Reducing incompatibility in a local AHP-group decision making context

In the context of local analytic hierarchy process-group decision making (AHP-GDM), this paper presents a theoretical framework and a semi-automatic procedure for reducing incompatibility between the actors involved in the decision making process and the collective position. The row geometric mean is employed as the prioritisation procedure and the geometric compatibility index ( $$\textrm{GCOMPI}$$ GCOMPI ) as the incompatibility measure; individual pairwise comparison matrices are considered as the input of the reduction process, whilst the collective vector is the output. The reduction is attained by slightly modifying, in relative terms, the judgements of the collective pairwise comparison matrix, irrespective of the method used to obtain it, that further improve the $$\textrm{GCOMPI}$$ GCOMPI . The resulting judgements of the collective matrix and the associated collective priorities are close to the initial collective values. The procedure does not modify the judgements of the initial individual matrices and this simplifies the process of reaching consensus. A simulation analysis is utilised to study the performance of the algorithm along with an illustrative numerical example. The analysis proves that the proposed algorithm is easy to implement and efficient, it provides mathematically closed results and significantly reduces the $$\textrm{GCOMPI}$$ GCOMPI associated with the precise consistency consensus matrix which is one of the AHP-GDM tools. The framework allows the procedure to be adapted to specific interests.