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Multicriteria Group Decision Making: Optimal Priority Synthesis from Pairwise Comparisons

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Abstract

We propose an optimization based hybrid approach for multicriteria group decision making that takes advantage of aggregating individual judgments and aggregating individual priority methods. Different error structures and criteria with particular emphasis on weighted least square measure and weighted least logarithmic square measure for additive and multiplicative error structures are studied. We evaluate also the statistical properties of the derived group preference and new measures to assess consistency. The proposed methods provide an iterative and flexible framework for guiding group decision making.

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References

  1. KEENEY, L. R., and RAIFFA, H., Decisions with Multiple Objectives: Preferences and Value Tradeoffs, Wiley, New York, NY, 1976.

    Google Scholar 

  2. YU, P. L., Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions, Plenum Press, New York, NY, 1989.

    Google Scholar 

  3. DYER, J. S., Remarks on the Analytic Hierarchy Process, Management Science, Vol. 36, pp. 249–258, 1990.

    Article  MathSciNet  Google Scholar 

  4. HARKER, P. T., and VARGAS, L. G., Reply to “Remarks on the Analytic Hierarchy Process,” Management Science, Vol. 36, pp. 269–273, 1990.

  5. SAATY, T. L., An Exposition of the AHP in Reply to the Paper “Remarks on the Analytic Hierarchy Process,” Management Science, Vol. 36, pp. 259–268, 1990.

  6. PRATT, J. W., RAIFFA, H., and SCHLAIFER, R., Introduction to Statistical Decision Theory, MIT Press, Cambridge, Massachusetts, 1995.

    Google Scholar 

  7. SAATY, T. L., The Analytic Hierarchy Process, McGraw-Hill Book Company, New York, NY, 1980.

    MATH  Google Scholar 

  8. CARRIZOSA, E., and MORALES, D. R., Combining Minsum and Minmax: A Goal Programming Approach, Operations Research, Vol. 49, pp. 169–174, 2004.

    Article  Google Scholar 

  9. COUGER, J. D., Creative Problem Solving and Opportunity Finding, Boyd and Fraser Publishing Company, Ferncroft Village, Danvers, Massachusetts, 1995.

    Google Scholar 

  10. KHORRAMSHAHGOL, R., and MOUSTAKIS, V. S., Delphic Hierarchy Process: A Methodology for Priority Setting Derived from the Delphi Method and Analytical Hierarchy Process, European Journal of Operational Research, Vol. 37, pp. 347–354, 1988.

    Article  MATH  Google Scholar 

  11. SCHMOLDT, D.L., KANGAS, J., MENDOZA, G. A., and PESONEN, M., The Analytic Hierarchical Process in Natural Resource and Environmental Decision Making, Kluwer Academic Publishers, Dordrecht, Netherlands, 2001.

    Google Scholar 

  12. KHASNABIS, S., ALSAIDI, E., LIU, L., and ELLIS, R. D., Comparative Study of Two Techniques of Transit Performance Assessment: AHP and GAT, Journal of Transportation Engineering, ASCE, Vol. 128, pp. 499–508, 2000.

    Article  Google Scholar 

  13. SAATY, T. L., A Scaling Method for Priorities in Hierarchical Structures, Journal of Mathematical Psychology, Vol. 15, pp. 57–68, 1977.

    Article  MathSciNet  Google Scholar 

  14. SAATY, T. L., Fundamentals of Decision-Making and Priority Theory with the AHP, RWS Publications, Pittsburgh, Pennsylvania, 1994.

    Google Scholar 

  15. SAATY, T. L., Axiomatic Foundations of the Analytic Hierarchy Process, Management Science, Vol. 32, pp. 841–855, 1983.

    MathSciNet  Google Scholar 

  16. CHU, A. T. W., KALABA, R. E., and SPRINGARN, K., A Comparison of Two Methods for Determining the Weights of Belonging to Fuzzy Set, Journal of Optimization Theory and Applications, Vol. 27, pp. 531–538, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  17. SUN, L., and DENG, X., Weight Analysis in Evaluation Systems, Journal of Systems Science and Systems Engineering, Vol. 6, pp. 137–147, 1997.

    Google Scholar 

  18. CRAWFORD, G., and WILLIAMS, C., A Note on the Analysis of Subjective Judgment Matrices, Journal of Mathematical Psychology, Vol. 29, pp. 387–405, 1985.

    Article  MATH  Google Scholar 

  19. ACZEL, J., and SAATY, T., Procedures for Synthesizing Ratio Judgments, Journal of Mathematical Psychology, Vol. 27, pp. 93–102, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  20. RAMANATHAN, R., and GANESH, L. S., Group Preference Aggregation Methods Employed in AHP: An Evaluation and Intrinsic Process for Deriving Members’ Weightages, European Journal of Operational Research, Vol. 79, pp. 249–265, 1994.

    Article  MATH  Google Scholar 

  21. FORMAN, E., and PENIWATI, K., Aggregating Individual Judgments and Priorities with the Analytic Hierarchy Process, European Journal of Operational Research, Vol. 108, pp. 165–169, 1998.

    Article  MATH  Google Scholar 

  22. ZAHIR, S., Geometry of Decision-Making and the Vector Space Formulation of the Analytic Hierarchy Process, European Journal of Operational Research, Vol. 112, pp. 373–396, 1999.

    Article  MATH  Google Scholar 

  23. TRIANTAPHYLLOU, E., Multicriteria Decision-Making Methods: A Comprehensive Study, Kluwer Academic Publishers, Dordrecht, Netherlands, 2000.

    Google Scholar 

  24. DYER, J. S., and WENDELL, R. E. A Critique of the Analytic Hierarchy Process” Working Paper 84/85-4-24, Department of Management, University of Texas, Austin, Texas, 1985.

  25. ARBEL, A., and VARGAS, L. G., The Analytic Hierarchy Process with Interval Judgments, Multiple-Criteria Decision-Making, Edited by A. Goicoechea and L. Duckstein, Springer, New York, NY, pp. 61–70, 1992.

    Google Scholar 

  26. PAULSON, D., and ZAHIR, M. S., Consequences for Uncertainty in the Analytic Hierarchy Process: A Simulation Approach, European Journal of Operational Research, Vol. 87, pp. 45–56, 1995.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Catholic University of America, Washington, DC, USA

    L. Sun (Assistant Professor)

  2. Department of Information, Risk andOperations Management, University of Texa, Austin, Texas, USA

    B. S. Greenberg (Professor)

Authors
  1. L. Sun
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  2. B. S. Greenberg
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Additional information

Communicated by P.L. Yu

The authors thank Professor P.I. Yu and two anonymous reviewers for insightful comments and helpful suggestions.

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Sun, L., Greenberg, B.S. Multicriteria Group Decision Making: Optimal Priority Synthesis from Pairwise Comparisons. J Optim Theory Appl 130, 317–339 (2006). https://doi.org/10.1007/s10957-006-9107-7

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  • DOI: https://doi.org/10.1007/s10957-006-9107-7

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