The entropy change in extension principle

Wen June Wang; Chih Hui Chiu

doi:10.1016/S0165-0114(97)00162-0

The entropy change in extension principle

Wen June Wang, Chih Hui Chiu

Department of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

There is a continuous function which is one-to-one mapping from the support of the original fuzzy set into the support of the image fuzzy set. With the aid of the extension principle, this paper investigates the entropy relationship between the original fuzzy set and image fuzzy set. We also derive some useful formulas by which the entropy of the image fuzzy set can be obtained directly without calculating its membership function.

Original language	English
Pages (from-to)	153-162
Number of pages	10
Journal	Fuzzy Sets and Systems
Volume	103
Issue number	1
DOIs	https://doi.org/10.1016/S0165-0114(97)00162-0
State	Published - 1 Apr 1999

Keywords

Entropy
Extension principle
Measures of fuzziness
Membership functions

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10.1016/S0165-0114(97)00162-0

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abstract = "There is a continuous function which is one-to-one mapping from the support of the original fuzzy set into the support of the image fuzzy set. With the aid of the extension principle, this paper investigates the entropy relationship between the original fuzzy set and image fuzzy set. We also derive some useful formulas by which the entropy of the image fuzzy set can be obtained directly without calculating its membership function.",

keywords = "Entropy, Extension principle, Measures of fuzziness, Membership functions",

author = "Wang, {Wen June} and Chiu, {Chih Hui}",

note = "Funding Information: * Corresponding author. Fax: + 886-3-425-5830; e-mail: [email protected]. 1T his work was supported by the National Science Council of Taiwan, ROC under the Grant NSC 85-2213-E008-019.",

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AU - Chiu, Chih Hui

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N2 - There is a continuous function which is one-to-one mapping from the support of the original fuzzy set into the support of the image fuzzy set. With the aid of the extension principle, this paper investigates the entropy relationship between the original fuzzy set and image fuzzy set. We also derive some useful formulas by which the entropy of the image fuzzy set can be obtained directly without calculating its membership function.

AB - There is a continuous function which is one-to-one mapping from the support of the original fuzzy set into the support of the image fuzzy set. With the aid of the extension principle, this paper investigates the entropy relationship between the original fuzzy set and image fuzzy set. We also derive some useful formulas by which the entropy of the image fuzzy set can be obtained directly without calculating its membership function.

KW - Entropy

KW - Extension principle

KW - Measures of fuzziness

KW - Membership functions

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DO - 10.1016/S0165-0114(97)00162-0

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SN - 0165-0114

VL - 103

SP - 153

EP - 162

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 1

ER -

The entropy change in extension principle

Abstract

Keywords

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