A TFN-Based AHP Model for Solving Group Decision-Making Problems

  • Jian Cao
  • Gengui Zhou
  • Feng Ye
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3801)


Because the expert(s) usually give the judgment with an uncertainty degree in general decision-making problems, combined the analytic hierarchy process (AHP) with the basic theory of the triangular fuzzy number (TFN), a TFN-based AHP model is suggested. The proposed model makes decision-makers’ judgment more accordant with human thought mode and derives priorities from TFN-based judgment matrices regardless of their consistency. In addition, formulas of the model are normative, they can be operated by programming easily and no human intervention is needed while applying the model-based software system. The results of an illustrative case indicate that, by applying the proposed model, fair and reasonable conclusions are obtained and the deviation scope of the priority weight of every decision element is given easily.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  2. 2.
    Saaty, T.L.: How to Make a Decision: The AHP. European Journal of Operational Research 48, 9–26 (1990)zbMATHCrossRefGoogle Scholar
  3. 3.
    Millet, I., Satty, T.L.: On the Relativity of Relative Measures – Accommodating Both Rank Preservation and Rank Reversals in the AHP. European Journal of Operational Research 121, 205–212 (2000)zbMATHCrossRefGoogle Scholar
  4. 4.
    Chang, D.Y.: Application of the Extent Analysis Method on Fuzzy AHP. European Journal of Operational Research 95, 649–655 (1996)zbMATHCrossRefGoogle Scholar
  5. 5.
    Zhu, K.J., Yu, J.: A Discussion on Extent Analysis Method and Applications of Fuzzy AHP. European Journal of Operational Research 116, 450–456 (1999)zbMATHCrossRefGoogle Scholar
  6. 6.
    Kaufmamm, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic Theory and Applications. Van Nostrand Reinhold, New York (1991)Google Scholar
  7. 7.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  8. 8.
    Yu, C.S.: A GP-AHP Method for Solving Group Decision-making Fuzzy AHP Problems. Computer & Operation Research 29, 1969–2001 (2002)zbMATHCrossRefGoogle Scholar
  9. 9.
    Grawford, G., Williams, C.A.: A Note on the Analysis of Subjective Judgment Matrices. Journal of Mathematical Psychology 29, 387–405 (1985)CrossRefGoogle Scholar
  10. 10.
    Kwiesielewicz, M., Uden, E.V.: An Additional Result of Monsuur’s Paper about Intrinsic Consistency Threshold for Reciprocal Matrices. European Journal of Operational Research 140, 88–92 (2002)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jian Cao
    • 1
  • Gengui Zhou
    • 1
  • Feng Ye
    • 1
  1. 1.Institute of Information Intelligence and Decision-making OptimizationZhejiang University of TechnologyHangzhouChina

Personalised recommendations