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CP28_Multicriteria_Group - Combining criteria ranks for...

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Combining criteria ranks for calculating their weights in group MCDM Hesham K. Alfares Systems Engineering Department, PO Box 5067 Dhahran 31261, Saudi Arabia [email protected] Abstract An empirical methodology is presented to determine aggregate numerical weights from group ordinal ranks of multiple decision criteria. Assuming such ordinal rankings are obtained from several decision makers, aggregation procedures are proposed to combine individual rank inputs into group weights. In developing this methodology, we utilize empirical results for an individual decision maker, in which a simple relationship provides the weight for each criterion as function of its rank and the total number of criteria. Three different weight aggregation procedures are proposed and empirically compared using a set of experiments. The proposed methodology can be used to determine relative weights for any set of criteria, given only criteria ranks provided by several decision makers. Keywords Criteria ranking, Criteria weights, Multi-criteria Decision making, Group decisions 1. Introduction : Determining criteria weights is a problem that arises frequently in many multi-criteria decision-making (MCDM) techniques, such as goal programming, Analytic Hierarchy Process (AHP), and the weighted score method. In practice, it is difficult even for a single decision maker to supply numerical relative weights of different decision criteria. Naturally, obtaining criteria weights from several decision makers is more difficult. Quite often, decision makers 1
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are much more comfortable in simply assigning ordinal ranks to the different criteria under consideration. In such cases, relative criteria weights can be derived from criteria ranks supplied by decision makers. The objective of this paper is to combine individual criteria rankings supplied by different decision makers into aggregate group weights for all criteria. Specifically, an empirical methodology is developed to assign weights to each criterion based on its rank, and subsequently to aggregate the weights into an overall group weight for each factor. In determining criteria weights for any individual, we assume that a universal functional relationship exists between criteria ranks and average weights. Empirical evidence from the literature supports this assumption. Moreover, given criteria ranks by several decision makers, we assume that this functional relationship can be used to combine the various rank inputs into a set of aggregate (group) criteria weights. Experiments involving university students and faculty were conducted to collect necessary data for developing this methodology. Several aggregation methods have been investigated, assuming the ranks provided by different individuals correspond to the same set of criteria. The four methods use different combinations of arithmetic and geometric means of the ranks and the weights to determine overall group weights. The best aggregation
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