Annals of Fuzzy Mathematics and Informatics

The Natural Science Institute Wonkwang University (원광대학교 기초자연과학연구소)
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Soft sets in fuzzy setting

  • Chen, Xueyou (School of Mathematics, Shandong University of Technology)
  • Received : 2018.05.03
  • Accepted : 2018.06.25
  • Published : 2018.10.25
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Abstract

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. In 1982, Pawlak initiated the rough set theory, Dubois and Prade combined fuzzy sets and rough sets all together. In 1999, Molodtsov introduced the concept of soft sets to solve complicated problems and various types of uncertainties. Maji et al. studied the (Zadeh's) fuzzification of the soft set theory. As a generalization, I define the notion of a soft set in L-set theory, introduce several operators for L-soft set theory, and investigate the rough operators on $L^X$ induced by an L-soft set.

Keywords

References

  1. R. Belohlavek, Fuzzy relational systems, Foundations and Principles, Kluwer, New York 2002.
  2. Xueyou Chen, The lattice structure of L-contact relations, Advances in Fuzzy Systems 2016 (2016), Article ID 3942416, 8 pages http://dx.doi.org/10.1155/2016/3942416.
  3. Xueyou Chen, Rough approximations induced by a soft relation , Ann. Fuzzy Math. Inform. 11 (1) (2016) 135-144.
  4. Xueyou Chen and Qingguo Li, Construction of Rough Approximations in Fuzzy Setting, Fuzzy Sets and Systems 158 (2007) 2641-2653. https://doi.org/10.1016/j.fss.2007.05.016
  5. Xueyou Chen, Rough Soft Sets in Fuzzy Setting, Lecture Notes in Computer Science 7928 (2013) 530-539.
  6. D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems 17 (1990) 191-209. https://doi.org/10.1080/03081079008935107
  7. F. Feng, C. Li, B. Davvaz and M. I. Ali, Soft sets combined with fuzzy sets and rough sets a tentative approach, Soft Comput. 14 (6) (2010) 899-911. https://doi.org/10.1007/s00500-009-0465-6
  8. F. Feng, X. Y Liu, Violeta Leoreanu-Fotea and Young Bae Jun, Soft sets and soft rough sets, Inform. Sci. 181 (2011) 1125-1137. https://doi.org/10.1016/j.ins.2010.11.004
  9. B. Ganter and R. Wille, Formal concept analysis, Springer-Verlag 1999.
  10. J. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145-174. https://doi.org/10.1016/0022-247X(67)90189-8
  11. J. Jarvinen, On the structure of rough approximations, In: Alpigini. J. J., Peter J. F, Skowron A, Zhong N, eds. Proceedings of the 3rd International Conference on Rough sets and Current Trends in Computing(RSCTC 2002) LNAI 2475, Heidelberg: Springer-Verlag (2002) 123-130.
  12. P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 589-602.
  13. P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (2003) 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  14. Dan Meng, Xiaohong Zhao and Keyun 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
  15. D. Molodtsov, Soft Set Theory First Results, Computers and Mathematics with Applications 37 (1999) 19-31.
  16. M. I. Ali, Feng Feng, Xiaoyan Liu, Won Keun Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications 57 (2009) 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
  17. M. I. Ali, M. Shabir, Comments on De Morgan's law in fuzzy soft sets, J. Fuzzy Math. 18 (3) (2010) 679-686.
  18. M. I. Ali, A note on soft sets, rough sets and fuzzy sets, Appl. Soft Comput. 11 (2011) 3329- 3332. https://doi.org/10.1016/j.asoc.2011.01.003
  19. Z. Pawlak, Rough sets, International Journal of Computer and Information Science 11 (1982) 341-356. https://doi.org/10.1007/BF01001956
  20. G. Senel, A New Approach to Hausdorff Space Theory via the Soft Sets, Mathematical Problems in Engineering 2016 (9), DOI : 10.1155/2016/2196743.
  21. G. Senel, A Comparative Research on the Definition of Soft Point, International Journal of Computer Applications 163 (2), DOI : 10.5120/ijca2017913471.
  22. G. Senel, The Parameterization Reduction of Soft Point and its Applications with Soft Matrix, International Journal of Computer Applications 164 (1), DOI : 10.5120/ijca2017913564.
  23. Y. Y. Yao, Constructive and algebraic methods of the theory of rough sets, Inform. Sci. 109 (1998) 21-47. https://doi.org/10.1016/S0020-0255(98)00012-7
  24. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.