Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

AN EXTENSION OF SOFT ROUGH FUZZY SETS

  • Received : 2016.12.04
  • Accepted : 2017.03.01
  • Published : 2017.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.

Keywords

References

  1. H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences 177 (2007), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
  2. M. I. Ali, A note on soft sets, rough sets and fuzzy soft sets, Applied Soft Computing 11 (2011), 3329-3332. https://doi.org/10.1016/j.asoc.2011.01.003
  3. I. Beg and S. Ashraf, Fuzzy relational calculus, Bulletin of the Malaysian Mathematical Sciences Society (2) 37 (1) (2014), 203-237.
  4. I. Beg and T. Rashid, TOPSIS for hesitant fuzzy linguistic term sets, International Journal of Intelligent Systems 28 (2013), 1162-1171. https://doi.org/10.1002/int.21623
  5. R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management Science 17 (4) (1970), 141-164. https://doi.org/10.1287/mnsc.17.4.B141
  6. D. Dubois and H. Prade, Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Dordrecht - 2000.
  7. F. Feng, C. X. Li, B. Davvaz and M. I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14 (2010), 899-911. https://doi.org/10.1007/s00500-009-0465-6
  8. F. Feng, X. Liu, V. Leoreanu-Fotea and Y. B. Jun, Soft sets and soft rough sets, Information Sciences 181 (2011), 1125-1137. https://doi.org/10.1016/j.ins.2010.11.004
  9. X. Ge, Z. Li and Y. Ge, Topological spaces and soft sets, Journal of Computational Analysis and Applications 13 (2011), 881-885.
  10. S. Greco, B. Matarazzo and R. Slowinski, Rough set theory for multicriteria decision analysis, European Journal of Operational Research 129 (2001), 1-47. https://doi.org/10.1016/S0377-2217(00)00167-3
  11. T. Herawan and M. M. Deris, A soft set approach for association rules mining, Knowledge-Based Systems 24 (2011), 186-195. https://doi.org/10.1016/j.knosys.2010.08.005
  12. T. B. Iwinski, Algebraic approach to rough sets, Bulletin of the Polish Academy of Sciences, Mathematics 35 (9-10) (1987).
  13. Y. B. Jun, Roughness of ideals in BCK-algebra, Scientiae Mathematicae Japonica 57 (1) (2003), 165-169.
  14. S. J. Kalayathankal and G. S. Singh, A fuzzy soft ood alarm model, Mathematics and Computers in Simulation 80 (2010), 887-893. https://doi.org/10.1016/j.matcom.2009.10.003
  15. P. K. Maji, R. Biswas and R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  16. D. Meng, X. Zhang and K. Qin, Soft rough fuzzy sets and soft fuzzy rough sets, Computers and Mathematics with Applications 62 (2011), 4635-4645. https://doi.org/10.1016/j.camwa.2011.10.049
  17. D. Molodtsov, Soft set theory - first results, Computers and Mathematics with Applications 37 (1999), 19-31.
  18. M. M. Musharif, S. Sengupta and A. K. Ray, Texture classification using a novel, soft set theory based classification algorithm, Lecture Notes in Computer Science 3851 (2006), 246-254.
  19. Z. Pawlak, Rough sets, International Journal of Computing and Information Sciences 11 (1982), 341-356. https://doi.org/10.1007/BF01001956
  20. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Boston, 1991.
  21. Z. Pawlak, Rough set approach to knowledge-based decision support, European Journal of Operational Research 99 (1997), 48-57. https://doi.org/10.1016/S0377-2217(96)00382-7
  22. Z. Pawlak, Rough set theory and its applications, Journal of Telecommunications and Information Technology 3 (2002).
  23. Z. Pawlak and A. Skowron, Rudiments of rough sets, Information Sciences 177 (2007), 3-27. https://doi.org/10.1016/j.ins.2006.06.003
  24. H. Qin, X. Ma, J. M. Zain and T. Herawan, A novel soft set approach in selecting clustering attribute, Knowledge-Based Systems 36 (2012), 139-145. https://doi.org/10.1016/j.knosys.2012.06.001
  25. A. S. Sezer, A new view to ring theory via soft union rings, ideals and bi-ideals, Knowledge-Based Systems 36 (2012), 300-314. https://doi.org/10.1016/j.knosys.2012.04.031
  26. M. Shabir, M. I. Ali and T. Shaheen, Another approach to soft rough sets, Knowledge-Based Systems 40 (2013), 72-80. https://doi.org/10.1016/j.knosys.2012.11.012
  27. L. Shanmei and X. Xiaohao, Vulnerability analysis for airport networks based on fuzzy soft sets: from the structural and functional perspective, Chinese Journal of Aeronautics 28 (2015) DOI:http://dx.doi.org/10.1016/j.cja.2015.04.002
  28. H. Tang, A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster-Shafer theory of evidence, Applied Soft Computing 31 (2015), 317-325 https://doi.org/10.1016/j.asoc.2015.03.015
  29. Z. Tao, H. Chen, X. Song, L. Zhou and J. Liu, Uncertain linguistic fuzzy soft sets and their applications in group decision making, Applied Soft Computing 34 (2015), 587-605 https://doi.org/10.1016/j.asoc.2015.04.051
  30. Z. Xio, K. Gong and Y. Zou, A combined forecasting approach based on fuzzy soft sets, Journal of Computational and Applied Mathematics 228 (2009), 326-333 https://doi.org/10.1016/j.cam.2008.09.033
  31. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  32. H. J. Zimmermann, Fuzzy Set Theory and its Applications, second edition, Kluwer Academic Publishers, Boston, (1991).

Cited by

  1. Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance vol.2018, pp.None, 2017, https://doi.org/10.1155/2018/4160905