Building a class of fuzzy equivalence relations

被引：14

作者：

Foulloy, L ^{[1
]}

Benoit, E ^{[1
]}

机构：

[1] Univ Savoie, LISTIC, ESIA, F-74016 Annecy, France

来源：

FUZZY SETS AND SYSTEMS | 2006年 / 157卷 / 11期

关键词：

fuzzy equivalence relations; approximate equalities; strict t-norms; reflexivity; fuzzy meanings and descriptions; fuzzy partitions;

D O I：

10.1016/j.fss.2006.01.013

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we propose a practical method, given a strict triangular norm with a convex additive generator, for deriving a fuzzy equivalence relation whose reflexivity condition generalizes Ruspini's definition of fuzzy partitions. The properties of the relations, their comparison, their transitivity, the construction of fuzzy equivalence relations on cartesian products are presented. A large part of the paper is devoted to applications with fuzzy partitions defined on the real line. Several examples, including the fairy-tale problem from De Cock and Kerre [On (un)suitable fuzzy relations to model approximate equality, Fuzzy Sets and Systems 133 (2) (2003) 137-153), the comparison of colored objects and comfort situations are proposed. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：1417 / 1437

页数：21

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