IFI-ideals of lattice implication algebras

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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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  -