Distance Measures between the Interval-Valued Complex Fuzzy Sets

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-06, Vol.7 (6), p.549
Main Authors: Dai, Songsong, Bi, Lvqing, Hu, Bo
Format: Article
Language:English
Subjects:
Amplitudes
Complex numbers
Decision making
Distance measurement
distance measures
Euclidean geometry
Fuzzy sets
Interval-valued complex fuzzy sets
Invariance
Mathematics
Real numbers
reflectional invariance
rotational invariance
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7060549