An extension of the concept of distance as functions of several variables

English

Kiss, Gergely[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Marichal, Jean-Luc[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Teheux, Bruno[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Feb-2016

36th Linz Seminar on Fuzzy Set Theory (LINZ 2016) - Functional Equations and Inequalities

De Baets, Bernard

Mesiar, Radko

Saminger-Platz, Susanne

Klement, Erich Peter

53-56

Yes

No

International

36th Linz Seminar on Fuzzy Set Theory (LINZ 2016) - Functional Equations and Inequalities

from February 2 to February 6, 2016

Linz

Austria

[en] Extensions of the concept of distance to more than two elements have been recently proposed in the literature to measure to which extent the elements of a set are spread out. Such extensions may be particularly useful to define dispersion measures for instance in statistics or data analysis. In this note we provide and discuss an extension of the concept of distance, called n-distance, as functions of n variables. The key feature of this extension is a natural generalization of the triangle inequality. We also provide some examples of n-distances that involve geometric and graph theoretic constructions.