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Construction of some algebras of logic by using fuzzy ideals in MV-modules
- Authors
- Bakhshi, M.; Ahn, S. S.; Jun, Y. B.; Xin, X. L.; Borzooei, R. A.
- Issue Date
- Jan-2023
- Publisher
- IOS Press
- Keywords
- MV-module; fuzzy A-ideal; fuzzy congruence; distributive lattice
- Citation
- Journal of Intelligent and Fuzzy Systems, v.44, no.3, pp 4509 - 4519
- Pages
- 11
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Intelligent and Fuzzy Systems
- Volume
- 44
- Number
- 3
- Start Page
- 4509
- End Page
- 4519
- ISSN
- 1064-1246
1875-8967
- Abstract
- We study the lattice structure of fuzzy A-ideals in an MV-module M (Faid(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 Faid(M) can be embedded into the lattice of fuzzy congruences.
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