Some Remarks Regarding MTL and Divisible Residuated Algebras

Cristina Flaut (), Dana Piciu and Radu Vasile
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Cristina Flaut: Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527 Constanta, Romania
Dana Piciu: Faculty of Science, University of Craiova, A.I. Cuza Street, 13, 200585 Craiova, Romania
Radu Vasile: Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527 Constanta, Romania

Mathematics, 2025, vol. 13, issue 22, 1-22

Abstract: Divisible residuated lattices and MTL algebras are algebraic structures connected with algebras in t-norm-based fuzzy logics, being examples of residuated lattices. They are an important topic in the study of fuzzy logic. The purpose of this paper is to investigate and give classifications of these types of algebras. From computational considerations, we analyze the structure of these residuated lattices of small size n (2 ≤ n ≤ 5), and we give summarizing statistics. To extend these results to higher sizes, we used a computer and a constructive algorithm for generating all finite residuated lattices.

Keywords: (divisible) residuated lattice; MTL algebra; ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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