Transitivity-preserving fuzzification schemes for cardinality-based similarity measures

被引：36
作者：
De Baets, B
De Meyer, H
机构：
[1] Univ Ghent, Dept Appl Math, B-9000 Ghent, Belgium
[2] Univ Ghent, Dept Appl Math & Comp Sci, B-9000 Ghent, Belgium
来源：
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH | 2005年 / 160卷 / 03期
关键词：
similarity measure; fuzzy similarity measure; reflexivity; transitivity; triangular norm; frank t-norm;
D O I：
10.1016/j.ejor.2003.06.036
中图分类号：
C93 [管理学];
学科分类号：
12 ; 1201 ; 1202 ; 120202 ;
摘要：
A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. The family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets. In particular, the fuzzy set intersections are pointwisely generated by Frank t-norms. The fuzzification schemes are applied to a variety of previously studied rational cardinality-based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process. (C) 2003 Elsevier B.V. All rights reserved.
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收藏
页码：726 / 740
页数：15
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