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Some Remarks Regarding MTL and Divisible Residuated Algebras

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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)

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.

Suggested Citation

  • Cristina Flaut & Dana Piciu & Radu Vasile, 2025. "Some Remarks Regarding MTL and Divisible Residuated Algebras," Mathematics, MDPI, vol. 13(22), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:22:p:3697-:d:1797145
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