Fuzzy congruences and ideals on basic algebras

Jing Wang; Qiuyan Zhan; Yichuan Yang

doi:10.1007/s00500-026-11294-y

Fuzzy congruences and ideals on basic algebras

Jing Wang
, Qiuyan Zhan
, Yichuan Yang^*

^*Corresponding author for this work

School of Mathematical Sciences

Qilu University of Technology
Shanghai Maritime University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that fuzzy ideal lattices and fuzzy congruence lattices on basic algebras are not one–one correspondent in the sense of Murali. Then we define fuzzy (weak, respectively) congruence relations on basic algebras in a new way, which guarantees the one–one correspondence between fuzzy (weak, respectively) ideal lattices and fuzzy (weak, respectively) congruence lattices on basic algebras.

Original language	English
Journal	Soft Computing
DOIs	https://doi.org/10.1007/s00500-026-11294-y
State	Accepted/In press - 2026

Keywords

Basic algebras
Fuzzy congruence relations
Fuzzy ideals
MV-algebras

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10.1007/s00500-026-11294-y

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title = "Fuzzy congruences and ideals on basic algebras",

abstract = "We show that fuzzy ideal lattices and fuzzy congruence lattices on basic algebras are not one–one correspondent in the sense of Murali. Then we define fuzzy (weak, respectively) congruence relations on basic algebras in a new way, which guarantees the one–one correspondence between fuzzy (weak, respectively) ideal lattices and fuzzy (weak, respectively) congruence lattices on basic algebras.",

keywords = "Basic algebras, Fuzzy congruence relations, Fuzzy ideals, MV-algebras",

author = "Jing Wang and Qiuyan Zhan and Yichuan Yang",

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AU - Wang, Jing

AU - Zhan, Qiuyan

AU - Yang, Yichuan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2026.

PY - 2026

Y1 - 2026

N2 - We show that fuzzy ideal lattices and fuzzy congruence lattices on basic algebras are not one–one correspondent in the sense of Murali. Then we define fuzzy (weak, respectively) congruence relations on basic algebras in a new way, which guarantees the one–one correspondence between fuzzy (weak, respectively) ideal lattices and fuzzy (weak, respectively) congruence lattices on basic algebras.

AB - We show that fuzzy ideal lattices and fuzzy congruence lattices on basic algebras are not one–one correspondent in the sense of Murali. Then we define fuzzy (weak, respectively) congruence relations on basic algebras in a new way, which guarantees the one–one correspondence between fuzzy (weak, respectively) ideal lattices and fuzzy (weak, respectively) congruence lattices on basic algebras.

KW - Basic algebras

KW - Fuzzy congruence relations

KW - Fuzzy ideals

KW - MV-algebras

UR - https://www.scopus.com/pages/publications/105031621414

U2 - 10.1007/s00500-026-11294-y

DO - 10.1007/s00500-026-11294-y

M3 - 文章

AN - SCOPUS:105031621414

SN - 1432-7643

JO - Soft Computing

JF - Soft Computing

ER -

Fuzzy congruences and ideals on basic algebras

Abstract

Keywords

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