Nothing Special   »   [go: up one dir, main page]
Skip to main content
SpringerLink
Log in

Three-Valued Random Fuzzy Sets

  • Conference paper
  • First Online:
Fuzzy Systems & Operations Research and Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 367))

  • 970 Accesses

Abstract

The theory of fuzzy sets was founded by Zadeh as an approach to cope with the pressing need to deal with phenomena which cannot be modelled properly by conventional mathematics because they contain factors which are fuzzy in nature. However, in this frame of the theory of fuzzy sets, we cannot discern two conflicting fuzzy conceptions properly, and therefore, the excluded middle law is violated. In this theory, one does not differ fuzzy sets from their membership functions. That is, a fuzzy set in the sense of Zadeh is equivalent to its membership function. This may be the main reason why the excluded middle law was violated. In this paper, we use the concept of three-valued fuzzy sets to provide a mathematical frame of fuzzy sets theory, such that it can eliminate the suspicion for the objective reality of membership functions of fuzzy sets. In our frame, fuzzy sets and their membership functions are not equivalent conceptions.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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

Similar content being viewed by others

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Landles, R.H., Wolfe, D.A.: Introduction to the Theory of Nonparamelvic Statistics. Wiley, New York (1979)

    Google Scholar 

  3. Hirota, K.: Concepts of probabilistic sets. Fuzzy Set Syst. 5, 31–46 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  4. Luo, C.Z.: Fuzzy sets and set-embeddings. Fuzzy Math. 4, (Chinese) (1983)

    Google Scholar 

  5. Wang, P.Z., Liu, X.H.: Set valued statistics. J. Eng. Math. (first issue), (Chinese)

    Google Scholar 

  6. Wang, P.Z.: Fuzzy Sets and Random Falling Shadows. Beijing Normal University, Beijing (Chinese) (1985)

    Google Scholar 

  7. Suzuki, H.: Fuzzy sets and membership functions. Fuzzy Sets Syst. 58, 123–132 (1993)

    Article  MATH  Google Scholar 

  8. Li, Q., Wang, P., Lee, E.S.: r-Fuzzy Set. Comput. Math. Appl. 31(2), 49–61 (1996)

    Google Scholar 

  9. Yuan, X.H., Li, H.X., Sun, K.B.: The cut sets, decomposition theorems and representation theorems on Intuitionistic fuzzy Sets and interval-valued fuzzy sets. Sci. China Inf. Sci. 53, 1–18 (2010). doi:10.1007/s11432-010-4078-6

    Google Scholar 

Download references

Acknowledgments

We thank the referee for several suggestions that improved the article.

Author information

Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Bin Yu & Xue-Hai Yuan

  2. School of Science, Dalian Ocean University, Dalian, 116023, China

    Bin Yu

Authors
  1. Bin Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xue-Hai Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Yu .

Editor information

Editors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Bing-Yuan Cao

  2. Foreign Affairs Office, National Defense University, Beijing, China

    Zeng-Liang Liu

  3. Higher Education Mega Center, Guangzhou University, Guangzhou, China

    Yu-Bin Zhong

  4. Zhuhai Campus, Beijing Normal University, Zhuhai, China

    Hong-Hai Mi

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Yu, B., Yuan, XH. (2016). Three-Valued Random Fuzzy Sets. In: Cao, BY., Liu, ZL., Zhong, YB., Mi, HH. (eds) Fuzzy Systems & Operations Research and Management. Advances in Intelligent Systems and Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-19105-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19105-8_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19104-1

  • Online ISBN: 978-3-319-19105-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation