Skip to main content
SpringerLink
Log in
Book cover

Fuzzy Information and Engineering pp 503–512Cite as

A Method for Estimating Criteria Weights from Intuitionistic Preference Relations

  • Conference paper

Part of the book series: Advances in Soft Computing ((AINSC,volume 40))

Abstract

Intuitionistic preference relation is a powerful means to express decision maker’s intuitionistic preference information over criteria in the process of multi-criteria decision making. In this paper, we define the concept of consistent intuitionistic preference relation and give the equivalent interval fuzzy preference relation of an intuitionistic preference relation. Then we develop a method for estimating criteria weights from intuitionistic preference relations, and finally, we use two numerical examples to illustrate the developed method.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Atanassov, K., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31, 343–349 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. De, S.K., Biswas, R., Roy, A.R.: Some operations on intuitionistic fuzzy sets. Fuzzy Sets and Systems 114, 477–484 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117, 209–213 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133, 227–235 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bustince, H., Burillo, P.: Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 74, 237–244 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gerstenkorn, T., Mańko, J.: Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems 44, 39–43 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hong, D.H., Hwang, S.Y.: Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets and Systems 75, 77–81 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hung, W.L., Wu, J.W.: Correlation of intuitionistic fuzzy sets by centroid method. Information Sciences 144, 219–225 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mitchell, H.B.: A correlation coefficient for intuitionistic fuzzy sets. International Journal of Intelligent Systems 19, 483–490 (2004)

    Article  MATH  Google Scholar 

  11. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114, 505–518 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Li, D.F., Cheng, C.T.: New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition letters 23, 221–225 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Liang, Z.Z., Shi, P.F.: Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Letters 24, 2687–2693 (2003)

    Article  MATH  Google Scholar 

  14. Grzegorzewski, P.: Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems 148, 319–328 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wang, W.Q., Xin, X.L.: Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters 26, 2063–2069 (2005)

    Article  Google Scholar 

  16. Deschrijver, G., Cornelis, C., Kerre, E.E.: On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems 12, 45–61 (2004)

    Article  Google Scholar 

  17. Deschrijver, G., Kerre, E.E.: Implicators based on binary aggregation operators in interval-valued fuzzy set theory. Fuzzy Sets and Systems 153, 229–248 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Park, J.H.: Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 22, 1039–1046 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Park, J.H., Park, J.K.: Hausdorffness on generalized intuitionistic fuzzy filters. Information Sciences 168, 95–110 (2004)

    MATH  MathSciNet  Google Scholar 

  20. Mondal, T.K., Samanta, S.K.: Generalized intuitionistic fuzzy sets. Journal of Fuzzy Mathematics 10, 839–861 (2002)

    MATH  MathSciNet  Google Scholar 

  21. Deschrijver, G., Kerre, E.E.: Uninorms in L*-fuzzy set theory. Fuzzy Sets and Systems 148, 243–262 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. International Journal of Approximate Reasoning 35, 55–95 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Gutiérrez García, J., Rodabaugh, S.E.: Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued “intuitionistic” sets, “intuitionistic” fuzzy sets and topologies. Fuzzy Sets and Systems 156, 445–484 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  24. Dudek, W.A., Davvaz, B., Jun, Y.B.: On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups. Information Sciences 170, 251–262 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  25. Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems 35, 417–433 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  26. Szmidt, E., Kacprzyk, J.: Using intuitionistic fuzzy sets in group decision making. Control and Cybernetics 31, 1037–1053 (2002)

    Google Scholar 

  27. Xu, Z.S.: Intuitionistic preference relations and their application in group decision making. Information Sciences, in press (2007)

    Google Scholar 

  28. Herrrera, F., Martínez, L., Sánchez, P.J.: Managing non-homogeneous information in group decision making. European Journal of Operational Research 166, 115–132 (2005)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  30. Xu, Z.S.: On compatibility of interval fuzzy preference matrices. Fuzzy Optimization and Decision Making 3, 217–225 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  31. Xu, Z.S.: A C-OWA operator based approach to decision making with interval fuzzy preference relation. International Journal of Intelligent Systems 21, 1289–1298 (2006)

    Article  MATH  Google Scholar 

  32. Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems 1, 155–167 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  33. Tanino, T.: Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems 12, 117–131 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  34. Kacprzyk, J., Roubens, M.: Non-conventional preference relations in decision-making. Springer, Berlin (1988)

    MATH  Google Scholar 

  35. Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems 97, 33–48 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  36. Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating multiplicative preference relations in a multipurpose decision-making based on fuzzy preference relations. Fuzzy Sets and Systems 122, 277–291 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  37. Xu, Z.S., Da, Q.L.: The uncertain OWA operator. International Journal of Intelligent Systems 17, 569–575 (2002)

    Article  MATH  Google Scholar 

  38. Xu, Z.S., Da, Q.L.: A least deviation method to obtain a priority vector of a fuzzy preference relation. European Journal of Operational Research 164, 206–216 (2005)

    Article  MATH  Google Scholar 

  39. Chiclana, F., Herrera, F., Herrera-Viedma, E.: A note on the internal consistency of various preference representations. Fuzzy Sets and Systems 131, 75–78 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  40. Xu, Z.S.: Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, Beijing (2004)

    Google Scholar 

  41. Wang, Y.M., Yang, J.B., Xu, D.L.: A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets and Systems 152, 475–498 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management Science and Engineering, School of Economics and Management, Tsinghua University, Beijing 100084, China

    Zeshui Xu

Authors
  1. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Bing-Yuan Cao

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xu, Z. (2007). A Method for Estimating Criteria Weights from Intuitionistic Preference Relations. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_55

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71441-5_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71440-8

  • Online ISBN: 978-3-540-71441-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation