Bayesian aggregation methods for analytic hierarchy process and analytic network process in group decision making

The problems whose objective is to search the best alternative or to rank the alternatives in terms of a number of conflicting criteria are the multi-criteria decision making (MCDM) problems. As the interdisciplinary teams, composed of different scientists developed in different sectors, group decision making in MCDM problems gains more importance and necessity. The increasing complexity of the group decision problems requires the use of more ? exible approaches.The Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP) are widely used approaches for solving complex MCDM problems. The AHP group decision making (AHP-GDM) method decomposes a complex MCDM problem into a system of hierarchies and selects the best alternative in terms of some criteria by making pairwise comparisons. The extension of AHP-GDM to the case of dependence and feedback is called the ANP group decision making (ANP-GDM).In order to aggregate the individual?s group judgements in a group setting ?the aggregation of individual judgements (AIJ)? and ?the aggregation of individual priorities (AIP)? methods are used. However these classical methods have some assumptions such as: the pairwise comparison matrices of decision makers are complete and consistent. In real life problems, it is hard to satisfy these assumptions due to the complexity of the problem or inexperience of the decision makers.This research proposes Bayesian aggregation procedures for AHP-GDM and ANP-GDM which do not require intermediate filters for the decision makers? initial judgements. The weights of the decision makers are inversely proportional to their consistency levels. The proposed procedures are extended to the analysis of incomplete pairwise comparison matrices where they provide more robust manner than classical methods in terms of the priorities and have lower values of the mean square errors. The methodology has been illustrated with case studies and compared with the conventional aggregation method.