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

被引：108

作者：

Trutschnig, Wolfgang ^{[2
]}

Gonzalez-Rodriguez, Gil ^{[1
]}

Colubi, Ana ^{[3
]}

Angeles Gil, Maria ^{[3
]}

机构：

[1] European Ctr Soft Comp, Res Unit Intelligent Data Anal & Graph Models, Mieres 33600, Spain

[2] Vienna Univ Technol, Inst Stat & Probabil Theory, A-1040 Vienna, Austria

[3] Univ Oviedo, Dpto Estadist & IO & DM, Oviedo 33007, Spain

来源：

INFORMATION SCIENCES | 2009年 / 179卷 / 23期

关键词：

Distance; Generalized mid and spread; Convex compact sets; Imprecise data analysis; Fuzzy sets; Support functions; RANDOM-VARIABLES;

D O I：

10.1016/j.ins.2009.06.023

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

One of the most important aspects of the (statistical) analysis of imprecise data is the usage of a suitable distance on the family of ail 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. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：3964 / 3972

页数：9

共 22 条

[1] A generalized real-valued measure of the inequality associated with a fuzzy random variable [J].