Two Classes of Entropy Measures for Complex Fuzzy Sets

Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy meas...

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Main Authors:	Lvqing Bi, Zhiqiang Zeng, Bo Hu, Songsong Dai
Format:	Article
Language:	English
Published:	MDPI AG 2019-01-01
Series:	Mathematics
Subjects:	complex fuzzy sets entropy rotational invariance
Online Access:	http://www.mdpi.com/2227-7390/7/1/96

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record_format	Article
spelling	doaj-9ee8c93a523b46ecaf7e8a633a69bd912020-11-25T00:21:44ZengMDPI AGMathematics2227-73902019-01-01719610.3390/math7010096math7010096Two Classes of Entropy Measures for Complex Fuzzy SetsLvqing Bi0Zhiqiang Zeng1Bo Hu2Songsong Dai3School of Physics and Telecommunication Engineering, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, ChinaSchool of Physics and Telecommunication Engineering, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, ChinaCollege of Electronic Science and Technology, Xiamen University, Xiamen 361005, ChinaCollege of Electronic Science and Technology, Xiamen University, Xiamen 361005, ChinaComplex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.http://www.mdpi.com/2227-7390/7/1/96complex fuzzy setsentropyrotational invariance
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Lvqing Bi Zhiqiang Zeng Bo Hu Songsong Dai
spellingShingle	Lvqing Bi Zhiqiang Zeng Bo Hu Songsong Dai Two Classes of Entropy Measures for Complex Fuzzy Sets Mathematics complex fuzzy sets entropy rotational invariance
author_facet	Lvqing Bi Zhiqiang Zeng Bo Hu Songsong Dai
author_sort	Lvqing Bi
title	Two Classes of Entropy Measures for Complex Fuzzy Sets
title_short	Two Classes of Entropy Measures for Complex Fuzzy Sets
title_full	Two Classes of Entropy Measures for Complex Fuzzy Sets
title_fullStr	Two Classes of Entropy Measures for Complex Fuzzy Sets
title_full_unstemmed	Two Classes of Entropy Measures for Complex Fuzzy Sets
title_sort	two classes of entropy measures for complex fuzzy sets
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-01-01
description	Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.
topic	complex fuzzy sets entropy rotational invariance
url	http://www.mdpi.com/2227-7390/7/1/96
work_keys_str_mv	AT lvqingbi twoclassesofentropymeasuresforcomplexfuzzysets AT zhiqiangzeng twoclassesofentropymeasuresforcomplexfuzzysets AT bohu twoclassesofentropymeasuresforcomplexfuzzysets AT songsongdai twoclassesofentropymeasuresforcomplexfuzzysets
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Two Classes of Entropy Measures for Complex Fuzzy Sets

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