Generalized Multi-fuzzy Soft Set and Its Application in Decision Making

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By introducing a generalization parameter which itself is multi-fuzzy, we define generalized multi-fuzzy soft sets which are an extension to the multi-fuzzy soft sets. Some operations on a generalized multi-fuzzy soft set are investigated, such as complement operation, union and intersection operations, “AND” and “OR” operations. Finally, application of generalized multi-fuzzy soft sets in decision making problems has been shown.


Multi-fuzzy set Multi-fuzzy soft set Generalized multi-fuzzy soft set Decision making 



The authors would like to thank the anonymous referees for their valuable comments and suggestions. This work is supported by the National Natural Science Foundation of China (No. 71261022) and the Fundamental Research Funds for the Central Universities of Northwest University for Nationalities (No. 31920130003).


  1. 1.
    Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37, 19–31 (1999)Google Scholar
  2. 2.
    Aktas, H., Cagman, N.: Soft sets and soft groups. Inf. Sci. 177, 2726–2735 (2007)Google Scholar
  3. 3.
    Molodtsov, D.: The Theory of Soft Sets. Moscow, URSS Publishers (2004)Google Scholar
  4. 4.
    Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003)Google Scholar
  5. 5.
    Jun, Y.B.: Soft BCK/BCI-algebras. Comput. Math. Appl. 56, 1408–1413 (2008)Google Scholar
  6. 6.
    Jun, Y.B., Park, C.H.: Applications of soft sets in ideal theory of BCK/BCI-algebras. Inf. Sci. 178, 2466–2475 (2008)Google Scholar
  7. 7.
    Feng, F., Jun, Y.B., Zhao, X.Z.: Soft semirings. Comput. Math. Appl. 56, 2621–2628 (2008)Google Scholar
  8. 8.
    Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)Google Scholar
  9. 9.
    Qin, K.Y., Hong, Z.Y.: On soft equality. J. Comput. Appl. Math. 234, 1347–1355 (2010)Google Scholar
  10. 10.
    Park, J.H., Kima, O.H., Kwun, Y.C.: Some properties of equivalence soft set relations. Comput. Math. Appl. 63, 1079–1088 (2012)Google Scholar
  11. 11.
    Maji, P.K., Samanta, S.K.: Generalized fuzzy soft sets. Comput. Math. Appl. 59, 1425–1432 (2010)Google Scholar
  12. 12.
    Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft set. J. Fuzzy Math. 9(3), 589–602 (2001)Google Scholar
  13. 13.
    Yang, X.B., Lin, T.Y., Yang, J.Y., Li, Y., Yu, D.: Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 58(3), 521–527 (2009)Google Scholar
  14. 14.
    Gorzalczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 21, 1–17(1987)Google Scholar
  15. 15.
    Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 133, 227–235 (2003)Google Scholar
  16. 16.
    Deschrijver, G., Kerre, E.E.: Implicators based on binary aggregation operators in interval-valued fuzzy set theory. Fuzzy Sets Syst. 153, 229–248 (2005)Google Scholar
  17. 17.
    Feng, F., Li, C.X., Davvaz, B., Ali, M.I.: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14, 899–911 (2010)Google Scholar
  18. 18.
    Shabir, M., Ali, M.I., Shaheen, T.: Another approach to soft rough sets. Knowl. Based Syst. 40, 72–80 (2013)Google Scholar
  19. 19.
    Sebastian, S., Ramakrishnan, T.V.: Multi-fuzzy sets: an extension of fuzzy sets. Fuzzy Inf. Eng. 1, 35–43 (2011)Google Scholar
  20. 20.
    Yang, Y., Tan, X., Meng, C.C.: The multi-fuzzy soft set and its application in decision making. Appl. Math. Model. 37, 4915–4923 (2013)Google Scholar
  21. 21.
    Agarwal, M., Biswas, K.K., Hanmandlu, M.: Generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl. Soft Comput. 13, 3552–3566 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceNorthwest University for NationalitiesLanzhouChina

Personalised recommendations