Skip to main content
SpringerLink
Log in

Discussion on Natural Fuzzy Extension and Joint Fuzzy Extension of the Rational Function

  • Conference paper
Fuzzy Information and Engineering 2010

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

  • 1053 Accesses

Abstract

According to the knowledge of interval analysis, relations between natural fuzzy extension and joint fuzzy extension of rational function are discussed in this paper . On the basis of the natural fuzzy extension of rational function , two solutions to the joint fuzzy extension of rational function are put forward. Based on the structured element method, the fuzzy arithmetic with equality constraints is turned into the operation of two monotone functions with the same monotonic form on [0,1]. From this transition we get analytical expression of joint fuzzy extension of the rational function.

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Chang, S.S.L., Zadeh, L.A.: On fuzzy mapping and control. IEEE Trans. Syst., Man Cybern. 2, 30–40 (1972)

    MATH  MathSciNet  Google Scholar 

  3. Shen, Z.H.: Interval analytical method and its application. Applied Mathematics and Computational Mathematics 2, 1–28 (1983)

    Google Scholar 

  4. Wu, C.X., Ma, M.: Fundamentals of Fuzzy Analysis. National Defence Industry Press, Bei Jing (1991)

    Google Scholar 

  5. Guo, S.Z., Su, Z.X., Wang, L.: Method of structured Element in Fuzzy Analysis and Calculation. Fuzzy System and Mathematics 18(3), 68–75 (2004)

    MathSciNet  Google Scholar 

  6. Guo, S.Z.: Transformation group of monotone funtions with same monotonic form on [-1,1]and operations of fuzzy numbers. Fuzzy System and Mathematics 19(3), 105–110 (2005)

    Google Scholar 

  7. Guo, S.Z.: Principle of Fuzzy Mathematical Analysis Based on Strutured Element. Northeastern University Press, Shen Yang (2004)

    Google Scholar 

  8. Guo, S.Z., Liu, H.T.: Equality and Identity of Fuzzy Numbers and Fuzzy Arithmetic with Equality Constraints. Fuzzy System and Mathematics 22(6), 76–82 (2008)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, LiaoNing Technical University, Fuxin, 123000, China

    Shihui Wang & Sizong Guo

Authors
  1. Shihui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sizong Guo
    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

Wang, S., Guo, S. (2010). Discussion on Natural Fuzzy Extension and Joint Fuzzy Extension of the Rational Function. 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_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14880-4_8

  • 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