待翻譯：Triangular Fuzzy Rescaling Distance

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--> [Submitted on 4 Aug 2026] Title:Triangular Fuzzy Rescaling Distance View a PDF of the paper titled Triangular Fuzzy Rescaling Distance, by Eddy Soria and 2 other authors View PDF Abstract:Decision-making in complex systems often involves dealing with imprecise or uncertain information, frequently represented using fuzzy sets, particularly Triangular Fuzzy Numbers (TFNs). A crucial aspect of many fuzzy methods is the quantification of distance between TFNs. Many distance measures assume that all values are in the same scale, requiring a preliminary normalization stage when applied to heterogeneous attributes with different scales or units. This paper proposes the Triangular Fuzzy Rescaling Distance (d_{TR}), a metric designed to address this challenge. The d_{TR} uniquely integrates Linear Rescaling (LRE) directly into the distance calculation, ensuring normalization during the comparison of fuzzy numbers. We formally prove that d_{TR} satisfies the properties of a metric, including non-negativity, identity, symmetry, and the triangle inequality. Furthermore, we demonstrate that d_{TR} is bounded, scale-invariant, and origin-invariant. These properties, combined with a weighting vector for prioritizing dimensions, make d_{TR} suitable for applications involving heterogeneous fuzzy data, such as the construction of synthetic indicators, distance-based machine learning algorithms or multicriteria-decision aiding. Comments: 12 pages, 2 tables Subjects: Machine Learning (cs.LG) Cite as: arXiv:2608.19234 [cs.LG] (or arXiv:2608.19234v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.19234 arXiv-issued DOI via DataCite Related DOI: https://doi.org/10.1007/978-3-032-00891-6_10 DOI(s) linking to related resources Submission history From: Eddy Soria [view email] [v1] Tue, 4 Aug 2026 20:20:13 UTC (369 KB) Full-text links: Access Paper: View a PDF of the paper titled Triangular Fuzzy Rescaling Distance, by Eddy Soria and 2 other authors View PDF view license Current browse context: cs.LG new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)