Complete meet-continuous codomain lattice and extremal solutions of L-valued fuzzy relation equations

Vanja Stepanović1, Andreja Tепavčević2,3

  1. Faculty of Agriculture, University of Belgrade
    Nemanjina 6, 11080 Beograd
    vanja@agrif.bg.ac.rs
  2. Mathematical Institute of Serbian Academy of Sciences and Arts
    Kneza Mihaila 36, 11000 Beograd
  3. Faculty of Sciences, University of Novi Sad
    Trg Dositeja Obradovića 4, 21000 Novi Sad
    andreja@dmi.uns.ac.rs (corresponding author)

Abstract

We prove the existence of a maximal solution to any lattice-valued fuzzy relational equation, inequation, or system, in which infimum, supremum, and the standard composition are used. This result holds under the assumption that, in the codomain lattice, the infimum operation commutes with suprema of chains. To establish this result, we first recall and extend several lattice-theoretic properties under the assumption of meet-continuity. In particular, we recall that meet-continuity of the codomain lattice ensures composition-continuity in the lattice of L-valued relations. Building on these properties, we introduce algorithms for constructing the least solution to a broad class of equations and inequations, and prove that these algorithms terminate after at most countably many steps.

Key words

Meet-Continuity, Lattice-Valued Relations, Relational Equations, Relational Inequations

Digital Object Identifier (DOI)

https://doi.org/10.2298/CSIS251214033S

Publication information

Volume 23, Issue 4 (September 2026)
Year of Publication: 2026
ISSN: 2406-1018 (Online)
Publisher: ComSIS Consortium

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How to cite

Stepanović, V., Tepavčević, A.: Complete meet-continuous codomain lattice and extremal solutions of L-valued fuzzy relation equations. Computer Science and Information Systems, 23(4) (2026). https://doi.org/10.2298/CSIS251214033S