Skip to main content
SpringerLink
Log in

Ranking Fuzzy Variables in Terms of Credibility Measure

  • Conference paper
Fuzzy Systems and Knowledge Discovery (FSKD 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4223))

Included in the following conference series:

Abstract

Fuzzy variables are used for representing imprecise numerical quantities in a fuzzy environment, and the comparison of fuzzy variables is considered an important and complicated issue in fuzzy logic theory and applications. In this paper, we propose a new type of method for ranking fuzzy variables in the setting of credibility measure. Some basic properties of this type of ranking fuzzy variable in terms of credibility measure are investigated. As an illustration, the case of ranking rule for typical trapezoidal fuzzy variables is examined.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bortolan, G., Degani, R.: A review of some methods for ranking fuzzy subsets. Fuzzy Sets and Systems 15, 1–19 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cheng, C.-H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems 95, 307–317 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chu, T.-C., Tsao, C.-T.: Ranking fuzzy numbers with an area between the centroid point and original point. Computers & Mathematics with Applications 43, 111–117 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Detyniecki, M., Yager, R.R.: Ranking fuzzy numbers using alpha-weighted valuations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 573–592 (2001)

    Article  MathSciNet  Google Scholar 

  5. Facchinetti, G., Ricci, R.G.: A characterization of a general class of ranking functions on triangular fuzzy numbers. Fuzzy Sets and Systems 146, 297–312 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Facchinetti, G., Ricci, R.G., Muzzioli, S.: Note on ranking fuzzy triangular numbers. International Journal of Intelligent Systems 13, 613–622 (1998)

    Article  Google Scholar 

  7. Fortemps, P., Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems 82, 319–330 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Herrera-Viedma, E., Herrera, F., Chiclana, F., Luque, M.: Some issues on consistency of fuzzy preference relations. European Journal of Operational Research 154, 98–109 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lee, S., Lee, K.H., Lee, D.: Ranking the sequences of fuzzy values. Information Sciences 160, 41–52 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lee, E.S., Li, R.J.: Comparison of fuzzy numbers based on the probability measure of fuzzy events. Computer and Mathematics with Applications 15, 887–896 (1987)

    Article  MathSciNet  Google Scholar 

  11. Liou, T.-S., Wang, M.J.: Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems 50, 247–255 (1992)

    Article  MathSciNet  Google Scholar 

  12. Liu, B.: Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg (2002)

    MATH  Google Scholar 

  13. Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  14. Liu, B.: A survey of credibility theory. Fuzzy Optimization and Decision Making 5, 1–19 (2006)

    Google Scholar 

  15. Liu, B., Liu, Y.-K.: Expected value of fuzzy variable and fuzzy expected value model. IEEE Transactions on Fuzzy Systems 10, 445–450 (2002)

    Article  Google Scholar 

  16. Modarres, M., Sadi-Nezhad, S.: Ranking fuzzy numbers by preference ratio. Fuzzy Sets and Systems 118, 429–436 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Peng, J., Mok, H.M.K., Tse, W.-M.: Fuzzy dominance based on credibility distributions. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 295–303. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Sun, H., Wu, J.: A new approach for ranking fuzzy numbers based on fuzzy simulation analysis method. Applied Mathematics and Computation 174, 755–767 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. Tran, L., Duckstein, L.: Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Sets and Systems 130, 331–341 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I)(II). Fuzzy Sets and Systems 118, 375–385, 387–405 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  21. Yager, R.R., Detyniecki, M., Bouchon-Meunier, B.: A context-dependent method for ordering fuzzy numbers using probabilities. Information Sciences 138, 237–255 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  22. Yager, R.R., Filev, D.: On ranking fuzzy numbers using valuations. International Journal of Intelligent Systems 14, 1249–1268 (1999)

    Article  MATH  Google Scholar 

  23. Yoon, K.P.: A probabilistic approach to rank complex fuzzy numbers. Fuzzy Sets and Systems 80, 3167–3176 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information Sciences, Huanggang Normal University, Huanggang City, Hubei, 438000, China

    Jin Peng, Huanbin Liu & Gang Shang

Authors
  1. Jin Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huanbin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gang Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University,, Block S1, Nanyang Avenue, 639798, Singapore

    Lipo Wang

  2. Life Science Research Center, School of Electronic Engineering, Xidian University,, 710071, Xi’an, Shaanxi, China

    Licheng Jiao

  3. School of Electrical and Electronic Engineering, Xidian University, 710071, Xi’an, China

    Guanming Shi

  4. School of Information Technology and Electrical Engineering, The University of Queensland, 4072, Brisbane, Queensland, Australia

    Xue Li

  5. College of Mathematics and Information Science, Hebei Normal University, 050016, Shijiazhuang, Hebei, P.R. China

    Jing Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Peng, J., Liu, H., Shang, G. (2006). Ranking Fuzzy Variables in Terms of Credibility Measure. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2006. Lecture Notes in Computer Science(), vol 4223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881599_24

Download citation

  • DOI: https://doi.org/10.1007/11881599_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45916-3

  • Online ISBN: 978-3-540-45917-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation