Skip to main content
SpringerLink
Log in
SpringerLink
Log in

A New Method for Decision Making in the Intuitionistic Fuzzy Setting

  • Conference paper
Artificial Intelligence and Soft Computing – ICAISC 2008 (ICAISC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5097))

Included in the following conference series:

Abstract

The main problem of known methods for Multiple Criteria Decision Making in the Intuitionistic Fuzzy setting is that they are generally based on the intermediate type reduction. Such approaches lead inevitable to the loss of important information. Another problem is the choice of an appropriate method for the local criteria aggregation taking into account their ranks. The aim of this paper is to present a new method which makes it possible to solve the first problem and facilitates the solution of the second one. The method is based on the Dempster-Shafer Theory (DST). It allows to solve the Multiple Criteria Decision Making problem without intermediate type reduction for different approaches to aggregation of the local criteria. The usefulness of elaborated method is illustrated with known example of Multiple Criteria Decision Making problem.

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 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Atanassov, K., Pasi, G., Yager, R.: Intuitionistic fuzzy interpretations of multi-person multicriteria decision making. In: Proceedings of 2002 First International IEEE Symposium Intelligent Systems, vol. 1, pp. 115–119 (2002)

    Google Scholar 

  3. Atanassov, K., Pasi, G., Yager, R., Atanassova, V.: Intuitionistic fuzzy group interpretations of multi-person multicriteria decision making. In: Proceedings of the Third Conference of the European Society for Fuzzy Logic and Technology EUSFLAT’2003, Zittau, September 10-12, pp. 177–182 (2003)

    Google Scholar 

  4. Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79, 403–405 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cornelis, C., Deschrijver, G., Kerre, 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 

  6. Chen, S.M., Tan, J.M.: Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67, 163–172 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dempster, A.P.: Upper and lower probabilities induced by a muilti-valued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dempster, A.P.: A generalization of Bayesian inference (with discussion). J. Roy. Stat. Soc., Series B 30(2), 208–247 (1968)

    MathSciNet  Google Scholar 

  9. Deschrijver, G., Cornelis, C., Kerre, E.: On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems 12(1), 45–61 (2004)

    Article  MathSciNet  Google Scholar 

  10. Deschrijver, G., Kerre, E.E.: On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Information Sciences 177, 1860–1866 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dimova, L., Sevastianov, P., Sevastianov, D.: MCDM in a fuzzy setting: investment projects assessment application. International Journal of Production Economics 100, 10–29 (2006)

    Article  Google Scholar 

  12. Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans. Systems Man Cybernet 23, 610–614 (1993)

    Article  MATH  Google Scholar 

  13. Goodman, I.R., Nguyen, H.T.: Uncertainty Models for Knowledge-Based System. North-Holand, Amsterdam (1985)

    Google Scholar 

  14. Grzegorzewski, P., Mrowka, E.: Some notes on (Atanassov’s) intuitionistic fuzzy sets. Fuzzy Sets and Systems 156, 492–495 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Honga, D.H., Choi, C.-H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114, 103–113 (2000)

    Article  Google Scholar 

  16. Jaulin, L., Kieffir, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)

    MATH  Google Scholar 

  17. Li, D.-F.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences 70, 73–85 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lin, L., Yuan, X.-H., Xia, Z.-Q.: Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. Journal of Computer and System Sciences 73, 84–88 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. Liu, H.-W., Wang, G.-J.: Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research 179, 220–233 (2007)

    Article  MATH  Google Scholar 

  20. Nikolova, M., Nikolov, M., Cornelis, C., Deschrijver, G.: Survey of the research on intuitionistic fuzzy sets. Advanced Studies in Contemporary Mathematics 4, 127–157 (2002)

    MATH  MathSciNet  Google Scholar 

  21. Moore, R.E.: Interval analysis. Prentice-Hall, Englewood Cliffs (1966)

    MATH  Google Scholar 

  22. Pasi, G., Atanassov, K., Melo Pinto, P., Yager, R., Atanassova, V.: Multi-person multi-criteria decision making: Intuitionistic fuzzy approach and generalized net model. In: Proceedings of the 10th ISPE International Conference on Concurrent Engineering Advanced Design, Production and Management Systems, Madeira, July 26-30, pp. 1073–1078 (2003)

    Google Scholar 

  23. Pasi, G., Yager, Y., Atanassov, K.: Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making:Generalized net approach. In: Proceedings of 2004 second International IEEE Conference Intelligent Systems, vol. 2, pp. 434–439 (2004)

    Google Scholar 

  24. Sevastjanov, P.: Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster-Shafer theory. Information Sciences 177, 4645–4661 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  25. Sevastjanov, P., Figat, P.: Aggregation of aggregating modes in MCDM. Synthesis of Type 2 and Level 2 fuzzy sets, Omega 35, 505–523 (2007)

    Google Scholar 

  26. Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  27. Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy sets in decision making. Notes IFS 2, 15–32 (1996)

    MathSciNet  Google Scholar 

  28. Szmidt, E., Kacprzyk, J.: Remarks on some applications on intuitionistic fuzzy sets in decision making. Notes IFS 2, 22–31 (1996)

    MATH  MathSciNet  Google Scholar 

  29. Szmidt, E., Kacprzyk, J.: Group decision making under intuitionistic fuzzy preference relations. In: Proc. Seventh Int. Conf. IMPU 1998, Paris, pp. 172–178 (1998)

    Google Scholar 

  30. Szmidt, E., Kacprzyk, J.: Applications ofintuitionistic fuzzy sets in decision making. In: Proc. Eighth Cong. EUSFLAT 1998, Pampelona, pp. 150–158 (1998)

    Google Scholar 

  31. Vasseur, P., Pegard, C., Mouad, E., Delahoche, L.: Perceptual organization approach based on Dempster-Shafer theory. Pattern Recognition 32, 1449–1462 (1999)

    Article  Google Scholar 

  32. Yager, R.R.: Multiple objective decision-making using fuzzy sets. International Journal of Man-Machine Studies 9, 375–382 (1979)

    Article  Google Scholar 

  33. Yager, R.R., Kacprzyk, J., Fedrizzi, M.: Advances in Dempster-Shafer Theory of Evidence. Wiley, New York (1994)

    MATH  Google Scholar 

  34. Zimmerman, H.J.: Fuzzy Sets, Decision-Making and Expert Systems. Kluwer Academic Publishers, Dordrecht (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Comp.& Information Sci., Technical University of Czestochowa, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Ludmila Dymova, Izabela Róg & Pavel Sevastjanov

Authors
  1. Ludmila Dymova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Izabela Róg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pavel Sevastjanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Leszek Rutkowski Ryszard Tadeusiewicz Lotfi A. Zadeh Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dymova, L., Róg, I., Sevastjanov, P. (2008). A New Method for Decision Making in the Intuitionistic Fuzzy Setting. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2008. ICAISC 2008. Lecture Notes in Computer Science(), vol 5097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69731-2_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69731-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69572-1

  • Online ISBN: 978-3-540-69731-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation