Skip to main content

A Ranking Approach with Inclusion Measure in Multiple-Attribute Interval-Valued Decision Making

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4482))

Abstract

This paper first presents a brief survey of the existing works on comparing and ranking any two interval numbers and then, on the basis of this, gives the inclusion measure approach to compare any two interval numbers. The monotonic inclusion measure is defined over the strict partial order set proposed by Moore and illustrate that the possibility degrees in the literature are monotonic inclusion measures defined in this paper; Then a series of monotonic inclusion measures are constructed based on t-norms. Finally, we give illustrations by using the monotonic inclusion measures and gain good results.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  Google Scholar 

  2. Da, Q.-L., Liu, X.-W.: Interval Number Linear Programming and Its Satisfactory Solution. Systems Engineering-theory and Practice 19, 3–7 (1999)

    Google Scholar 

  3. Xu, Z.-S., Da, Q.-L.: Possibility degree method for ranking interval numbers andits application. Systems Engineering-theory and Practice 18, 67–70 (2003)

    Google Scholar 

  4. Qiu, Q.-F., Li, H.-Z.: Measurement and Construct with Inclusion Degree for Priority of Interval Numbers. Operations Research and Management Science 12, 13–17 (2003)

    Google Scholar 

  5. Ishibuchi, H., Tanaka, H.: Multiobjective programming in optimization of the onterval objective function. European Journal of Operational Resarch 48, 219–225 (1990)

    Article  MATH  Google Scholar 

  6. Moore, R.E.: Method and Application of Interval Analysis. SIAM, Philadelphia (1979)

    Book  Google Scholar 

  7. Qiu, G.-F., et al.: A knowledge processing for intelligent systems based on inclusion degree. Expert Systems 4, 187–195 (2000)

    Google Scholar 

  8. Sengupta, A., Pal, T.K.: On comparing interval numbers. European Journal of Operational Research 127, 28–43 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, W.-X., Leung, Y.: The Uncertainty Reasoning Principles. Xi’an Jiaotong University Press, Xi’an (1996a)

    Google Scholar 

  10. Klir, G.J., Yuan, B.: Fuzzy Logic: Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  11. Zhang, Q., et al.: A Ranking Approach for Interval Numbers in Uncertain Multiple Attribute Decision Making Problems. Systems Engineering-theory and Practice 19, 129–132 (1999)

    Google Scholar 

  12. Smets, P., Magrez, P.: Implication in fuzzy logic. Int. J. Approximate reasoning 1, 327–347 (1987)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Kosko, B.: Fuzzy entropy and conditioning. Inform. Sci 40, 165–174 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bodjanova, S.: Approximation of fuzzy concepts in decision making. Fuzzy Sets and Systems 85, 23–29 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kaburlasos, V.G., Petridis, V.: Fuzzy lattice neurocomputing (FLN): a novel connectionist scheme for versatile learning and decision daking by clustering. Internat. J. Comput. Appl. 4, 31–43 (1997)

    Google Scholar 

  17. Petridis, V., Kaburlasos, V.G.: Fuzzy lattice neural network (FLNN): a hybrid model for learning. IEEE Trans. Neural Networks 9, 877–890 (1998)

    Article  Google Scholar 

  18. Zhang, W.-X., Qiu, G.-F.: Uncertain Decision Making Based On Rough Sets. Tsinghua University Press, Beijing (2005)

    Google Scholar 

  19. Zhang, W.-X., Leung, Y., Wu, W.-Z.: Information Systems and Knowledge Discovery. Science Press, Beijing (2003)

    Google Scholar 

  20. Sinha, D., Dougherty, E.R.: Fuzzication of set inclusion: theory and applications. Fuzzy Sets and Systems 55, 15–42 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  21. Frago, N.: Morfologia matematica borrosa basada en operadores generalizados de Łukasiewicz: procesiamento de imagines. Ph.D. Thesis, Universidal publica de Navarra (1996)

    Google Scholar 

  22. Young, V.R.: Fuzzy subsethood. Fuzzy Sets and Systems 77, 371–384 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, HY., Su, YJ. (2007). A Ranking Approach with Inclusion Measure in Multiple-Attribute Interval-Valued Decision Making. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2007. Lecture Notes in Computer Science(), vol 4482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72530-5_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72530-5_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72529-9

  • Online ISBN: 978-3-540-72530-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics