Decision Making by Potential Method

A common procedure in Multi-Criteria Decision Analysis is pairwise comparison of alternatives with respect to some criteria. The result of this comparison, whether exact or subjective, is a weight associated to the pair of alternatives measured on some scales. Some authors organize their results in pairwise comparison matrix as a base for further calculation. Potential Method (PM), introduced here, uses a preference flow F , defined on a directed graph, which generated a ’value function’ called potential on the set of alternatives. Each criterion, or decision maker, has his own preference flow and MCDM based on PM preferes these flows (graphs) rather then potentials in aggregation process. Preference flow can be complete (all pairs are evaluated) or incomplete (missing data). In both cases potential can be calculated as a solution of normal equation associated to the preference flow. If the preference graph is not connected potential is calculated for each connected component. The notion of inconsistency measure (i(F)) is associated to the preference flow and has the property that i(F) = 0 if and only if the flow is consistent. It is also shown that Geometric Mean Method (GMM) can be considered as a special case of PM which gives to GMM an inconsistency measure. Comparison with PROMETHEE, eigenvalue method and Evidential Reasoning method is done, showing the priority of PM in both, computational complexity, and simplicity, specially if incompleteness in the data is present.