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Mathematics 2019, 7(1), 96; https://doi.org/10.3390/math7010096

Two Classes of Entropy Measures for Complex Fuzzy Sets

1,2,†
,
1,†
,
2,3
and
2,*
1
School of Physics and Telecommunication Engineering, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China
2
College of Electronic Science and Technology, Xiamen University, Xiamen 361005, China
3
School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 19 December 2018 / Revised: 15 January 2019 / Accepted: 15 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue Fuzziness and Mathematical Logic)
Full-Text   |   PDF [1531 KB, uploaded 17 January 2019]   |  

Abstract

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. View Full-Text
Keywords: complex fuzzy sets; entropy; rotational invariance complex fuzzy sets; entropy; rotational invariance
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Bi, L.; Zeng, Z.; Hu, B.; Dai, S. Two Classes of Entropy Measures for Complex Fuzzy Sets. Mathematics 2019, 7, 96.

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