• Computer Science > Artificial Intelligence [Submitted on 18 Feb 2026] Title:An order-oriented approach to scoring hesitant fuzzy elements View PDF HTML (experimental)Abstract:Traditional scoring approaches on hesitant fuzzy sets often lack a formal base in order theory. • This paper proposes a unified framework, where each score is explicitly defined with respect to a given order. • This order-oriented perspective enables more flexible and coherent scoring mechanisms. • We examine several classical orders on hesitant fuzzy elements, that is, nonempty subsets in [0,1], and show that, contrary to prior claims, they do not induce lattice structures. • In contrast, we prove that the scores defined with respect to the symmetric order satisfy key normative criteria for scoring functions, including strong monotonicity with respect to unions and the Gärdenfors condition. • Following this analysis, we introduce a class of functions, called dominance functions, for ranking hesitant fuzzy elements.
Article Summaries:
- A recent AI paper proposes a new “order‑oriented” framework for scoring hesitant fuzzy sets-collections of non‑empty subsets of [0,1] that capture uncertainty. Unlike earlier methods that lacked a formal order basis, the authors define each score relative to a chosen order, allowing more flexible and coherent evaluations. They show that common orders on hesitant fuzzy elements do not form lattices, but the symmetric order satisfies key normative criteria, including strong monotonicity and the Gärdenfors condition. The paper also introduces dominance functions, such as discrete and relative dominance, to rank elements against control sets with acceptability thresholds, enabling the construction of fuzzy preference relations for group decision‑making.
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