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Some Examples of BL-Algebras Using Commutative Rings.
- Source :
-
Mathematics (2227-7390) . Dec2022, Vol. 10 Issue 24, p4739. 15p. - Publication Year :
- 2022
-
Abstract
- BL-algebras are algebraic structures corresponding to Hajek's basic fuzzy logic. The aim of this paper is to analyze the structure of BL-algebras using commutative rings. Due to computational considerations, we are interested in the finite case. We present new ways to generate finite BL-algebras using commutative rings and provide summarizing statistics. Furthermore, we investigated BL-rings, i.e., commutative rings whose the lattice of ideals can be equipped with a structure of BL-algebra. A new characterization for these rings and their connections to other classes of rings is established. Furthermore, we give examples of finite BL-rings for which the lattice of ideals is not an MV-algebra and, using these rings, we construct BL-algebras with 2 r + 1 elements, r ≥ 2 , and BL-chains with k elements, k ≥ 4. In addition, we provide an explicit construction of isomorphism classes of BL-algebras of small n size ( 2 ≤ n ≤ 5 ). [ABSTRACT FROM AUTHOR]
- Subjects :
- *FUZZY logic
*RESIDUATED lattices
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 24
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 161003074
- Full Text :
- https://doi.org/10.3390/math10244739