Fuzzy Equivalence on Standard and Rough Neutrosophic Sets and Applications to Clustering Analysis

  • Nguyen Xuan Thao
  • Le Hoang Son
  • Bui Cong Cuong
  • Mumtaz Ali
  • Luong Hong Lan
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 672)


In this paper, we propose the concept of fuzzy equivalence on standard neutrosophic sets and rough standard neutrosophic sets. We also provide some formulas for fuzzy equivalence on standard neutrosophic sets and rough standard neutrosophic sets. We also apply these formulas for cluster analysis. Numerical examples are illustrated.


Fuzzy equivalence Neutrosophic set Rough set Rough neutrosophic set Fuzzy clustering 



This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.01-2017.02.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Nguyen Xuan Thao
    • 1
  • Le Hoang Son
    • 2
  • Bui Cong Cuong
    • 3
  • Mumtaz Ali
    • 4
  • Luong Hong Lan
    • 5
  1. 1.Vietnam National University of AgricultureHanoiVietnam
  2. 2.VNU University of Science, Vietnam National UniversityHanoiVietnam
  3. 3.Institute of MathematicsHanoiVietnam
  4. 4.University of Southern Queensland, Springfield CampusQueenslandAustralia
  5. 5.Thai Nguyen University of EducationThai NguyenVietnam

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