Relationship between similarity measure and entropy of interval valued fuzzy sets

被引：275

作者：

Zeng, Wenyi ^{[1
]}

Li, Hongxing

机构：

[1] Beijing Normal Univ, Dept Math, Sch Math Sci, Beijing 100875, Peoples R China

[2] Karolinska Inst, Dept Med Epidemiol & Biostat, SE-17177 Stockholm, Sweden

来源：

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

基金：

中国国家自然科学基金;

关键词：

interval valued fuzzy set; fuzzy set; entropy; similarity measure;

D O I：

10.1016/j.fss.2005.11.020

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we introduce concepts of entropy of interval valued fuzzy set which is different from Bustince and Burillo [Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78 (1996) 305-316] and similarity measure of interval valued fuzzy sets, discuss their relationship between similarity measure and entropy of interval valued fuzzy sets in detail, prove three theorems that similarity measure and entropy of interval valued fuzzy sets can be transformed by each other based on their axiomatic definitions and put forward some formulas to calculate entropy and similarity measure of interval valued fuzzy sets. (C) 2005 Elsevier B.V. All rights reserved.

引用

页码：1477 / 1484

页数：8

共 21 条

[1]

Atanassov K. T., 1999, INTUITIONISTIC FUZZY

[2] INTUITIONISTIC FUZZY-SETS [J].

ATANASSOV, KT .

FUZZY SETS AND SYSTEMS, 1986, 20 (01) :87-96

[3] Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets [J].

Burillo, P ;

Bustince, H .

FUZZY SETS AND SYSTEMS, 1996, 78 (03) :305-316

[4] Vague sets are intuitionistic fuzzy sets [J].

Bustince, H ;

Burillo, P .

FUZZY SETS AND SYSTEMS, 1996, 79 (03) :403-405

[5]

Cross V.V., 2002, Similarity and Compatibility in Fuzzy Set Theory. Assessment and Applications

[6] DEFINITION OF NONPROBABILISTIC ENTROPY IN SETTING OF FUZZY SETS THEORY [J].

DELUCA, A ;

TERMINI, S .

INFORMATION AND CONTROL, 1972, 20 (04) :301-&

[7] On the relationship between some extensions of fuzzy set theory [J].

Deschrijver, G ;

Kerre, EE .

FUZZY SETS AND SYSTEMS, 2003, 133 (02) :227-235

[8] Distance measure and induced fuzzy entropy [J].

Fan, JL ;

Xie, WX .

FUZZY SETS AND SYSTEMS, 1999, 104 (02) :305-314

[9]

Gorzalczany B., 1983, P POLISH S INTERVAL, P89

[10] Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric [J].

Grzegorzewski, P .

FUZZY SETS AND SYSTEMS, 2004, 148 (02) :319-328

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