Distance Measures between the Interval-Valued Complex Fuzzy Sets

Songsong Dai, Lvqing Bi and Bo Hu
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Songsong Dai: School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, China
Lvqing Bi: 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
Bo Hu: School of Mechanical and Electrical Engineering, Guizhou Normal University , Guiyang 550025, China

Mathematics, 2019, vol. 7, issue 6, 1-12

Abstract: Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.

Keywords: Interval-valued complex fuzzy sets; distance measures; rotational invariance; reflectional invariance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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