Skip to main content
SpringerLink
Log in

Parameter Reduction of Fuzzy Soft Sets: An Adjustable Approach Based on the Three-Way Decision

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Parameter reduction is one of the major steps in decision-making problems. It refers to determine a minimal subset of a parameter set which preserves the final decision based on the whole set of parameters. The applicability of soft set (SS) theory to bring out a pattern for parameter reduction is discussed by some researchers. Several algorithms have been proposed for computing a reduction of a soft set; however, they have some drawbacks and limitations. These methods, that are based on the binary-decision rules, are usually inspired from the rough set (RS) technique for deleting dispensable parameters, while the difference between SS theory and RS theory has not received any significant attention. This paper studies a new approach for parameter reduction based on the three-way decision methodology under fuzzy soft models. We first review some existing approaches for reduction of a soft set. Then, we design our algorithm for parameter reduction of fuzzy soft sets according to results of Khameneh et al. (Int J Fuzzy Syst, 2016. https://doi.org/10.1007/s40815-016-0280-z) paper. The comparison results on a common dataset show the efficiency of our proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aktaş, H., Çaǧman, N.: Soft sets and soft groups. Inf. Sci. 177, 2726–3332 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ali, M.I.: Another view on reduction of parameters in soft sets. Appl. Soft Comput. 12, 1814–1821 (2012)

    Article  Google Scholar 

  3. Ali, M.I., Feng, F., liu, X., Min, W.K.: On some new operations in soft set theory. Comput. Math. Appl. 57(9), 1547–1553 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Borzooei, R.A., Mobini, M., Ebrahimi, M.M.: The category of soft sets. J. Intell. Fuzzy Syst. 28(1), 157–167 (2015)

    MathSciNet  MATH  Google Scholar 

  5. Çaǧman, N., Karataş, S., Enginoǧlü, S.: Soft topology. Comput. Math. Appl. 62, 351–358 (2011)

    Article  MathSciNet  Google Scholar 

  6. Chatterjee, R., Majumdar, P., Samanta, S.K.: Type-2 soft sets. J. Intell. Fuzzy Syst. 29(2), 885–898 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, D., Tsang, E.C.C., Yeung, D.S., Wang, X.: The parameterization reduction of soft sets and its applications. Comput. Math. Appl. 49, 757–763 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Danjuma, S., Ismail, M.A., Herawan, T.: An alternative approach to normal parameter reduction algorithm for soft set theory. IEEE Access 5, 4732–4746 (2017)

    Article  Google Scholar 

  9. Feng, F., Jun, Y.B., Liu, X., Li, L.: An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 234, 10–20 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Feng, F., Li, Y., Leoreanu-Fotea, V.: Application of level soft sets in decision making based on interval-valued fuzzy soft sets. Comput. Math. Appl. 60, 1756–1767 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jiang, Y., Tang, Y., Chen, Q.: An adjustable application to intuitonistic fuzzy soft sets based decision making. Appl. Math. Model. 35, 824–836 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Khameneh, A.Z., Kilicman, A., Salleh, A.R.: Fuzzy soft product topology. Ann. Fuzzy Math. Inf. 7(6), 935–947 (2014a)

    MathSciNet  MATH  Google Scholar 

  13. Khameneh, A.Z., Kilicman, A., Salleh, A.R.: Fuzzy soft boundary. Ann. Fuzzy Math. Inf. 8(5), 687–703 (2014b)

    MathSciNet  MATH  Google Scholar 

  14. Khameneh, A.Z., Kilicman, A., Salleh, A.R.: An adjustable method for data ranking based on fuzzy soft sets, Indian. J. Sci. Technol. (2015) https://doi.org/10.17485/ijst/2015/v8i21/72587

    Google Scholar 

  15. Khameneh, A.Z., Kilicman, A., Salleh, A.R. : An adjustable approach to multi-criteria group decision-making based on a preference relationship under fuzzy soft information. Int. J. Fuzzy Syst. (2016) https://doi.org/10.1007/s40815-016-0280-z

