Skip to main content

Generalization of Soft Set Theory: From Crisp to Fuzzy Case

  • Conference paper
Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((AINSC,volume 40))

Abstract

The traditional soft set is a mapping from parameter to the crisp subset of universe. However, the situation may be more complex in real world because the fuzzy characters of parameters. In this paper, the traditional soft set theory is expanded to be a fuzzy one, the fuzzy membership is used to describe parameter-approximate elements of fuzzy soft set. Furthermore, basic fuzzy logic operators are used to define generalized operators on fuzzy soft set and then the DeMorgan’s laws are proved. Finally, the parametrization reduction of fuzzy soft set is defined, a decision-making problem is analyzed to indicate the validity of the fuzzy soft set.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Molodtsov, D.: Soft Set Theory–First Results. Computers and Mathematics with Applications 37, 19–31 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Zadeh, L.A.: Fuzzy Set. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  3. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  4. Pawlak, Z.: Rough sets and intelligent data analysis. International Journal of Information Sciences 147, 1–12 (2002)

    MATH  MathSciNet  Google Scholar 

  5. Maji, P.K., Biswas, R., Roy, A.R.: Soft Set Theory. Computers and Mathematics with Applications 45, 555–562 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Maji, P.K., Roy, A.R.: An Application of Soft Sets in A Decision Making Problem. Computers and Mathematics with Applications 44, 1077–1083 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Denggang, C., et al.: The Parameterization Reduction of Soft Sets and its Applications. Computers and Mathematics with Applications 49, 757–763 (2005)

    Article  MathSciNet  Google Scholar 

  8. Yao, Y.Y.: Relational Interpretations of Neighbourhood Operators and Rough Set Approximation Operators. International Journal of Information Sciences 111, 239–259 (1998)

    Article  MATH  Google Scholar 

  9. Radzikowska, A.M., Kerre, E.E.: A Comparative Study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Morsi, N.N., Yakout, M.M.: Axiomatics For Fuzzy Rough Set. Fuzzy Sets and Systems 100, 327–342 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bing-Yuan Cao

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yang, X., Yu, D., Yang, J., Wu, C. (2007). Generalization of Soft Set Theory: From Crisp to Fuzzy Case. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71441-5_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71440-8

  • Online ISBN: 978-3-540-71441-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics