{"ok":true,"article":{"slug":"triangular-fuzzy-rescaling-distance-f0bb0b44","title":"Triangular Fuzzy Rescaling Distance","url":"https://arxiv.org/abs/2608.19234","canonical":"https://www.aimode.news/article/triangular-fuzzy-rescaling-distance-f0bb0b44","sourceName":"arXiv cs.LG","summary":"arXiv:2608.19234v1 Announce Type: new 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.","category":"AI","image":null,"lang":"en","publishedAt":"2026-08-21T04:00:00+00:00","createdAt":"2026-08-21T04:00:13.407173+00:00"}}