Reducing incompatibility in a local AHP-group decision making context
针对层次分析法群体决策中个体与集体意见的不兼容问题，提出一个理论框架和半自动流程，通过微调集体成对比较矩阵的判断来降低不兼容性，且不修改个体矩阵，便于达成共识。
Abstract 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 ( $$\textrm{GCOMPI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>GCOMPI</mml:mtext> </mml:math> ) 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 $$\textrm{GCOMPI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>GCOMPI</mml:mtext> </mml:math> . 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 $$\textrm{GCOMPI}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>GCOMPI</mml:mtext> </mml:math> 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.