Article Sidebar

Submitted
December 31, 2022
Accepted
July 15, 2023
Published
March 31, 2024
Download
PDF
Statistic
Read Counter : 499 Download : 375

Downloads

Download data is not yet available.

Main Article Content

Abstract

Recently Jun and Hur proposed (m, n)-fuzzy sets which can handle vagueness and uncertainty in information very efficiently in the process of solving complex problems. They defined basic operations over (m, n)-fuzzy sets. The present paper created some new operations over this super class of fuzzy sets and established many theorems related to the their properties. Further some distance and similarity measures of (m, n)-fuzzy sets are proposed and their properties are examined. Moreover, the proposed similarity measures are applied to the problem of pattern recognition.

Keywords

(m, n)-fuzzy sets operations and similarity measure of (m, n)-fuzzy sets

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite
Thakur, S. S., Banafar, A. S. ., Thakur, M., Pandey Bajpai, J. ., & Prasad, A. K. (2024). Operations and Similarity Measures Between (m,n)-Fuzzy Sets. Journal of the Indonesian Mathematical Society, 30(1), 21–39. https://doi.org/10.22342/jims.30.1.1354.21-39
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Al-shami,T.M., ”(2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods”, Complex and Intelligent Systems,(2022); https://doi.org/10.1007/s40747-022-00878-4
  2. Atanassov, K.,T., ”Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20(1986), 87-96.
  3. Bryniarska, A., ”The n-Pythagorean fuzzy sets”,Symmetry, 12(11)(2020), 1772;
  4. https://doi.org/10.3390/sym12111772.
  5. Ejegwa, P. A., Onyeke, I.C., ”Fermatean fuzzy similarity measure algorithm, and its application in students admission process”, International Journal of Fuzzy Computation and Modelling 4(1) (2022),34-50.
  6. Hussian, Z., Yang, M.S.,” Distance, and similarity measures of Pythagorean fuzzy sets based on Hausdorff metric with application to fuzzy TOPSIS”Journal of Intelliegent Systems 2019,1-22.
  7. Ibrahim, H., Z., Al-shami, T. M.and Elbarbary, O. G., ”(3, 2)-fuzzy sets and their applications to topology and optimal choice”,Computational Intelligence and Neuroscience, 2021, Article ID 1272266, 14 pages https://doi.org/10.1155/2021/1272266.
  8. Ibrahim, H., Z. and Murad, K. K., ”(3, 4)-fuzzy sets and their topological spaces” Journal
  9. of Mathematics and Computer Science, 28(2)(2022), 158-170.
  10. Jun, Y. B. and Hur Kul,” The (m, n)-fuzzy set and its application in BCK-algebras”, Annals
  11. of Fuzzy Mathematics and Informatics, 24(1)(2022), 17-29.
  12. Kiri¸sci, M., ”New cosine similarity, and distance measures for Fermatean fuzzy sets and
  13. TOPSIS approach”, Knowledge and Information Systems, 65(2023), 855–868.
  14. Liu, D., Chen, X., Peng, D. ”Some cosine similarity measures, and distance measures between
  15. q-rung orthopair fuzzy sets”, International Journal of Intelligent Systems, 34(2019), 2454-
  16. Peng, X.; Liu, L. ”Information measures for q-rung orthopair fuzzy sets”, International
  17. Journal of Intelligent Systems, 34(2019),1795-1834.
  18. Sahoo, L., ”Similarity measures for Fermatean fuzzy sets, and applications in group decision
  19. making”, Decision Science Letters, 11 (2022), 167-180.
  20. Senapati, T. and Yager,R. R., ”Fermatean fuzzy sets”, Journal of Ambient Intelligence and
  21. Humanized Computing, 11(2020), 663—674.
  22. Senapati, T. and Yager,R. R., ”Some new operations over fermatean fuzzy numbers and application of fermatean fuzzy WPM in multi-criteria decision making”, Informatica, 30(2)(2019),
  23. –412.
  24. Szmidt, E., Distances and similarities in intuitionistic fuzzy sets, Springer International
  25. Publishing, Switzerland (2014).
  26. Szmidt, E. and Kacprzyk, J., ”Distances between inuitionistic fuzzy sets”,Fuzzy Sets and
  27. Systems, 114(3)(2000),505–518.
  28. Wang, W., Xin, X.,” Distance measure between intuitionistic fuzzy sets”, Pattern Recog
  29. Letters, 26(2009),2063–2069.
  30. Yager, R. R., ”Pythagorean fuzzy subsets” In : Editor, Pedrycz, W. Reformat, Marek,
  31. Z.,(eds) Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting
  32. (IFSA/NAFIPS) IEEE, Edmonton, Canada (2013),57-61.
  33. Zadeh, L. A., ”Fuzzy sets”, Information and Control, 8 (1965), 338-353.
  34. Zeng, W., Li, D., Yin, Q. ”Distance and similarity measures of Pythagorean fuzzy sets
  35. and their applications to multiple criteria group decision making”, International Journal of
  36. Intelligent Systems, 33(2018),2236–2254