DOI QR코드

DOI QR Code

A Generalized Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems

  • Park, Jin-Han (Department of Applied Mathematics, Pukyong National University) ;
  • Kwun, Young-Chel (Department of Mathematics, Dong-A University) ;
  • Son, Mi-Jung (Department of Data Information, Korea Maritime University)
  • Received : 2011.04.06
  • Accepted : 2011.05.18
  • Published : 2011.06.25

Abstract

The problem of decision making under imprecise environments are widely spread in real life decision situations. We present a method of object recognition from imprecise multi observer data, which extends the work of Roy and Maji [J Compu. Appl. Math. 203(2007) 412-418] to generalized intuitionistic fuzzy soft set theory. The method involves the construction of a comparison table from a generalized intuitionistic fuzzy soft set in a parametric sense for decision making.

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, "Anapplication 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 RSFD-GrC 2009, Lecture Notes in Computer Science, vol. 5908, pp. 231-240, 2009.
  21. J.H. Park, M.G. Gwak and Y.C. Kwun, "Generalized intuitionistic fuzzy soft sets and their properties," submitted.
  22. T.K. Mondal and S.K. Samanta, "Generalized intuitionistic fuzzy sets," Journal of Fuzzy Mathematics, vol. 10, pp. 839-861, 2002.

Cited by

  1. Lattice Structure of Generalized Intuitionistic Fuzzy Soft Sets vol.24, pp.2, 2014, https://doi.org/10.5391/JKIIS.2014.24.2.201
  2. On Idempotent Intuitionistic Fuzzy Matrices of T-Type vol.16, pp.3, 2016, https://doi.org/10.5391/IJFIS.2016.16.3.181
  3. Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making pp.1573-7497, 2017, https://doi.org/10.1007/s10489-017-0981-5
  4. A Brief Review and Future Outline on Decision Making Using Fuzzy Soft Set vol.7, pp.2, 2018, https://doi.org/10.4018/IJFSA.2018040101
  5. Intertemporal Choice of Fuzzy Soft Sets vol.10, pp.9, 2018, https://doi.org/10.3390/sym10090371
  6. Hesitant Picture 2-Tuple Linguistic Aggregation Operators Based on Archimedean T-Norm and T-Conorm and Their Use in Decision-Making vol.10, pp.11, 2018, https://doi.org/10.3390/sym10110629