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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)

Abstract

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.

Keywords

Fuzzy equivalence Neutrosophic set Rough set Rough neutrosophic set Fuzzy clustering 

Notes

Acknowledgements

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

References

  1. 1.
    Smarandache, F.: Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.gallup.unm.edu/eBook-neutrosophics6.pdf(last edition online).
  2. 2.
    Zadeh, L. A.: Fuzzy Sets. Information and Control 8(3) (1965) 338–353.Google Scholar
  3. 3.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Fuzzy set and systems 20 (1986) 87–96.Google Scholar
  4. 4.
    Wang, H., Smarandache, F., Zhang, Y.Q. et al: Interval NeutrosophicSets and Logic: Theory and Applications in Computing. Hexis, Phoenix, AZ (2005).Google Scholar
  5. 5.
    Wang, H.,Smarandache, F., Zhang, Y.Q.,et al., Single Valued NeutrosophicSets. Multispace and Multistructure 4 (2010) 410–413.Google Scholar
  6. 6.
    Ye, J.: A Multi criteria Decision-Making Method Using Aggregation Operators for Simplified Neutrosophic Sets. Journal of Intelligent & Fuzzy Systems 26 (2014) 2459–2466.Google Scholar
  7. 7.
    Cuong, B.C.: Picture Fuzzy Sets. Journal of Computer Science and Cybernetics 30(4) (2014) 409–420.Google Scholar
  8. 8.
    Cuong, B.C., Son, L.H., Chau, H.T.M.: Some Context Fuzzy Clustering Methods for Classification Problems. Proceedings of the 1st International Symposium on Information and Communication Technology (2010) 34–40.Google Scholar
  9. 9.
    Son, L.H., Thong, P.H.: Some Novel Hybrid Forecast Methods Based On Picture Fuzzy Clustering for Weather Nowcasting from Satellite Image Sequences. Applied Intelligence 46 (1) (2017) 1–15.Google Scholar
  10. 10.
    Son, L.H., Tuan, T.M.: A cooperative semi-supervised fuzzy clustering framework for dental X-ray image segmentation. Expert Systems With Applications 46 (2016) 380–393.Google Scholar
  11. 11.
    Son, L.H., Viet, P.V., Hai, P.V.: Picture Inference System: A New Fuzzy Inference System on Picture Fuzzy Set. Applied Intelligence (2017) https://doi.org/10.1007/s10489-016-0856-1.
  12. 12.
    Son, L.H.: A Novel Kernel Fuzzy Clustering Algorithm for Geo-Demographic Analysis. Information Sciences 317 (2015) 202–223.Google Scholar
  13. 13.
    Son, L.H.: Generalized Picture Distance Measure and Applications to Picture Fuzzy Clustering. Applied Soft Computing 46 (2016) 284–295.Google Scholar
  14. 14.
    Son, L.H.: Measuring Analogousness in Picture Fuzzy Sets: From Picture Distance Measures to Picture Association Measures. Fuzzy Optimization and Decision Making (2017) https://doi.org/10.1007/s10700-016-9249-5.
  15. 15.
    Son, L.H.: DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets. Expert systems with applications 42 (2015) 51–66.Google Scholar
  16. 16.
    Thong, P.H., Son, L.H., Fujita, H.: Interpolative Picture Fuzzy Rules: A Novel Forecast Method for Weather Nowcasting. Proceeding of the 2016 IEEE International Conference on Fuzzy Systems (2016) 86–93.Google Scholar
  17. 17.
    Thong, P.H., Son, L.H.: A Novel Automatic Picture Fuzzy Clustering Method Based On Particle Swarm Optimization and Picture Composite Cardinality. Knowledge-Based Systems 109 (2016) 48–60.Google Scholar
  18. 18.
    Thong, P.H., Son, L.H.: Picture Fuzzy Clustering for Complex Data. Engineering Applications of Artificial Intelligence 56 (2016) 121–130.Google Scholar
  19. 19.
    Thong, P.H., Son, L.H.: Picture Fuzzy Clustering: A New Computational Intelligence Method. Soft Computing 20(9) (2016) 3544–3562.Google Scholar
  20. 20.
    Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11 (5) (1982) 341–356.Google Scholar
  21. 21.
    Fodor, J., Yager, R. R.: Fuzzy Set Theoretic Operations and Quantifers. Fundermentals of Fuzzy Sets. Klwuer (2000).Google Scholar
  22. 22.
    Dubois, D., Prade, H.: Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems 17 (1990) 191–209.Google Scholar
  23. 23.
    Yao, Y.Y: Combination of Rough and Fuzzy Sets Based on \( \alpha - \) level sets. Rough sets and Data mining: analysis for imprecise data. Kluwer Academic Publisher, Boston (1997) 301–321.Google Scholar
  24. 24.
    Broumi, S. and Smarandache, F.: Rough neutrosophic sets. Italian Journal of Pure and Applied Mathematics, N.32, (2014) 493–502.Google Scholar
  25. 25.
    Broumi, S. and Smarandache, F.: Lower and upper soft interval valued neutrosophic rough approximations of an IVNSS-relation, Sisom& Acoustics, (2014) 8 pages.Google Scholar
  26. 26.
    Broumi, S. and Smarandache, F.: Interval–Valued Neutrosophic Soft Rough Set, International Journal of Computational Mathematics. Volume 2015 (2015), Article ID 232919, 13 pages http://dx.doi.org/10.1155/2015/232919.
  27. 27.
    Cuong, B. C., Phong, P. H. and Smarandache, F.: Standard Neutrosophic Soft Theory: Some First Results. Neutrosophic Sets and Systems 12 (2016) 80–91.Google Scholar
  28. 28.
    Thao, N. X., Dinh, N. V.: Rough Picture Fuzzy Set and Picture Fuzzy Topologies. Journal of Science computer and Cybernetics 31 (3) (2015) 245–254.Google Scholar
  29. 29.
    Thao, N.X., Cuong. B. C., Smarandache, F.: Rough Standard Neutrosophic Sets: An Application on Standard Neutrosophic Information Systems. International Conference on Communication, Management and Information Technology, in press.Google Scholar

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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