ON THE AGGREGATION OF INDIVIDUAL PRIORITIES IN INCOMPLETE HIERARCHIES

One way to conduct group decision-making in AHP is asking judgments from different experts. The following step is the aggregation of these judgments. However, at first, it is important to note if experts share common values. That is, if they work for the same company or department, for instance. In this case, the aggregation of individual judgments (shorted as AIJ) by their geometrical mean seems to be proper. If the experts came from different organizations, they may not act as unit: then, the indication is the aggregation of individual priorities (AIP). According to the literature, to AIP, one may either take geometric mean or arithmetic mean of the resulting priorities. This work addresses the AIP of incomplete hierarchies. An incomplete hierarchy is a structure when not all elements of a level connect to all elements from the higher level. A hierarchy with goal, criteria and sub-criteria and without alternatives is an example of incomplete hierarchy. A decision model without alternatives seems to be unusual. Nevertheless, this kind of situation is very common, in practice. There is a large number of AHP applications with incomplete hierarchies, including prioritization of customer needs, specification of product requirements, identification of weights for quality service evaluation, to name a few. This work shows that for incomplete hierarchies, the arithmetic mean must be used to AIP. That is, using the geometric mean, the priorities for the lower level elements will sum different from the priority of the higher element. A mathematical modeling of this observation is presented and illustrated with a simple numeric example with two criteria and four sub-criteria.