Skip to main content
SpringerLink
Log in

Fuzzy Linear Programming with Possibility and Necessity Relation

  • Conference paper
Fuzzy Information and Engineering 2010

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 78))

Abstract

A class of linear programming problems based on the possibility and necessity relation is introduced. By using the degree of possibility and necessity, the fulfillment of the constraints can be measured. Then the properties of ranking index are discussed. With this ranking index, the bound of optimal solution is obtained at different degree of possibility and necessity, that constitute a nested set. In the end, the membership function of fuzzy solution is also presented as well as a numerical example.

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 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.

References

  1. Bellman, R.E., Zadeh, L.A.: Decision Making in a Fuzzy Environment. Management Science 17, 141–164 (1970)

    Article  MathSciNet  Google Scholar 

  2. Julien, B.: A Extension to Possibilistic Linear Programming. Fuzzy Sets and Systems 64, 195–206 (1994)

    Article  MathSciNet  Google Scholar 

  3. Liu, X.W.: Measuring the Satisfaction of Constraints in Fuzzy Linear Programming. Fuzzy Sets and Systems 122, 263–275 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Maleki, H.R., Tata, M., Mashinchi, M.: Linear Programming with Fuzzy Variables. Fuzzy Sets and Systems 109, 21–33 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Liu, B.D., Kakuzo, I.: Chance Constrained Programming with Fuzzy Parameters. Fuzzy Sets and Systems 94, 227–237 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ramík, J.: Duality in Fuzzy Linear Programming with Possibility and Necessity Relations. Fuzzy Sets and Systems 157, 1283–1302 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dubois, D., Prade, H.: Ranking Fuzzy Numbers in the Setting of Possibility Theory. Information. Sci. 30, 183–224 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Wu, H.C.: Duality Theorems in Fuzzy Linear Programming Problems with Fuzzy Coefficients. Fuzzy Optimization and Decision Making 2, 61–73 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, LongDong University, Gansu, QingYang, 745100, P.R. China

    Hongxia Li

  2. College of Mathematics and Science Information, Northwest Normal University, Gansu, LanZhou, 730070, P.R. China

    Zengtai Gong

Authors
  1. Hongxia Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zengtai Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics and Information Science Guangzhou Higher Education Mega Center , Guangzhou University, 230Wai Huan Xi Road, ZIP 510006, Guangdong, China

    Bing-yuan Cao

  2. Shaanxi Normal University, China

    Guo-jun Wang

  3. Institute of Mathematics and Systems Science, Liaoning Technical University , 123000, China

    Si-zong Guo

  4. School of Science, Jimei University , 361021, Xiamen, Fujian, China

    Shui-li Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, H., Gong, Z. (2010). Fuzzy Linear Programming with Possibility and Necessity Relation. In: Cao, By., Wang, Gj., Guo, Sz., Chen, Sl. (eds) Fuzzy Information and Engineering 2010. Advances in Intelligent and Soft Computing, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14880-4_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14880-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14879-8

  • Online ISBN: 978-3-642-14880-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation