Construction of some algebras of logic by using fuzzy ideals in mv-modules-Reference-Cited by-同舟云学术

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

Published:2023-03-09 Issue:3 Volume:44 Page:4509-4519
ISSN:1064-1246
Container-title:Journal of Intelligent & Fuzzy Systems
language:
Short-container-title:IFS

Author:

Bakhshi M.¹,Ahn S. S.²,Jun Y. B.³,Xin X. L.⁴,Borzooei R. A.⁵

Affiliation:

1. Department of Mathematics, University of Bojnord, Bojnord, Iran

2. Department of Mathematics Education, Dongguk University, Seoul, Korea

3. Department of Mathematics Education, Gyeongsang National University, Jinju, Korea

4. Department of Mathematics, Northwest University, Xi’an, P.R. China

5. Department of Mathematics, Shahid Beheshti University of Tehran, Tehran, Iran

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.

Publisher

IOS Press

Subject

Artificial Intelligence,General Engineering,Statistics and Probability

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