained, and Ψ() which is composed of all –ideals constitutes a closure system. Finally, we prove that ∀α ∈ [01] = (µ ) is an –ideal of lattice implication algebra if and only if is a lattice implication algebra.

Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
6 - 6
Pages
1002 - 1011
Publication Date
2013/11/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.1080/18756891.2013.816024How to use a DOI?
Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Hua Zhu
AU  - Jianbin Zhao
AU  - Yang Xu
PY  - 2013
DA  - 2013/11/01
TI  - IFI-ideals of lattice implication algebras
JO  - International Journal of Computational Intelligence Systems
SP  - 1002
EP  - 1011
VL  - 6
IS  - 6
SN  - 1875-6883
UR  - https://doi.org/10.1080/18756891.2013.816024
DO  - 10.1080/18756891.2013.816024
ID  - Zhu2013
ER  -