A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread

  • Authors:

  • Wolfgang Trutschnig;Gil González-Rodríguez;Ana Colubi;María Ángeles Gil

  • Affiliations:

  • Institute for Statistics and Probability Theory, Vienna University of Technology, A-1040 Vienna, Austria;Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing, 33600 Mieres, Spain;Dpto. de Estadística e I.O. y D.M., Universidad de Oviedo, 33007 Oviedo, Spain;Dpto. de Estadística e I.O. y D.M., Universidad de Oviedo, 33007 Oviedo, Spain

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

One of the most important aspects of the (statistical) analysis of imprecise data is the usage of a suitable distance on the family of all compact, convex fuzzy sets, which is not too hard to calculate and which reflects the intuitive meaning of fuzzy sets. On the basis of expressing the metric of Bertoluzza et al. [C. Bertoluzza, N. Corral, A. Salas, On a new class of distances between fuzzy numbers, Mathware Soft Comput. 2 (1995) 71-84] in terms of the mid points and spreads of the corresponding intervals we construct new families of metrics on the family of all d-dimensional compact convex sets as well as on the family of all d-dimensional compact convex fuzzy sets. It is shown that these metrics not only fulfill many good properties, but also that they are easy to calculate and easy to manage for statistical purposes, and therefore, useful from the practical point of view.