Open Journal Systems

AHP PRIORITIES AND MARKOV-CHAPMAN-KOLMOGOROV STEADY-STATES PROBABILITIES

Stan Lipovetsky

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.

 

Keywords


AHP; Markov stochastic modeling; Chapman-Kolmogorov equations

Full Text:

PDF

References


Lipovetsky, S. (1996) The Synthetic Hierarchy Method: An Optimizing Approach to Obtaining Priorities in the AHP, European Journal of Operational Research, 93, 550-564.

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.




DOI: http://dx.doi.org/10.13033/ijahp.v7i2.243