Abstract
In this paper, we use Saaty's Eigenvector Method and the Power Method as well as Ω=1, 2, ⋯ , 9, 1/2, 1/3, ⋯ , 1/9} and Ω-={1,2, ⋯ ,9,1, 1/2, ⋯ ,1/9} as the sets from which the pairwise comparison judgments are assigned at random to examine the variation in the values determined for the mean random consistency index. By extensive simulation analysis, we found that both methods produce the same values for the mean random consistency random index. Also, we found that the reason for producing two different sets of values is the use of Ω vs. Ω- and not the selection of the Power Method vs. Saaty's Eigenvector Method.
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REFERENCES
Bronson, R. (1991), Matrix Methods: An Introduction. San Diego, CA: Academic Press.
Forman, E.H. (1990), Random indices for incomplete pairwise comparison matrices, European Journal of Operational Research 48: 153–155.
Golden, B.L. and Wang, Q. (1990), An alternative measure of consistency, in B.L. Golden, E.A. Wasil and P.T. Harker (eds.), Analytic Hierarchy Process: Applications and Studies, pp. 68–81. New York: Springer Verlag.
Golub, G.H. and Van Loan, C.F. (1989), Matrix Computations. Baltimore: John Hopkins University Press.
Lane, E.F. and Verdini, W.A. (1989), A consistency test for AHP decision makers, Decision Sciences 20: 575–590.
Noble, E.E. (1990), Consistency in the Analytic Hierarchy Process. Master's Thesis, Department of Operations Research and Information Systems, Eastern Michigan University, Ypsilanti, Michigan, USA.
Noble, E.E. and Sanchez, P.P. (1990a), A note on the information content of a consistent pairwise comparison judgment matrix of an AHP decision maker, Theory and Decision 34: 99–108.
Park, S.K. and Miller, K.W. (1988), Random number generators: Good ones are hard to find, Communications of the ACM 31(10): 1192–1201.
Ripley, B.D. (1987), Stochastic Simulation. New York: John Wiley & Sons.
Saaty, T.L. (1988), Multicriterion Decision Making: The Analytic Hierarchy Process — Planning, Priority Setting, Research Allocation. Pittsburgh, PA: RWS Publishers.
Saaty, T.L. (1991), Fundamentals of Decision Making and Priority Theory with the Analytic Hierarchy Process. Pittsburgh, PA: RWS Publishers.
Sanchez, P.P. and Noble, E.E. (1990b), An improved measure of mean random inconsistencies for AHP decision makers, Proceedings of the 22nd Annual Meeting of the Decision Sciences Institute, pp. 212–215.
Tuma, J.J. (1987), Engineering Mathematics Handbook, 3rd edn. New York: McGraw-Hill.
Tummala, V.M.R. and Wan, Y.W. (1994), On the mean random inconsistency index of analytic hierarchy process (AHP), Computers and Industrial Engineering 27(1–4): 401–404.
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Rao Tummala, V., Ling, H. A Note on the Computation of the Mean Random Consistency Index of the Analytic Hierarchy Process (Ahp). Theory and Decision 44, 221–230 (1998). https://doi.org/10.1023/A:1004953014736
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DOI: https://doi.org/10.1023/A:1004953014736