Geometric Compatibility Indexes in a Local AHP-Group Decision Making Context: A Framework for Reducing Incompatibility

Abstract

This paper deals with the measurement of the compatibility in a local AHP-Group Decision Making context. Compatibility between two individuals or decision makers is understood as the property that reflects the proximity between their positions or preferences, usually measured by a distance function. An acceptable level of incompatibility between the individual and the group positions will favour the acceptance of the collective position by the individuals. To facilitate the compatibility measurement, the paper utilises four indicators based on log quadratic distances between matrices or vectors which can be employed in accordance with the information that is available from the individual decision makers and from the group. The indicators make it possible to measure compatibility in decision problems, regardless of how the collective position and the priorities are obtained. The paper also presents a theoretical framework and a general, semi-automatic procedure for reducing the incompatibility measured by the four indicators. Using relative variations, the procedure identifies and slightly modifies the judgement of the collective matrix that further improves the indicator. This process is undertaken without modifying the initial information provided by the individuals. A numerical example illustrates the application of the theoretical framework and the procedure.