Deriving Weights from Group Fuzzy Pairwise Comparison Judgement Matrices

  • Tarifa S. Almulhim
  • Ludmil Mikhailov
  • Dong-Ling Xu
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 206)


Several Multi-Criteria Decision Making (MCDM) methods involve pairwise comparisons to obtain the preferences of decision makers (DMs). This paper proposes a fuzzy group prioritization method for deriving group priorities/weights from fuzzy pairwise comparison matrices. The proposed method considers the different importance weights of multiple DMs by extending the Fuzzy Preferences Programming Method (FPP). The elements of the group pairwise comparison matrices are presented as fuzzy numbers rather than exact numerical values in order to model the uncertainty and imprecision in the DMs’ judgments. Unlike the known fuzzy prioritization techniques, the proposed method is able to derive crisp weights from incomplete and fuzzy set of comparison judgments and doesn’t require additional aggregation procedures. A prototype of a decision tool is developed to assist DMs to use the proposed method for solving fuzzy group prioritization problems. A detailed numerical example is used to illustrate the proposed approach.


Fuzzy Non-linear Programming Fuzzy Preferences Programming Method Multiple Criteria Decision-Making Triangular Fuzzy Number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Choo, E., Wedley, W.: A common framework for deriving preference values from pairwise comparison matrices. Computers & Operations Research 31, 893–908 (2004)zbMATHCrossRefGoogle Scholar
  2. 2.
    Ittersum, K.V., Pennings, J.M., Wansink, B., van Trijp, H.C.: The validity of attribute-importance measurement: A review. Journa of Business Research 60, 1177–1190 (2007)CrossRefGoogle Scholar
  3. 3.
    Edwards, W.: How to use multiattribute utility measurement for social decision making. IEEE Transactions on Systems, Man, and Cybernetics 7, 326–340 (1977)CrossRefGoogle Scholar
  4. 4.
    Von Winterfeldt, D., Edwards, W.: Decision analysis and behavioural research. Cambridge University Press, Cambridge (1986)Google Scholar
  5. 5.
    Edwards, W., Barron, F.H.: SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes 60, 306–325 (1994)CrossRefGoogle Scholar
  6. 6.
    Thurstone, L.: A law of comparative judgment. Psychological Review 34, 273–286 (1927)CrossRefGoogle Scholar
  7. 7.
    Saaty, T.L.: The analytic hierarchy process: Planning, Priority setting, resource allocation. McGraw-Hill, NY (1980)zbMATHGoogle Scholar
  8. 8.
    Saaty, T.L.: Decision making with dependence and feedback: the Analytic Network Process. RWA Publications, PA (1996)Google Scholar
  9. 9.
    Brans, J., Mareschal, B.: Promethee methods: In multiple criteria decision analysis: state of the art surveys. International Series in Operations Research & Management Science 78, 163–186 (2005)CrossRefGoogle Scholar
  10. 10.
    Xu, D.L., Yang, J.B., Lama, J.: Group-based ER–AHP system for product project screening. Expert Systems with Applications 35, 1909–1929 (2008)CrossRefGoogle Scholar
  11. 11.
    Chu, A., Kalaba, R., Springam, K.: A comparison of two methods for determining the weights of belonging to fuzzy sets. Journal of Optimization Theory and Application 27, 531–541 (1979)zbMATHCrossRefGoogle Scholar
  12. 12.
    Saaty, T.L., Vargas, L.G.: Comparison of Eigenvalue, Logarithmic Least Squares and Least Squares Methods in Estimating Rations. Mathematical Modelling 5, 309–324 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Mikhailov, L.: A Fuzzy Programming Method for Deriving Prioritises in Analytic Hierarchy Process. The Journal of Operational Research Society 51, 341–349 (2000)zbMATHGoogle Scholar
  14. 14.
    Buckley, J.J.: Fuzzy Hierarchical Analysis. Fuzzy Sets and System 17, 233–247 (1984)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Laarhoven, P.J.M., Pedrycz, W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and System 11, 229–241 (1983)zbMATHCrossRefGoogle Scholar
  16. 16.
    Chang, D.: Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research 95, 649–655 (1996)zbMATHCrossRefGoogle Scholar
  17. 17.
    Mikhailov, L.: Deriving priorities from fuzzy pair-wise comparison judgments. Fuzzy Sets and System 134, 365–385 (2003)zbMATHCrossRefGoogle Scholar
  18. 18.
    Tiwari, R.N., Dharmar, S., Rao, J.R.: Fuzzy goal programming-an additive model. Fuzzy Sets and System 24, 27–34 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Higham, D.J., Higham, N.J.: MATLAB Guide, 2nd edn. SIAM (2005)Google Scholar
  20. 20.
    Mikhailov, L., Didehkhani, H., Sadi-Nezhad, S.: Weighted Prioritization Models in the Fuzzy Analytic Hierarchy Process. International Journal of Information Technology & Decision Making 10, 681–694 (2011)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tarifa S. Almulhim
    • 1
  • Ludmil Mikhailov
    • 1
  • Dong-Ling Xu
    • 1
  1. 1.Manchester Business SchoolUniversity of ManchesterManchesterUK

Personalised recommendations