AHP PRIORITIES AND MARKOV-CHAPMAN-KOLMOGOROV STEADY-STATES PROBABILITIES
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
An AHP matrix of the quotients of the pair comparison priorities is transformed to a matrix of shares of the preferences which can be used in Markov stochastic modeling via the Chapman-Kolmogorov system of equations for the discrete states. It yields a general solution and the steady-state probabilities. The AHP priority vector can be interpreted as these probabilities belonging to the discrete states corresponding to the compared items. The results of stochastic modeling correspond to robust estimations of priority vectors not prone to influence of possible errors among the elements of a pairwise comparison matrix.
ÂHow to Cite
Downloads
##plugins.themes.bootstrap3.article.details##
AHP, Markov stochastic modeling, Chapman-Kolmogorov equations
Lipovetsky, S. (2005) Analytic Hierarchy Processing in Chapman-Kolmogorov Equations, International Journal of Operations and Quantitative Management, 11, 219-228.
Lipovetsky, S. & Tishler, A. (1999) Interval Estimation of Priorities in the AHP, European Journal of Operational Research, 114, 153-164.
Lipovetsky, S., & Conklin, W.M. (2002) Robust Estimation of Priorities in the AHP, European Journal of Operational Research, 137, 110-122.
Lipovetsky, S., & Conklin, W.M. (2003). Priority Estimations by Pair Comparisons: AHP, Thurstone Scaling, Bradley-Terry-Luce, and Markov Stochastic Modeling, Proceedings of the ASA Joint Statistical Meeting, JSM’03, 2473-2478, San Francisco, CA.
Lootsma, F. (1999) Multi-Criteria Decision Analysis via Ratio and Difference Judgement, Kluwer Academic Publishers, Dordrecht.
Saaty, T.L., (1980). The Analytic Hierarchy Process. McGraw-Hill, New York.
Saaty, T.L. (1996). Decision Making with Dependence and Feedback: The Analytic Network Process, RWS Publications, Pittsburgh.
Saaty, T.L. & Kearns, K.P. (1985) Analytical Planning, Pergamon Press, New York.
Saaty, T.L. & Vargas, L.G. (1984) Comparison of Eigenvalue, Logarithmic Least Squares and Least Squares Methods in Estimating Ratios, Mathematical Modelling, 5, 309-324.
Saaty, T.L. & Vargas, L.G. (1994) Decision Making in Economic, Political, Social and Technological Environment with the Analytic Hierarchy Process, RWS Publications, Pittsburgh, PA.
Copyright of all articles published in IJAHP is transferred to Creative Decisions Foundation (CDF). However, the author(s) reserve the following:
- All proprietary rights other than copyright, such as patent rights.
- The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In case of whole articles, such third parties must obtain permission from CDF as well. However, CDF may grant rights with respect to journal issues as a whole.
- The right to use all or parts of this article in future works of their own, such as lectures, press releases, reviews, textbooks, or reprint books.
- The authors affirm that the article has been neither copyrighted nor published, that it is not being submitted for publication elsewhere, and that if the work is officially sponsored, it has been released for open publication.
The only exception to the statements in the paragraph above is the following: If an article published in IJAHP contains copyrighted material, such as a teaching case, as an appendix, then the copyright (and all commercial rights) of such material remains with the original copyright holder.
CDF will receive permission for publication of copyrighted material in IJAHP. This permission is not transferable to third parties. Permission to make electronic and paper copies of part or all of the articles, including all computer files that are linked to the articles, for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage.
This permission does not apply to previously copyrighted material, such as teaching cases. In paper copies of the article, the copyright notice and the title of the publication and its date should be visible. To copy otherwise is permitted provided that a per-copy fee is paid.
To republish, to post on servers, or redistribute to lists requires that you post a link to the IJAHP article, which is available in open access delivery mode. Do not upload the article itself.
Authors are permitted to present a talk, based on a paper submitted to or accepted by IJAHP, at a conference where the paper would not be published in a copyrighted publication either before or after the conference and where the author did not assign copyright to the conference or related publisher.