Skip to main content
SpringerLink
Log in

Duality Theorem and Model Based on Fuzzy Inequality

  • Chapter
  • First Online:
Fuzzy Information & Engineering and Operations Research & Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 211))

  • 1238 Accesses

Abstract

This article reports a study on duality theorem and model with fuzzy approaches. The study focuses on the economical interpretation of duality theorem as well as on solving duality problems in a fuzzy mathematical perspective. Besides the regular duality concepts, this article puts forward the methods of drawing non-symmetric fuzzy duality programming from that of symmetric fuzzy duality and drawing symmetric fuzzy duality programming from that of non-symmetric fuzzy duality. It sums up the general rules of forming fuzzy duality programming and proves symmetric duality theorem of fuzzy inequality type.

Foundation Item: NSFC:71201019 Author: Liu Xin (1961-), female(Fuxin, Liaoning), professor, mainly work on the study of fuzzy logic and economy optimization.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

References

  1. hen, S., Li, J., Wang X.: Fuzzy Set Theory and its applications Beijing, China, Science Press, (2004)

    Google Scholar 

  2. Li, A., Zhang, Z,, etc., Fuzzy Mathematics and its applications, Beijing, China, Metallurgical Industry Press, (1994)

    Google Scholar 

  3. Cao, Bingyuan: Appli. Fuzzy Math. Syst. Science Press, Beijing, China (2005)

    Google Scholar 

  4. Masahiro Inuiguchi, Jaroslar Ramik, Tetsuzo Tanino, ctal. Satisfying solutions and duality in interval and fuzzy linear programming. Fuzzy sets syst. 135, 151–177 (2003)

    Google Scholar 

  5. Bactor, C.R., Chandra S.: On duality in linear programming under fuzzy environment. Fuzzy sets and systems, 125, pp. 317–325 (2002)

    Google Scholar 

  6. Xia, S.: Operations Research, Beiing, China, QingHua University Press, (2005)

    Google Scholar 

  7. Li, C., Xu, X., Zhan, D.: Joint replenishment Problem with fuzzy resource constraint, Comput. Int. Manuf. Syst. vol. 14 No.1 pp. 113–117 (2008)

    Google Scholar 

  8. Li, F., Jin, C., Liu, L,. Quasi-linear fuzzy number and its application in fuzzy programming, Syst. Eng.-Theory Practice. Vol. 29, No, 4. pp. 120–127(2009)

    Google Scholar 

  9. Andre, L., Walmir, C., Femando Gomide. Multivariable gaussian evolving fuzzy modeling system, IEEE Trans. Fuzzy Syst. 19(1). pp. 91-104. (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian, 116025, China

    Xin Liu

Authors
  1. Xin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xin Liu .

Editor information

Editors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University Higher Education Mega Center, Guangzhou, People's Republic of China

    Bing-Yuan Cao

  2. Department of Mathematics and Computer Sciences, Mazandaran University, Babolsar, Iran

    Hadi Nasseri

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Liu, X. (2014). Duality Theorem and Model Based on Fuzzy Inequality. In: Cao, BY., Nasseri, H. (eds) Fuzzy Information & Engineering and Operations Research & Management. Advances in Intelligent Systems and Computing, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38667-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38667-1_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38666-4

  • Online ISBN: 978-3-642-38667-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation