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Representation of the Minkowski metric as a fuzzy set

Abstract

This paper proposes a representation of the family of Minkowski distances using fuzzy sets. The proposed method helps to represent human-like perceptions about distances, which can help decision making in presence of non-probabilistic uncertainties such as imprecision and ambiguity. This way we propose to define a fuzzy set regarding the concept of closeness of two elements/sets measured by a Minkowski metric. Two application examples are presented, solved, and compared to some classical approaches. Finally some concluding remarks are provided and some interpretation issues are explained.

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Correspondence to Juan Carlos Figueroa-García.

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Figueroa-García, J.C., Melgarejo-Rey, M.A. & Hernández-Pérez, G. Representation of the Minkowski metric as a fuzzy set. Optim Lett 14, 395–408 (2020). https://doi.org/10.1007/s11590-018-1290-6

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Keywords

  • Minkowski distance
  • Fuzzy distance
  • Outlier detection