Characterizing idempotent uninorms on a bounded chain

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

doi:10.22111/ijfs.2026.10011

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	Characterizing idempotent uninorms on a bounded chain
Iranian Journal of Fuzzy Systems
دوره 23، شماره 4، مهر و آبان 2026، صفحه 69-74 اصل مقاله (347.14 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2026.10011
نویسندگان
Y. Su¹؛ W. Zong²؛ R. Mesiar^* ³^{، 4}
¹School of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China
²School of Mathematical Sciences, University of Jinan, Jinan, 250022, China
³Palack´y University Olomouc, Faculty of Science, Department of Algebra and Geometry, 17. listopadu 12, Olomouc, 771 46, Czech Republic
⁴Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinsk´eho 11, 810 05 Bratislava Slovakia
چکیده
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.
کلیدواژه‌ها
Aggregation operation؛ idempotent uninorm؛ bounded chain؛ Dedekind completion

مراجع
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Characterizing idempotent uninorms on a bounded chain