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The applications of vague soft sets and generalized vague soft sets

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Abstract

The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definitions, some novel methods of object recognition from an imprecise multiobserver data has been presented. Moreover, we introduce the notion of generalized vague soft sets and study some of its properties. The similarity measure of generalized vague soft sets is also presented and an application of this measure in decision making problems has been shown.

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References

  1. Aktaş, H., Çağman, N. Soft sets and soft groups. Information Science, 177(13): 2726–2735 (2007)

    Article  MATH  Google Scholar 

  2. Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M. On some new operations in soft set theory. Computers and Mathematics with Applications, 57(9): 1547–1553 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1): 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bustince, H., Burillo, P. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems, 79(3): 403–405 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, S.M. Measures of similarity between vague sets. Fuzzy Sets and Systems, 74(2): 217–223 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, D., Tsang, E.C., Yeung, D.S., Wang, X. The parameterization reduction of soft sets and its applications. Computers and Mathematics with Applications, 49(5-6): 753–763 (2005)

    MathSciNet  Google Scholar 

  7. Deschrijver, D., Kerre, E. On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133(2): 227–235 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Feng, F., Li, Y.M., Leoreanu-Fotea, V. Application of level soft sets in decision making based on intervalvalued fuzzy soft sets. Computers and Mathematics with Applications, 60(6): 1756–1767 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Feng, F., Li, C.X., Davvaz, B., Ali, M.I. Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Computing, 14(1): 899–911 (2010)

    Article  MATH  Google Scholar 

  10. Feng, F., Jun, Y.B, Liu, X., Li, L. An adjustable approach to fuzzy soft set based decision making. Journal of Computational and Applied Mathematics, 234(1): 10–20 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Feng, F., Liu, X.Y., Leoreanu-Fotea, V., Jun, Y.B. Soft sets and soft rough sets. Information Science, 181(6): 1125–1137 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Feng, F., Li, Y.M., Çağman, N. Generalized uni-int decision making schemes based on choice value soft sets. European Journal of Operational Research, 220(1): 162–170(2012)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gau, W.L., Buehrer, D.J. Vague sets. IEEE Transactions on Systems, Man and Cybernetics, 23(2): 610–614 (1993)

    Article  MATH  Google Scholar 

  14. Gorzalzany, M.B. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1): 1–17 (1987)

    Article  MathSciNet  Google Scholar 

  15. Jun, Y.B., Park, Ch.. Applications of soft sets in ideal theory of BCK/BCI-algebras. Information Science, 178(11): 2466–2475 (2008)

    MATH  MathSciNet  Google Scholar 

  16. Jun, Y.B., Lee, K.J., Park, Ch.. Soft set theory applied to ideals in d-algebras. Computers and Mathematics with Applications, 57(3): 367–378 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kong, Z., Gao, L., Wang, L., Li, S. The normal parameter reduction of soft sets and its algorithm. Computers and Mathematics with Applications, 56(12): 3029–3037 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Li, F., Xu, Z.Y. Measures of similarity between vague sets. Journal of Software, 12(6): 922–927 (2001)

    Google Scholar 

  19. Li, Y., Olson, D.L., Qin, Z. Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognition Letters, 28(2): 278–285 (2007)

    Article  Google Scholar 

  20. Maji, P.K., Biswas, R., Roy, A.R. Fuzzy soft sets. Journal of Fuzzy Mathematics, 9(3): 589–602 (2001)

    MATH  MathSciNet  Google Scholar 

  21. Maji, P.K., Biswas, R., Roy, A.R. Soft set theory. Computers and Mathematics with Applications, 45(4-5): 555–562 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  22. Majumdar, P., Samanta, S.K. Generalised fuzzy soft sets. Computers and Mathematics with Applications, 59(4): 1425–1432 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  23. Molodtsov, D. Soft set theory - First results. Computers and Mathematics with Applications, 37(4-5): 19–31 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  24. Pawlak, Z. Rough Sets. International Journal of Computer and Information Science, 11(5): 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  25. Qin, K., Hong, Z. On soft equality. Journal of Computational and Applied Mathematics, 234(5): 1347–2135 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  26. Wang, X.Z., He, Y.Y. Intuitionistic fuzzy sets and L-fuzzy sets. Fuzzy Sets and Systems, 110(2): 271–274 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  27. Xiao, Z., Gong, K., Zou, Y. A combined forecasting approach based on fuzzy soft sets. Journal of Computational and Applied Mathematics, 228(1): 326–333 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Xiao, Z., Gong, K., Xia, S., Zou, Y. Exclusive disjunctive soft sets. Computers and Mathematics with Applications, 59(6): 2128–2137 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  29. Xu, W., Ma, J., Wang, S., Hao, G. Vague soft sets and their properties. Computers and Mathematics with Applications, 59(2): 787–794 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  30. Zadeh, L.A. Fuzzy sets. Information and control, 8(3): 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  31. Zeng, W.Y., Guo, P. Normalized distance,similarity measure, inclusion measure and entropy of intervalvalued fuzzy sets and their relationship. Information Sciences, 178(5): 1334–1342 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  32. Zou, Y., Xiao, Z. Data analysis approaches of soft sets under incomplete information. Knowledge-Based Systems, 21(8): 941–945 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, China

    Chang Wang & An-jing Qu

Authors
  1. Chang Wang
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  2. An-jing Qu
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Corresponding author

Correspondence to Chang Wang.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant Nos.11571276, 11501444; the Postdoctoral Science Foundation of China under Grant Nos. 2013M532079, 2014T70932; the Science Research Foundation of Education Department of Shanxi Provincial Government under Grant No.15JK1735; the Science Research Foundation of Northwest University under Grant No.12NW04.

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Wang, C., Qu, Aj. The applications of vague soft sets and generalized vague soft sets. Acta Math. Appl. Sin. Engl. Ser. 31, 977–990 (2015). https://doi.org/10.1007/s10255-015-0517-x

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  • DOI: https://doi.org/10.1007/s10255-015-0517-x

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