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[2602.16827] An order-oriented approach to scoring hesitant fuzzy elements
Summary
This article presents a novel order-oriented approach to scoring hesitant fuzzy elements, proposing a unified framework that enhances scoring mechanisms through order theory.
Why It Matters
The research addresses limitations in traditional scoring methods for hesitant fuzzy sets, providing a more coherent and flexible framework. This has implications for decision-making processes in AI, particularly in scenarios involving uncertainty and ambiguity.
Key Takeaways
- Introduces an order-oriented framework for scoring hesitant fuzzy elements.
- Demonstrates that classical orders do not induce lattice structures as previously claimed.
- Establishes dominance functions for ranking hesitant fuzzy elements relative to control sets.
- Provides concrete examples of dominance functions applicable in group decision-making.
- Satisfies key normative criteria for scoring functions, enhancing their reliability.
Computer Science > Artificial Intelligence arXiv:2602.16827 (cs) [Submitted on 18 Feb 2026] Title:An order-oriented approach to scoring hesitant fuzzy elements Authors:Luis Merino, Gabriel Navarro, Carlos Salvatierra, Evangelina Santos View a PDF of the paper titled An order-oriented approach to scoring hesitant fuzzy elements, by Luis Merino and 2 other authors 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. They aim to compare hesitant fuzzy elements relative to control sets incorporating minimum acceptability thresholds. Two concrete examples of dominance functions for finite sets are provided: the discrete dominance function and the relative dominance function. We show that th...