    Google Scholar 

  16. Kong, Z., Gao, L., Wang, L., Li, S.: The normal parameter reduction of soft sets and its algorithm. Comput. Math. Appl. 56, 3029–3037 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kong, Z., Gao, L., Wang, L.: Comment on “A fuzzy soft set theoretic approach to decision making problems”. J. Comput. Appl. Math. 223(2), 540–542 (2009)

    Article  MATH  Google Scholar 

  18. Kong, Z., Jia, W., Zhang, G., Wang, L.: Normal parameter reduction in soft set based on particle swarm optimization algorithm. Appl. Math. Model. 39, 4808–4820 (2015)

    Article  MathSciNet  Google Scholar 

  19. Kule, M., Dost, S.: A textural view of semi-separation axioms in soft fuzzy topological spaces. J. Intell. Fuzzy Syst. 30(4), 2037–2053 (2016)

    Article  MATH  Google Scholar 

  20. Liang, D., Liu, D., Kobina, A.: Three-way group decisions with decision-theoretic rough sets. Inf. Sci. 345, 46–64 (2016)

    Article  Google Scholar 

  21. Ma, X., Sulaiman, N., Qin, H., Herawana, T., Zain, J.M.: A new efficient normal parameter reduction algorithm of soft sets. Comput. Math. Appl. 62, 588–598 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft set. J. Fuzzy Math. 9(3), 589–602 (2001)

    MathSciNet  MATH  Google Scholar 

  23. Maji, P.K., Roy, A.R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077–1083 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Min, W.K.: A note on soft topological spaces. Comput. Math. Appl. 62, 3524–3528 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37, 19–31 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  27. Pei, D., Miao, D.: From soft sets to information systems. Proc. IEEE Int. Conf. Granul. Comput. 2, 617–621 (2005)

    Google Scholar 

  28. Pawlak, A.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1965)

    Article  MATH  Google Scholar 

  29. Roy, A.R., Maji, P.K.: A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203, 412–418 (2007)

    Article  MATH  Google Scholar 

  30. Roy, S., Samanta, T.K.: A note on fuzzy soft topological spaces. Ann. Fuzzy Math. Inf. 3(2), 305–311 (2012)

    MathSciNet  MATH  Google Scholar 

  31. Sezgin, A., Atagun, A.O.: On operations of soft sets. Comput. Math. Appl. 61, 1457–1467 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  32. Shabir, M., Naz, M.: On soft topological spaces. Comput. Math. Appl. 61, 1786–1799 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  33. Tanay, B., Kandemir, M.B.: Topological structure of fuzzy soft sets. Comput. Math. Appl. 61, 2952–2957 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  34. Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, vol. 5, pp. 17–24. North-Holland, New York (1990)

    Google Scholar 

  35. Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inf. Sci. 178, 3356–3373 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180, 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  37. Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  38. Zhang, Z.: A rough set approach to intuitionistic fuzzy soft set based decision making. Appl. Math. Model. 36, 4605–4633 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang, Z., Zhang, S.: A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Appl. Math. Model. 37, 4948–4971 (2013)

    Article  MathSciNet  Google Scholar 

  40. Zhou, B.: Multi-class decision-theoretic rough sets. Int. J. Approx. Reason. 55, 211–224 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is partially supported by the Institute for Mathematical Research, Universiti Putra Malaysia Grant No. 5527179.

Author information

Authors and Affiliations

  1. Institute for Mathematical Research, Universiti Putra Malaysia, UPM, 43400, Serdang, Selangor, Malaysia

    Azadeh Zahedi Khameneh

  2. Institute for Mathematical Research and Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM, 43400, Serdang, Selangor, Malaysia

    Adem Kılıçman

Authors
  1. Azadeh Zahedi Khameneh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adem Kılıçman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Azadeh Zahedi Khameneh.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interests regarding the publication of this article, and that they do not have any direct financial relationships that could lead to a conflict of interest for any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khameneh, A.Z., Kılıçman, A. Parameter Reduction of Fuzzy Soft Sets: An Adjustable Approach Based on the Three-Way Decision. Int. J. Fuzzy Syst. 20, 928–942 (2018). https://doi.org/10.1007/s40815-017-0409-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0409-8

Keywords

Search

Navigation