Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Generalized Intuitionistic Fuzzy Soft Sets

  • Received : 2011.03.19
  • Accepted : 2011.05.21
  • Published : 2011.06.25
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Abstract

The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

Keywords

References

  1. S.R.S. Varadhan, Probability Theory, American Mathematical Society, 2001.
  2. L.A. Zadeh, "Fuzzy sets," Inform Control, vol. 8, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  3. L.A. Zadeh, "Is there a need for fuzzy logic," Information Sciences, vol. 178, no. 13, pp. 2751-2779, 2008. https://doi.org/10.1016/j.ins.2008.02.012
  4. K. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  5. K. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999.
  6. W.L. Gau and D.J. Buehrer, "Vague sets," IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 2, pp. 610-614, 1993. https://doi.org/10.1109/21.229476
  7. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, 1991.
  8. D. Molodtsov, "Soft set theory - first results," Computers and Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999. https://doi.org/10.1016/S0898-1221(99)00056-5
  9. P.K. Maji, R. Biswas and A.R. Roy, "Soft set theory," Computers and Mathematics with Applications, vol. 45, no. 4-5, pp. 555-562, 2003. https://doi.org/10.1016/S0898-1221(03)00016-6
  10. M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, "On some new operations in soft set theory," Computers and Mathematics with Applications, vol. 57, no. 9, pp. 1547-1553, 2009. https://doi.org/10.1016/j.camwa.2008.11.009
  11. P.K. Maji, A.R. Roy and R. Biswas, "An application of soft sets in a decision making problem," Computers and Mathematics with Applications, vol. 44, no. 8-9, pp. 1077-1083, 2002. https://doi.org/10.1016/S0898-1221(02)00216-X
  12. P.K. Maji, R. Biswas and A.R. Roy, "Fuzzy soft sets," Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589-602, 2001.
  13. A.R. Roy and P.K. Maji, "A fuzzy soft set theoretic approach to decision making problems," Journal of Computational and Applied Mathematics, vol. 203, no. 2, pp. 412-418, 2007. https://doi.org/10.1016/j.cam.2006.04.008
  14. Z. Kong, L. Gao and L. Wang, "Comment on "A fuzzy soft set theoretic approach to decision making problems"," Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 540-542, 2009. https://doi.org/10.1016/j.cam.2008.01.011
  15. Y. Zou and Z. Xiao, "Data analysis approaches of soft sets under incomplete information," Knowledge-Based Systems, vol. 21, no. 8, pp. 941-945, 2008. https://doi.org/10.1016/j.knosys.2008.04.004
  16. W. Xu, J. Ma, S. Wang and G. Hao, "Vague soft sets and their properties," Computers and Mathematics with Applications, vol. 59, no. 2, pp. 787-794, 2010. https://doi.org/10.1016/j.camwa.2009.10.015
  17. P. Majumdar and S.K. Samanta, "Generalised fuzzy soft sets," Computers and Mathematics with Applications, vol. 59, no. 4, pp. 1425-1432, 2010. https://doi.org/10.1016/j.camwa.2009.12.006
  18. P.K. Maji, R. Biswas and A.R. Roy, "Intuitionistic fuzzy soft sets," Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 677-692, 2001.
  19. P.K. Maji, A.R. Roy and R. Biswas, "On intuitionistic fuzzy soft sets," Journal of Fuzzy Mathematics, vol. 12, no. 3, pp. 669-683, 2004.
  20. P.K. Maji, More on intuitionistic fuzzy soft sets. In: H. Sakai, M.K. Chakraborty, A.E. Hassanien, D. Slezak and W. Zhu, Editors, Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing RSFDGrC 2009, Lecture Notes in Computer Science, vol. 5908, pp. 231-240, 2009.
  21. T.K. Mondal and S.K. Samanta, "Generalized intuitionistic fuzzy sets," Journal of Fuzzy Mathematics, vol. 10, pp. 839-861, 2002.
  22. X.B. Yang, T.Y. Lin, J.Y. Yang, Y. Li and D. Yu, "Combination of interval-valued fuzzy set and soft set," Computers and Mathematics with Applications, vol. 58, no.3, pp. 521-527, 2009. https://doi.org/10.1016/j.camwa.2009.04.019
  23. M.B. Gorzalczany, "A method of inference in approximate reasoning based on interval valued fuzzy sets," Fuzzy Sets and Systems, vol. 21, no. 1, pp. 1-17, 1987. https://doi.org/10.1016/0165-0114(87)90148-5
  24. G. Deschrijver and E.F. Kerre, "On the relationship between some extensions of fuzzy set theory," Fuzzy Sets and Systems, vol. 133, no. 2, pp. 227-235, 2003. https://doi.org/10.1016/S0165-0114(02)00127-6
  25. Y. Jiang, Y. Tang, Q. Chen, J. Wang and S. Tang, "Extending soft sets with description logics," Computers and Mathematics with Applications, vol. 59, no. 6, pp. 2087-2096, 2010. https://doi.org/10.1016/j.camwa.2009.12.014

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