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Distance Measures between the Interval-Valued Complex Fuzzy Sets

Author

Listed:
  • 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)

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.

Suggested Citation

  • Songsong Dai & Lvqing Bi & Bo Hu, 2019. "Distance Measures between the Interval-Valued Complex Fuzzy Sets," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:549-:d:240335
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    Citations

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    Cited by:

    1. Tahir Mahmood & Ubaid ur Rehman & Zeeshan Ali & Muhammad Aslam & Ronnason Chinram, 2022. "Identification and Classification of Aggregation Operators Using Bipolar Complex Fuzzy Settings and Their Application in Decision Support Systems," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    2. Tran Manh Tuan & Luong Thi Hong Lan & Shuo-Yan Chou & Tran Thi Ngan & Le Hoang Son & Nguyen Long Giang & Mumtaz Ali, 2020. "M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing," Mathematics, MDPI, vol. 8(5), pages 1-24, May.

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