Advertisement

Soft Sets and Soft Modules

  • Qiu-Mei Sun
  • Zi-Long Zhang
  • Jing Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5009)

Abstract

Molodtsov introduced the concept of soft sets. Recently, Aktaş et al. generalized soft sets by defining the concept of soft groups. In this paper, we present the definition of soft modules and construct some basic properties using modules and Molodtsov’s definition of soft sets.

Keywords

soft sets soft modules soft submodules soft homomorphism 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aktas, H., Cagman, N.: Soft Sets and Soft Groups. Inform. Sci. 177, 2726–2735 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Anderson, F.W., Fuller, K.R.: Rings and Categories of Modules. Springer, Heidelberg (1992)zbMATHGoogle Scholar
  3. 3.
    Chen, D.: The Parameterization Reduction of Soft Sets and Its Applications. Comput. Math. Appl. 49, 757–763 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Maji, P.K., Bismas, R., Roy, A.R.: Soft Set Theory. Comput. Math. Appl. 45, 555–562 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Molodtsov, D.: The Theory of Soft Sets. URSS Publishers, Moscow (2004)Google Scholar
  6. 6.
    Maji, P.K.: An Application of Soft Set in Decision Makeing Problem. Comput. Math. Appl. 44, 1077–1083 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Molodtsov, D.: Soft Set Theory: First Results. Comput. Math. Appl. 37, 19–31 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Pawlak, Z.: Rough Sets. Int. J. Inform. Comput. Sci. 11, 341–356 (1982)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Zadeh, L.A.: Fuzzy Sets. Inform. Control. 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kassel, C.: Quantum Groups. Springer, Berlin (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Qiu-Mei Sun
    • 1
  • Zi-Long Zhang
    • 1
  • Jing Liu
    • 1
  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangP.R. China

Personalised recommendations