Issues in Aggregating AHP/ANP Scales

  • William C. Wedley
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 4)


Additive synthesis of ratio scales requires the scales to be in a common unit of measure. Unlike regular ratio scales, the unit of measure for relative ratio scales is not readily identifiable. That obscurity complicates the problem of achieving commensurability before multiple scales are synthesized. Examples are given of how conventional AHP may fail to aggregate commensurable values. Several techniques are presented that address the issue of commensurability. The analysis is then extended to more complex forms of aggregation such as benefit/cost analysis and the ANP.


Analytic Hierarchy Process General Motor Relative Ratio Ratio Scale Criterion Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Belton, V., Gear, A.E.: On a shortcoming of Saaty’s method of analytic hierarchies. Omega 11, 228–230 (1983)CrossRefGoogle Scholar
  2. Bernhard, R.H., Canada, J.R.: Some problems in using benefit/cost ratios with the Analytic Hierarchy Process. The Engineering Economist 36(1), 56–65 (1990)CrossRefGoogle Scholar
  3. Choo, E.U., Schoner, B., Wedley, W.C.: Interpretation of criteria weights in multi-criteria decision making. Computers and Industrial Engineering Journal 37, 527–541 (1999)CrossRefGoogle Scholar
  4. Dyer, J.S.: Remarks on the analytic hierarchy process. Management Science 36(3), 249–258 (1990)CrossRefMathSciNetGoogle Scholar
  5. Finan, J.S., Hurley, W.J.: The analytic hierarchy process: can wash criteria be ignored? Computers & Operations Research 29, 1025–1030 (2002)zbMATHCrossRefGoogle Scholar
  6. Ford Motor Company, Annual Report (2008)Google Scholar
  7. General Motors Corp., Form 10-K, March 5 (2009)Google Scholar
  8. Harker, P.T., Vargas, L.G.: The theory of ratio scale estimation: Saaty’s analytic hierarchy process. Management Science 33(11), 1383–1403 (1987)CrossRefMathSciNetGoogle Scholar
  9. Harker, P.T., Vargas, L.G.: Reply to Remarks on the analytic hierarchy process. J. S. Dyer, Management Science 36(3), 269–275 (1990)CrossRefMathSciNetGoogle Scholar
  10. Kinoshita, E., Nakanishi, M.: Proposal of new AHP model in light of dominant relationship among alternatives. Journal of the Operations Research Society of Japan 42(2), 180–197 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  11. Kinoshita, E., Sekitani, K., Shi, J.: Mathematical properties of dominant AHP and concurrent convergence method. Journal of the Operations Research Society of Japan 45(2), 198–213 (2002)zbMATHMathSciNetGoogle Scholar
  12. Kinoshita, E., Sugiura, S.: A comparison of dominant AHP and similar dominant models. Journal of Research Institute of Meijo University 7, 113–116 (2008)Google Scholar
  13. Michell, J.: Quantitative science and the definition of measurement in psychology. British Journal of Psychology 88, 355–383 (1997)Google Scholar
  14. Michell, J.: Measurement in Psychology. Cambridge University Press, Cambridge (1999)CrossRefGoogle Scholar
  15. Millet, I., Schoner, B.: Incorporating negative values into the Analytic Hierarchy Process. Computers and Operations Research 32, 3163–3173 (2005)zbMATHCrossRefGoogle Scholar
  16. Saaty, T.L.: Rank generation, preservation, and reversal in the analytic hierarchy decision process. Decision Sciences 18, 157–177 (1987)CrossRefGoogle Scholar
  17. Saaty, T.L.: An exposition of the AHP in reply to the paper Remarks on the analytic hierarchy process. Management Science 36(3), 259–268 (1990)CrossRefMathSciNetGoogle Scholar
  18. Saaty, T.L.: Rank preservation and reversal: the AHP ideal and distributive modes. Mathematical and Computer Modelling 17(6), 1–16 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  19. Saaty, T.L.: Fundamental of decision making and priority theory. RWS Publications, Pittsburgh (1994)Google Scholar
  20. Saaty, T.L.: Decision Making with Dependence and Feedback: The Analytic Network Process. RWS Publications, Pittsburgh (1996)Google Scholar
