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The Parameters Reduction Algorithm and the Application in Decision-Making Based on the Bijective Soft Set

  • Bin Miao
  • Wei Wei
  • Tao Zhang
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 133)

Abstract

Bijective soft set theory is a new mathematical tool to solve the uncertain problems, which is a branch of the soft set. Base on other scholars’ research, this paper do a further study. Firstly, this paper reviewed the related theories including definition, operation and applications of the bijective soft set. Secondly, the paper gives out the discernible matrix parameters reduction algorithm in application part. Finally, the weight calculation method is given base on dependency and importance degree between two bijective soft sets, at the same time, the paper do a application case study.

Keywords

Bijective Soft Set Discernible Matrix Parameter Reduction Weight 

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References

  1. 1.
    Molodtsov, D.: Soft set theory—first results. Computers and Mathematics with Application 37, 19–31 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Gorzalzany, M.B.: A method of inference in approximate reasoning based on interval valued fuzzy sets. Fuzzy Sets and Systems 21, 1–17 (1987)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Atanassov, K.: Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 64, 159–174 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Pawlak, Z.: Rought sets. International Journal of Information Science 11, 341–356 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Pawlak, Z.: Rought sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers (1991)Google Scholar
  7. 7.
    MaJi, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. Fuzzy Math. 9, 589–602 (2001)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Roy, A.R., MaJi, P.K.: A fuzzy soft set theoretic approach to decision making problems. Journal of Computational and Applied Mathematics 203, 412–418 (2007)zbMATHCrossRefGoogle Scholar
  9. 9.
    Xu, W., Ma, J., Wang, S., Hao, G.: Vague soft set and their properties. Computers and Mathematics with Application 59, 787–794 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Jiang, Y., Tang, Y., Chen, Q., Liu, H., Tang, J.: Interval-valued instuitionstic fuzzy soft sets and their properties. Computers and Mathematics with Application 60, 906–918 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Xiao, Z., Gong, K., Li, D.: The Parameter Reduction based on the Bijective Soft Decision system. System Engineering Theory and Practice 31, 308–314 (2011)Google Scholar
  12. 12.
    Gong, K., Xiao, Z., Zhang, X.: The bijective soft set with its operations. Computers and Mathematics with Applications 60, 2270–2278 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Maji, P.K., Roy, A.R.: An application of soft sets in a decision making problem. Computers and Mathematics with Application 44, 1077–1083 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Chen, D., Tsang, E.C.C., Yeung, D.S., Wang, X.: The parameterization reduction of soft sets and its applications. Computers and Mathematics with Application 49, 757–763 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Xiao, Z., Gong, K.: A combined forecasting approach based on fuzzy soft sets. Journal of Computational and Applied Mathematics 228, 326–333 (2009)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  • Bin Miao
    • 1
  • Wei Wei
    • 1
  • Tao Zhang
    • 2
  1. 1.Faculty of Management and EconomicsKunming University of Science and TechnologyKunmingChina
  2. 2.Faculty of Economics and ManagementYunnan Agricultural UniversityKunmingChina

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