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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access A

Kernel fuzzy ideals and *-fuzzy congruences on pseudocomplemented almost distributive lattices

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pp. 459–478Vol. 26Issue 2March 2022DOI: 10.1080/09720529.2021.1959997 Crossmark XML
Received:
01 Jan 2021
Accepted:
05 May 2021
Published Online:
24 Feb 2022
Article type:
A
Language:
EN
Article no.:
JDMSC-1411
Pages:
459–478

Abstract

In this paper, we introduce the concept of *-fuzzy congruence relation on a pseudo-complemented almost distributive lattice and we provide a necessary and sufficient condition for a fuzzy congruence to be a *-fuzzy congruence. We also introduce the concept of kernel fuzzy ideals in terms of *-fuzzy congruence. Moreover, we give a set of equivalent condition for a fuzzy ideal to be a kernel fuzzy ideal. We show that every fuzzy filter of a pseudo-complemented ADL is a cokernel of some *-fuzzy congruence.

Keywords

Almost distributive lattice (ADL)Pseudo-complemented ADLKernel idealFuzzy idealFuzzy filterKernel fuzzy idealCokernel fuzzy filterFuzzy congruence relation

Subject Classifications

(2010) 06D7206F1508A72

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