Skip to main content

On the Classification and the Dependencies of the Ordering Methods

  • Chapter
Fuzzy Logic Foundations and Industrial Applications

Part of the book series: International Series in Intelligent Technologies ((ISIT,volume 8))

Abstract

In this paper, we classify all the approaches to order fuzzy quantities into three classes. Then we focus our attention on the investigation of dependency among the elements of the first class of ordering approaches.

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

Access this chapter

eBook
USD 16.99
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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. J.M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems 4 (1980) 207–219.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. R.R. Yager, Ranking fuzzy subsets over the unit interval, Proc. CDC (1978) 1435–1437.

    Google Scholar 

  4. R.R. Yager, On choosing between fuzzy subsets, Kybernetes 9 (1980) 151–154.

    Article  MATH  Google Scholar 

  5. R.R. Yager, A procedure for ordering fuzzy sets of the unit interval, Information Sciences 24 (1981) 143–161.

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Liou and J. Wang, Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems 50 (1992) 247–255.

    Article  MathSciNet  Google Scholar 

  7. F. Choobineh and H. Li, An index for ordering fuzzy numbers, Fuzzy Sets and Systems 54 (1993) 287–294.

    Article  MathSciNet  Google Scholar 

  8. L. Campos and A. Munoz, A subjective approach for ranking fuzzy numbers, Fuzzy Sets and Systems 29 (1989) 145–153.

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Chang, Ranking of fuzzy utilities with triangular membership functions, in: Proceedings of International Conference on Policy Analysis and Systems (1981) 263–272.

    Google Scholar 

  10. R. Jain, A procedure for multiple-aspect decision making using fuzzy set, International Journal of Systems Sciences 8 (1977) 1–7.

    Article  MATH  Google Scholar 

  11. EE. Kerre, The use of fuzzy set theory in eletrocardiological diagnostics, in: Approximate reasoning in decision-analysis (North-Holland Publishing Company, 1992) 277–282.

    Google Scholar 

  12. X. Wang, A class of approches to ordering alternatives, MSc thesis, Taiyuan University of Technology, 1987 (in Chinese).

    Google Scholar 

  13. S. Chen, Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems 17 (1985) 113–129.

    Article  MathSciNet  MATH  Google Scholar 

  14. K. Kim and K. S. Park, Ranking fuzzy numbers with index of optimism, Fuzzy Sets and Systems 35 (1990).

    Google Scholar 

  15. S.M. Baas and H. Kwakernaak, Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatic 13 (1977) 47–58.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. F. Baldwin and N. C. F. Guild, Comparison of fuzzy sets on the same decision space, Fuzzy Sets and Systems 2 (1979) 213–231.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information Sciences 30 (1983) 183–224.

    Article  MathSciNet  MATH  Google Scholar 

  18. K. Nakamura, Preference relations on a set of fuzzy utilities as a basis for decision making, Fuzzy Sets and Systems 20 (1986) 147–162.

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Delgado, J. L. Verdegay and M. A. Vila, Aprocedure for ranking fuzzy numbers, Fuzzy Sets and Systems 26 (1988) 49–62.

    Article  MathSciNet  MATH  Google Scholar 

  20. W. Kolodziejczyk, Orlovsky’s concept of decision-making with fuzzy preference relation: further results, Fuzzy Sets and Systems 19 (1990) 197–212.

    MathSciNet  Google Scholar 

  21. J. J. Saade and H. Schwarzlander, Ordering fuzzy sets over the real line: an approach based on decision making under uncertainty, Fuzzy Sets and Systems 50 (1992) 237–246.

    Article  MathSciNet  Google Scholar 

  22. Y. Yuan, Criteria for evaluating fuzzy ranking methods, Fuzzy Sets and Systems 43 (1991) 139–157.

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Chen and C. Hwang, Fuzzy Multiple Attribute Decision Making, (Springer-Verlag Berlin Heideberge, 1992) 101–486.

    MATH  Google Scholar 

  24. X. Wang and D. Ruan, On the transitivity of fuzzy preference relations in ranking fuzzy numbers, in: Fuzzy Set Theory and Advanced Mathematical Applications (Kluwer Academic Publishers, 1995) 155–173.

    Chapter  Google Scholar 

  25. T.L. Saaty, Fuzzy hierarchical analysis (McGraw-Hill, 1980).

    Google Scholar 

  26. J. J. Buckley and S. Chanas, A fast method of ranking alternatives using fuzzy numbers, Fuzzy Sets and Systems 30 (1989) 337–339.

    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

© 1996 Kluwer Academic Publishers

About this chapter

Cite this chapter

Wang, X., Kerre, E. (1996). On the Classification and the Dependencies of the Ordering Methods. In: Ruan, D. (eds) Fuzzy Logic Foundations and Industrial Applications. International Series in Intelligent Technologies, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1441-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-1441-7_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8627-1

  • Online ISBN: 978-1-4613-1441-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics