Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations

被引：60
|
作者：
Zeng, Wenyi [1 ]
Li, Hongxing
机构：
[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China
[2] Karolinska Inst, Dept Med Epidemiol & Biostat, SE-17177 Stockholm, Sweden
来源：
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS | 2006年 / 21卷 / 06期
关键词：
D O I：
10.1002/int.20152
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of fuzzy sets can be transformed by each other based on their axiomatic definitions, and propose some new formulas to calculate inclusion measures, similarity measures, and the fuzziness of fuzzy sets. These results can be applied in many fields, such as pattern recognition, image processing, fuzzy neural networks, fuzzy reasoning, and fuzzy control. (c) 2006 Wiley Periodicals, Inc.
引用
收藏
页码：639 / 653
页数：15
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