Abstract
In this paper, we present a statistical criterion for accepting/rejecting the pairwise reciprocal comparison matrices in the Analytic Hierarchy Process. We have studied statistically the consistency in random matrices of different sizes. We are not agree with the traditional criterion of accepting matrices due to their inflexibility and because it is too restrictive when the size of the matrix increases. Our system is capable to adapt the acceptance requirements to different scopes and consistency’s necessities. The advantages of our consistency system is the introduction of statistical relativity in the acceptance criterion and the simplicity of the used index, the eigenvalue (λ max).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Keeney, R., Raiffa, H.: Decisions with Multiple Objectives; Preferences and Values Tradeoffs. Wiley, New York (1976)
Saaty, T.L.: The Analytic Hierarchy Process, New York (1980)
Saaty, T.L.: Fundamentals of Decision Making and Priority Theory with the Analytic Hierarchy Process. RWS Publications, Pittsburgh (1994)
Fechner, G.T.: Elements of Psychophysics. In: Adler, H.E. (ed.) Elemente der Psychophysik, Breitkopf und Hârtel, Leipzig, vol. 1, Holt, Rinehart & Winston (1980)
Thurstone, L.L.: A law of comparative judgments. Psychological Reviews 34, 273–286 (1927)
Forman, E.H.: Random indices for Incomplete Pairwise Comparison Matrices. European Journal of Operational Research 48, 153–155 (1990)
Lane, E.F., Verdini, W.A.: A consistency test for AHP decision makers. Decision Science 20, 575–590 (1989)
Murphy, C.K.: Limits of the Analytical Hierarchy Process from its consistency index. European Journal of Operational Research 65, 138–139 (1993)
Salo A.A., Hämäläinen R.P.: On the measurement of preferences in the AHP. Research Report, Systems Analysis Laboratory, Helsinki University of Technology (1993)
Alonso, J.A., Lamata, M.T.: Estimation of the Random Index in the Analytic Hierarchy Process. In: Proceedings of Information Processing and Management of Uncertainty in Knowledge- Based Systems (IPMU 2004) Perugia, vol. I, pp. 317–322 (2004)
Kwiesielewicz, M., van Uden, E.: Inconsistent and contradictory judgements in pairwise comparison method in the AHP. Computers & Operations Research 31, 713–719 (2004)
Pelaez, J.I., Lamata, M.T.: A New Measure of Consistency for Positive Reciprocal Matrices. Computers and Mathematics with Applications 46, 1839–1845 (2003)
Lamata, M.T., Pelaez, J.I.: A method for improving the consistency of judgements. International Journal of Uncertainty Fuzzyness and Knowledge-based Systems 10, 677–686 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alonso, J.A., Lamata, M.T. (2005). A Statistical Criterion of Consistency in the Analytic Hierarchy Process. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2005. Lecture Notes in Computer Science(), vol 3558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526018_8
Download citation
DOI: https://doi.org/10.1007/11526018_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27871-9
Online ISBN: 978-3-540-31883-5
eBook Packages: Computer ScienceComputer Science (R0)