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A Statistical Study for Quantifier-Guided Dominance and Non-Dominance Degrees for the Selection of Alternatives in Group Decision Making Problems

  • J. M. Tapia
  • M. J. del Moral
  • S. Alonso
  • E. Herrera-Viedma
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 643)

Abstract

In a group decision making problem the selection process is decisive to find a solution. In these problems there is a widespread agreement to use fuzzy preference relations to express different preferences about possible alternatives. Previous papers have proposed different selection methods in this context. An usual way is the use of a ranking method to obtain a classification of the alternatives. One of the methods used is based on two choice degrees: quantifier guided dominance degree and quantifier guided non-dominance degree. This paper presents a limited comparative study about the application of the two previously cited quantifier guided choice degrees. By using statistical tools, it is concluded that both choice degrees can offer significantly different rankings of alternatives. In addition, it has been observed that the variability of the alternatives in the ranking obtained by dominance choice degree is generally greater, which may facilitate a better discrimination between different alternatives.

Keywords

Group decision making Fuzzy preferences Dominance choice degree Non-Dominance choice degree 

Notes

Acknowledgements

The authors would like to acknowledge FEDER financial support from the Projects TIN2013-40658-P and TIN2016-75850-R.

References

  1. 1.
    Chiclana, F., Herrera, F., Herrera-Viedma, E., Martinez, L.: A note on the reciprocity in the aggregation of fuzzy preference relations using OWA operators. Fuzzy Sets Syst. 137(1), 71–83 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Pedrycz, W., Parreiras, R., Ekel, P.: Fuzzy Multicriteria Decision-Making. Models, Methods and Applications. Wiley, Chichester (2011)zbMATHGoogle Scholar
  3. 3.
    Chiclana, F., Herrera, F., Herrera-Viedma, E., Poyatos, M.: A classification method of alternatives for multiple preference ordering criteria based on fuzzy majority. J. Fuzzy Math. 4, 801–813 (1996)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Millet, I.: The effectiveness of alternative preference elicitation methods in the analytic hierarchy process. J. Multi-Criteria Decis. Anal. 6(1), 41–51 (1997)CrossRefzbMATHGoogle Scholar
  6. 6.
    Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst. 18(2), 105–118 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst. 97(1), 33–48 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chiclana, F., Herrera, F., Herrera-Viedma, E.: A note on the internal consistency of various preference representations. Fuzzy Sets Syst. 131(1), 75–78 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Carlsson, C., Ehrenberg, D., Eklund, P., Fedrizzi, M., Gustafsson, P., Lindholm, P., Merkuryeva, G., Riissanen, T., Ventre, A.G.S.: Consensus in distributed soft environments. Eur. J. Oper. Res. 61(1–2), 165–185 (1992)CrossRefGoogle Scholar
  10. 10.
    Perez, I.J., Cabrerizo, F.J., Herrera-Viedma, E.: A mobile decision support system for dynamic group decision-making problems. IEEE Trans. Syst. Man Cybernet. Part A Syst. Hum. 40(6), 1244–1256 (2010)CrossRefGoogle Scholar
  11. 11.
    Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst. 49(1), 21–31 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kacprzyk, J., Nurmi, H., Fedrizzi, M.: Consensus Under Fuzziness, vol. 10. Kluwer Academic Publishers, Dordrecht (1997)zbMATHGoogle Scholar
  13. 13.
    Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Choice processes for non-homogeneous group decision making in linguistic setting. Fuzzy Sets Syst. 94(3), 287–308 (1998)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Some induced ordered weighted averaging operators and their use for solving group decision making problems based on fuzzy preference relations. Eur. J. Oper. Res. 182(1), 383–399 (2007)CrossRefzbMATHGoogle Scholar
  15. 15.
    Dubois, D., Prade, H.: A review of fuzzy set aggregation connectives. Inf. Sci. 36(1–2), 85–121 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)CrossRefzbMATHGoogle Scholar
  17. 17.
    Herrera, F., Herrera-Viedma, E., Chiclana, F.: A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making. Int. J. Intell. Syst. 18(6), 689–707 (2003)CrossRefzbMATHGoogle Scholar
  18. 18.
    Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, New Jersey (1988)zbMATHGoogle Scholar
  19. 19.
    Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18(9), 953–969 (2003)CrossRefzbMATHGoogle Scholar
  20. 20.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybernet. 18(1), 183–190 (1988)CrossRefzbMATHGoogle Scholar
  21. 21.
    Yager, R.R.: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11(1), 49–73 (1996)CrossRefGoogle Scholar
  22. 22.
    Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math Appl. 9(1), 149–184 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Herrera, F., Herrera-Viedma, E.: Choice functions and mechanisms for linguistic preference relations. Eur. J. Oper. Res. 120(1), 144–161 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Siegel, S.: Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, New York (1956)zbMATHGoogle Scholar
  25. 25.
    Lehmann, E.: Nonparametrics: Statistical Methods Based on Ranks. Holden-Day, San Francisco (1975)zbMATHGoogle Scholar
  26. 26.
    Wilcoxon, F.: Individual comparisons by ranking methods. Biom. Bull. 1(6), 80–83 (1945)CrossRefGoogle Scholar
  27. 27.
    Del Moral Avila, M.J., Tapia Garcia, J.M.: Tecnicas estadisticas aplicadas. Grupo Editorial Universitario, Granada (2006)Google Scholar
  28. 28.
    Rohatgi, V.K., Saleh, A.K.M.E.: An Introduction to Probability and Statistics, 2nd edn. Wiley-Interscience, New York (2011)zbMATHGoogle Scholar
  29. 29.
    Chiclana, F., Garcia, J.M.T., del Moral Avila, M.J., Herrera-Viedma, E.: A statistical comparative study of different similarity measures of consensus in group decision making. Inf. Sci. 221, 110–123 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University of GranadaGranadaSpain

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