Author:
Flaut Cristina,Piciu Dana
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 2r+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).
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference18 articles.
1. Abstract residuation over lattices;Dilworth;Bull. Am. Math. Soc.,1938
2. Residuated lattices;Ward;Trans. Am. Math. Soc.,1939
3. Ideal lattices and the structure of rings;Blair;Trans. Am. Math. Soc.,1953
4. Commutative rings whose ideals form an MV-algebra;Belluce;Math. Log. Quart.,2009
5. BL-rings;Lele;Log. J. IGPL,2016
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Remarks regarding some Algebras of Logic;Journal of Intelligent & Fuzzy Systems;2023-11-04