Construction of some algebras of logic by using fuzzy ideals in mv-modules

M. Bakhshi; S. S. Ahn; Y. B. Jun; X. L. Xin; R. A. Borzooei

doi:10.3233/JIFS-221552

Construction of some algebras of logic by using fuzzy ideals in mv-modules

M. Bakhshi
, S. S. Ahn
, Y. B. Jun
, X. L. Xin
, R. A. Borzooei

Department of Mathematics Education

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

2 Scopus citations

Abstract

We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.

Original language	English
Pages (from-to)	4509-4519
Number of pages	11
Journal	Journal of Intelligent and Fuzzy Systems
Volume	44
Issue number	3
DOIs	https://doi.org/10.3233/JIFS-221552
State	Published - 2023

Keywords

distributive lattice
fuzzy A-ideal
fuzzy congruence
mv-module

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title = "Construction of some algebras of logic by using fuzzy ideals in mv-modules",

abstract = "We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.",

keywords = "distributive lattice, fuzzy A-ideal, fuzzy congruence, mv-module",

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T1 - Construction of some algebras of logic by using fuzzy ideals in mv-modules

AU - Bakhshi, M.

AU - Ahn, S. S.

AU - Jun, Y. B.

AU - Xin, X. L.

AU - Borzooei, R. A.

PY - 2023

Y1 - 2023

N2 - We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.

AB - We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.

KW - distributive lattice

KW - fuzzy A-ideal

KW - fuzzy congruence

KW - mv-module

UR - https://www.scopus.com/pages/publications/85161993968

U2 - 10.3233/JIFS-221552

DO - 10.3233/JIFS-221552

M3 - Article

AN - SCOPUS:85161993968

SN - 1064-1246

VL - 44

SP - 4509

EP - 4519

JO - Journal of Intelligent and Fuzzy Systems

JF - Journal of Intelligent and Fuzzy Systems

IS - 3

ER -

Construction of some algebras of logic by using fuzzy ideals in mv-modules

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Keywords

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