International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 928–942 | Cite as

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

  • Azadeh Zahedi KhamenehEmail author
  • Adem Kılıçman


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. paper. The comparison results on a common dataset show the efficiency of our proposed algorithm.


Fuzzy soft set Three-way decisions Parameter reduction Multi-criteria group decision-making 



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

Compliance with Ethical Standards

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.


  1. 1.
    Aktaş, H., Çaǧman, N.: Soft sets and soft groups. Inf. Sci. 177, 2726–3332 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ali, M.I.: Another view on reduction of parameters in soft sets. Appl. Soft Comput. 12, 1814–1821 (2012)CrossRefGoogle Scholar
  3. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Borzooei, R.A., Mobini, M., Ebrahimi, M.M.: The category of soft sets. J. Intell. Fuzzy Syst. 28(1), 157–167 (2015)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Çaǧman, N., Karataş, S., Enginoǧlü, S.: Soft topology. Comput. Math. Appl. 62, 351–358 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chatterjee, R., Majumdar, P., Samanta, S.K.: Type-2 soft sets. J. Intell. Fuzzy Syst. 29(2), 885–898 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 34.
    Khameneh, A.Z., Kilicman, A., Salleh, A.R.: Fuzzy soft product topology. Ann. Fuzzy Math. Inf. 7(6), 935–947 (2014a)MathSciNetzbMATHGoogle Scholar
  13. 35.
    Khameneh, A.Z., Kilicman, A., Salleh, A.R.: Fuzzy soft boundary. Ann. Fuzzy Math. Inf. 8(5), 687–703 (2014b)MathSciNetzbMATHGoogle Scholar
  14. 36.
    Khameneh, A.Z., Kilicman, A., Salleh, A.R.: An adjustable method for data ranking based on fuzzy soft sets, Indian. J. Sci. Technol. (2015) Google Scholar
  15. 37.
    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) Google Scholar
  16. 12.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 13.
    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)CrossRefzbMATHGoogle Scholar
  18. 14.
    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)MathSciNetCrossRefGoogle Scholar
  19. 15.
    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)CrossRefzbMATHGoogle Scholar
  20. 16.
    Liang, D., Liu, D., Kobina, A.: Three-way group decisions with decision-theoretic rough sets. Inf. Sci. 345, 46–64 (2016)CrossRefGoogle Scholar
  21. 17.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 18.
    Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft set. J. Fuzzy Math. 9(3), 589–602 (2001)MathSciNetzbMATHGoogle Scholar
  23. 19.
    Maji, P.K., Roy, A.R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077–1083 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 20.
    Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 21.
    Min, W.K.: A note on soft topological spaces. Comput. Math. Appl. 62, 3524–3528 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 22.
    Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37, 19–31 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 23.
    Pei, D., Miao, D.: From soft sets to information systems. Proc. IEEE Int. Conf. Granul. Comput. 2, 617–621 (2005)Google Scholar
  28. 24.
    Pawlak, A.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1965)CrossRefzbMATHGoogle Scholar
  29. 25.
    Roy, A.R., Maji, P.K.: A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203, 412–418 (2007)CrossRefzbMATHGoogle Scholar
  30. 26.
    Roy, S., Samanta, T.K.: A note on fuzzy soft topological spaces. Ann. Fuzzy Math. Inf. 3(2), 305–311 (2012)MathSciNetzbMATHGoogle Scholar
  31. 27.
    Sezgin, A., Atagun, A.O.: On operations of soft sets. Comput. Math. Appl. 61, 1457–1467 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 28.
    Shabir, M., Naz, M.: On soft topological spaces. Comput. Math. Appl. 61, 1786–1799 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 29.
    Tanay, B., Kandemir, M.B.: Topological structure of fuzzy soft sets. Comput. Math. Appl. 61, 2952–2957 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 30.
    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. 31.
    Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inf. Sci. 178, 3356–3373 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 32.
    Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180, 341–353 (2010)MathSciNetCrossRefGoogle Scholar
  37. 33.
    Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)CrossRefzbMATHGoogle Scholar
  38. 38.
    Zhang, Z.: A rough set approach to intuitionistic fuzzy soft set based decision making. Appl. Math. Model. 36, 4605–4633 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 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)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Zhou, B.: Multi-class decision-theoretic rough sets. Int. J. Approx. Reason. 55, 211–224 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute for Mathematical ResearchUniversiti Putra Malaysia, UPMSerdangMalaysia
  2. 2.Institute for Mathematical Research and Department of Mathematics, Faculty of ScienceUniversiti Putra Malaysia, UPMSerdangMalaysia

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