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INTERVAL UNCERTAINTY OF ESTIMATES AND JUDGMENTS OF SUBJECT IN DECISION MAKING IN MULTI-CRITERIA PROBLEMS

Alexander Madera

Abstract


In this article, we propose a method of decision making in multi-criteria problems given an interval uncertainty of the estimates given by the subject in reference to the importance of one criterion over another and various alternatives for each criterion. The method is the development of the deterministic process of the Analytic Hierarchy Process, which uses deterministic point estimates of the importance of criteria and alternatives for each criterion for decision making in multi-criteria problems. While in the standard Analytic Hierarchy Process the values of global priorities corresponding to different alternatives are deterministic and unambiguous, in the interval process developed in this article the global priorities and alternatives are interval and uncertain. If in the standard deterministic Analytic Hierarchy Process the best alternative is selected by the maximum value of the global priority, then, to select the best interval alternative, here we introduce a criterion corresponding to the maximum values of the lower and upper boundaries of the intervals of global priorities of the alternatives. The application of the proposed method is demonstrated by a specific example. 


Keywords


interval; uncertainty; estimates; decision making; analytic hierarchy process

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References


Deng, H. (1999). Multicriteria analysis with fuzzy pairwise comparison. International Journal of Approximate Reasoning, 21, 215−231.

Eskandari, H., and Rabelo, L. (2007). Handling uncertainty in the Analytic Hierarchy Process: A stochastic approach. International Journal of Information Technology & Decision Making, 6(01), 177−189.

Haines, L.M., 1998 Haines, L. M. (1998). A statistical approach to the Analytic Hierarchy Process with interval judgements. (I). Distributions on feasible regions. European Journal of Operational Research, 110(1), 112−125.

Kahneman, D., Slovic, P., and Tversky, A. (2001). Judgment under uncertainty: heuristics and biases. Cambridge: Cambridge University Press.

Lipovetsky, S., and Tishler, A. (1999). Interval estimation of priorities in the AHP. European Journal of Operational Research, 114(1), 153−164.

Madera, A.G. (2010). Modeling and decision making in management. Moscow: LKI.

Madera, A.G. (2014). Risks and chances: Uncertainty, prediction and Evaluation. Moscow: Krasand.

Mikhailov, L. (2004). A fuzzy approach to deriving priorities from interval pairwise comparison judgements. European Journal of Operational Research, 159(3), 687−704.

Mikhailov, L., Didehkhani, H., Sadi-Nezhad, S. (2011). Weighted prioritization models in the fuzzy Analytic Hierarchy Process. International Journal of Information Technology and Decision Making,10(4), 1−14.

Podinovski, V.V. (2007). Interval articulation of superiority and precise elicitation of priorities. European Journal of Operational Research,180, 406 – 417.

Ross, S. (1993). Introduction to probability models, 5thed. New York: Academic Press.

Saaty, T.L. (2001). Decision making with dependence and feedback: The Analytic Network Process. Pittsburgh, PA: RWS Publications.

Salo, A.A., and Hämäläinen R.P. (1995). Preference programming through approximate ratio comparisons. European Journal of Operational Research,82, 458 – 475.

Wang Y.-M., Yang J.-B., Xu D.-L.(2005). Interval weight generation approaches based on consistency test and interval comparison matrices. Applied Mathematics and Computation,167, 252 – 273.




DOI: http://dx.doi.org/10.13033/ijahp.v7i2.240