Characterizing idempotent uninorms on a bounded chain

Su, Y.; Zong, W.; Mesiar, R.

doi:10.22111/ijfs.2026.10011

Document Type : Research Paper

Authors

¹ School of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China

² School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

³ Palack´y University Olomouc, Faculty of Science, Department of Algebra and Geometry, 17. listopadu 12, Olomouc, 771 46, Czech Republic

⁴ Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinsk´eho 11, 810 05 Bratislava Slovakia

https://doi.org/10.22111/ijfs.2026.10011

Abstract

Completeness is essential for characterizing idempotent uninorms on complete chains, as it guarantees the welldefinedness of their corresponding characterization functions. In the case of a general chain, one cannot define the
aforementioned characterization functions by taking the supremum or infimum of a prescribed subset. When constructing
the real numbers via the Dedekind completion of the rationals, each rational number is associated with a
rational cut, which forms a down-set. Inspired by this line of reasoning, this paper provides a direct characterization
of idempotent uninorms defined on bounded chains via decreasing symmetric set-valued functions that map the chain
to its family of down-sets.

Keywords

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Iranian Journal of Fuzzy Systems

Characterizing idempotent uninorms on a bounded chain

References

References

Volume 23, Issue 4
July and August 2026
Pages 69-74

Characterizing idempotent uninorms on a bounded chain

References

References

Volume 23, Issue 4July and August 2026Pages 69-74

Volume 23, Issue 4
July and August 2026
Pages 69-74