An order-oriented approach to scoring hesitant fuzzy elements

• URL: http://arxiv.org/abs/2602.16827v1
• Date: Wed, 18 Feb 2026 19:48:37 GMT
• Title: An order-oriented approach to scoring hesitant fuzzy elements
• Abstract summary: This paper proposes a unified framework, where each score is explicitly defined with respect to a given order.<n>We introduce a class of functions, called dominance functions, for ranking hesitant fuzzy elements.<n>We show that these can be employed to construct fuzzy preference relations on typical hesitant fuzzy sets and support group decision-making.
• Score: 4.991981804514581
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 these can be employed to construct fuzzy preference relations on typical hesitant fuzzy sets and support group decision-making.

Related papers

• Byzantine Accountability Without Consensus: Strong Eventual Consistency for Non-Associative, Stochastic, Robust Aggregation [0.0]
  ACFA replicates a content-addressed OR-Set of signed contributions and a grow-only set of self-authenticating equivocation proofs.<n>A prototype (10 nodes, 3 Byzantine) passes 16/16 falsification checks.
  arXiv  Detail & Related papers  (2026-07-11T13:23:06Z)
• Comparing Scalar Objective Functions for Multi-Criteria Engineering Optimization [0.0]
  This paper compares four formulations for normalized bi-criteria minimization: weighted sums, achievement scalarizing functions, desirability functions, and a fuzzy-logic-based formulation.<n>Two analytically defined Pareto fronts, one convex and one concave, isolate the effect of the objective formulation from numerical behavior.<n>Results show that weighted sums are simple but structurally limited on concave fronts, while achievement, desirability, and fuzzy formulations reach interior non-supported regions through different mechanisms.
  arXiv  Detail & Related papers  (2026-06-26T18:51:16Z)
• Deep Reasoning in General Purpose Agents via Structured Meta-Cognition [58.185853639335896]
  We introduce an inference-time approach for constructing task-specific scaffolds through structured meta-reasoning.<n>We instantiate this approach in a general-purpose agent that distributes complex tasks across more controlled reasoning threads.
  arXiv  Detail & Related papers  (2026-05-12T01:21:37Z)
• A low order Bargmann invariant hierarchy for set coherence [5.255419607027447]
  Set coherence is a basis-independent form of quantum coherence.<n>We show that fourth-order, ordering-sensitive Bargmann invariants give the first universal pairwise criterion for set coherence.
  arXiv  Detail & Related papers  (2026-05-11T05:28:15Z)
• Deconfounding Scores and Representation Learning for Causal Effect Estimation with Weak Overlap [75.41420283374737]
  Overlap is a key condition for causal treatment effect estimation.<n>We propose a class of feature representations called deconfounding scores.<n>We show that prognostic scores are overlap-optimal within this class.
  arXiv  Detail & Related papers  (2026-04-01T12:19:42Z)
• Structured Prediction with Abstention via the Lovász Hinge [0.24578723416255752]
  We show that the Lov'asz hinge is inconsistent with its desired target unless the set function used for evaluation is modular.<n>We show that one can combine the binary encoding construction of Ramaswamy et al. with our link construction to achieve an efficient consistent surrogate for a natural multiclass of the structured abstain problem.
  arXiv  Detail & Related papers  (2025-05-09T21:29:22Z)
• A Canonicalization Perspective on Invariant and Equivariant Learning [54.44572887716977]
  We introduce a canonicalization perspective that provides an essential and complete view of the design of frames. We show that there exists an inherent connection between frames and canonical forms. We design novel frames for eigenvectors that are strictly superior to existing methods.
  arXiv  Detail & Related papers  (2024-05-28T17:22:15Z)
• Exploiting hidden structures in non-convex games for convergence to Nash equilibrium [62.88214569402201]
  A wide array of modern machine learning applications can be formulated as non-cooperative Nashlibria. We provide explicit convergence guarantees for both deterministic and deterministic environments.
  arXiv  Detail & Related papers  (2023-12-27T15:21:25Z)
• Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets [24.890815871172745]
  Hesitant fuzzy sets find extensive application in specific scenarios involving uncertainty and hesitation.<n>As a type of sets, hesitant fuzzy sets necessitate a clear and explicit definition of the inclusion relationship.
  arXiv  Detail & Related papers  (2023-11-07T14:03:28Z)
• When Does Confidence-Based Cascade Deferral Suffice? [69.28314307469381]
  Cascades are a classical strategy to enable inference cost to vary adaptively across samples. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. Despite being oblivious to the structure of the cascade, confidence-based deferral often works remarkably well in practice.
  arXiv  Detail & Related papers  (2023-07-06T04:13:57Z)
• HiPerformer: Hierarchically Permutation-Equivariant Transformer for Time Series Forecasting [56.95572957863576]
  We propose a hierarchically permutation-equivariant model that considers both the relationship among components in the same group and the relationship among groups. The experiments conducted on real-world data demonstrate that the proposed method outperforms existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-05-14T05:11:52Z)
• Unifying Causal Inference and Reinforcement Learning using Higher-Order Category Theory [4.119151469153588]
  We present a unified formalism for structure discovery of causal models and predictive state representation models in reinforcement learning. Specifically, we model structure discovery in both settings using simplicial objects.
  arXiv  Detail & Related papers  (2022-09-13T19:04:18Z)
• Lattice Generalizations of the Concept of Fuzzy Numbers and Zadeh's Extension Principle [0.0]
  The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements. The use of partially ordered values in cognitive maps with comparison of expert assessments is considered.
  arXiv  Detail & Related papers  (2022-08-12T11:32:33Z)
• Topological and Algebraic Structures of the Space of Atanassov's Intuitionistic Fuzzy Values [8.518591988944358]
  We show that the space of intuitionistic fuzzy values (IFVs) with the linear order based on a score function and an accuracy function has the same algebraic structure as the one induced by the linear order based on a similarity function and an accuracy function. By introducing a new operator for IFVs via the linear order based on a score function and an accuracy function, we present that such an operator is a strong negation on IFVs.
  arXiv  Detail & Related papers  (2021-11-17T06:43:02Z)
• Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap [140.98628848491146]
  We introduce deconfounding scores, which induce better overlap without biasing the target of estimation. We show that deconfounding scores satisfy a zero-covariance condition that is identifiable in observed data. In particular, we show that this technique could be an attractive alternative to standard regularizations.
  arXiv  Detail & Related papers  (2021-04-12T18:50:11Z)
• GroupifyVAE: from Group-based Definition to VAE-based Unsupervised Representation Disentanglement [91.9003001845855]
  VAE-based unsupervised disentanglement can not be achieved without introducing other inductive bias. We address VAE-based unsupervised disentanglement by leveraging the constraints derived from the Group Theory based definition as the non-probabilistic inductive bias. We train 1800 models covering the most prominent VAE-based models on five datasets to verify the effectiveness of our method.
  arXiv  Detail & Related papers  (2021-02-20T09:49:51Z)
• Infinite Feature Selection: A Graph-based Feature Filtering Approach [78.63188057505012]
  We propose a filtering feature selection framework that considers subsets of features as paths in a graph. Going to infinite allows to constrain the computational complexity of the selection process. We show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori.
  arXiv  Detail & Related papers  (2020-06-15T07:20:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.