  21. Saaty, T.L.: Scales from measurement – not measurement from scales. In: Proceedings of the 17th International Conference on Multiple Criteria Decision Making, Whistler, B. C. Canada, August 6-11 (2004), (Accessed May 22, 2010)
  22. Saaty, T.L.: Rank from comparisons and from ratings in the analytic hierarchy/network processes. European Journal of Operational Research 186, 557–570 (2006)CrossRefMathSciNetGoogle Scholar
  23. Saaty, T.L.: Relative measurement and its generalization in decision-making – Why pairwise comparisons are central in mathematics for the measurement of intangible factors: The Analytic Hierarchy/Network Process. RACSAM, Revista de la Real Academia de Ciencias Serie A: Matemáticas 102(2), 251–318 (2008)zbMATHMathSciNetGoogle Scholar
  24. Saaty, T.L., Ozdemir, M.: Negative priorities in the Analytic Hierarchy Process. Mathematical and Computer Modelling 37, 1063–1075 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  25. Saaty, T.L., Sodenkamp, M.: Making decisions in hierarchic and network systems. International Journal of Applied Decision Sciences 1(1), 24–78 (2008)CrossRefGoogle Scholar
  26. Saaty, T.L., Vargas, L.G., Wendell, R.E.: Assessing attribute weights by ratios. Omega 11(1), 9–12 (1983)CrossRefGoogle Scholar
  27. Schoner, B., Wedley, W.C.: Ambiguous Criteria Weights in AHP: Consequences and Solutions. Decision Sciences 20(3), 462–475 (1989)CrossRefGoogle Scholar
  28. Schoner, B., Wedley, W.C., Choo, E.U.: A unified approach to AHP with linking pins. European Journal of Operational Research 64, 384–392 (1993)CrossRefGoogle Scholar
  29. Toyota Motor Corporation, FY 2009 Financial SummaryGoogle Scholar
  30. Triantaphyllou, E.: Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP. Journal of Multi-Criteria Decision Analysis 10, 11–25 (2001)zbMATHCrossRefGoogle Scholar
  31. Volkswagen Financial Services, Annual Report (2008)Google Scholar
  32. Watson, S.R., Freeling, A.N.S.: Assessing attribute weights by ratios. Omega 10(6), 582–583 (1982)CrossRefGoogle Scholar
  33. Watson, S.R., Freeling, A.N.S.: Comment on: Assessing attribute weights by ratios. Omega 11, 13 (1983)Google Scholar
  34. Wedley, W.C., Choo, E.U., Schoner, B.: Benchmark measurement: Between relative and absolute. In: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process, Burnaby, BC, Canada, pp. 335–345 (1996)Google Scholar
  35. Wedley, W.C., Choo, E.U., Schoner, B.: Magnitude adjustment for AHP benefit/cost ratios. European Journal of Operational Research 133, 342–351 (2001)zbMATHCrossRefGoogle Scholar
  36. Wedley, W.C., Choo, E.U.: Sharing the pie and distributing the reward: a case of bonus distribution among executives. Journal of Multi-Criteria Decision Analysis 15(5-6), 151–162 (2008)CrossRefGoogle Scholar
  37. Wijnmalen, D.J.D.: Analysis of benefits, opportunities, cost and risks (BOCR) with the AHP-ANP: a critical validation. Mathematical and Computer Modelling 46, 892–905 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  38. Wijnmalen, D.J.D., Wedley, W.C.: Non-discriminating Criteria in the AHP: removal and rank reversal. Journal of Multi-Criteria Decision Analysis 15(5-6), 143–149 (2008)CrossRefGoogle Scholar
  39. Wijnmalen, D.J.D., Wedley, W.C.: Correcting illegitimate rank reversals: proper adjustments of criteria weights prevent alleged AHP intransitivity. Journal of Multi-Criteria Decision Analysis 15(5-6), 135–141 (2008)CrossRefGoogle Scholar
  40. Whitaker, R.: Validation examples of the Analytic Hierarchy Process and Analytic Network Process. Mathematical and Computer Modelling 46, 840–859 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  41. Zahir, S.: A new approach to understanding and finding remedy for rank reversals in the additive Analytic Hierarchy Process. In: Conference Proceedings, Administrative Sciences Association of Canada, Ottawa (2007), (Accessed May 22, 2010 )

Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  • William C. Wedley
    • 1
  1. 1.Faculty of Business AdministrationSimon Fraser UniversityBurnabyCanada

Personalised recommendations