Zhang Bowen, Pedrycz Witold, Fayek Aminah Robinson, Dong Yucheng
IEEE Trans Cybern. 2022 Jul;52(7):6733-6744. doi: 10.1109/TCYB.2020.3035909. Epub 2022 Jul 4.
In the analytic hierarchy process (AHP), the reciprocal matrix is generated based on the pairwise comparisons completed among all the alternatives or attributes under consideration. To ensure reliability and validity of the decision solution, a certain modification of entries of the matrix is usually needed to improve the consistency of the reciprocal matrix. This study aims to present a consistency improvement method by admitting some level of information granularity in the evaluation process. This gives rise to a granular rather than numeric matrix of pairwise comparisons. First, with a given average level of information granularity, we present an optimal granularity model that is characterized by maximal consistency. One can maximize the consistency degree by invoking a process of allocation of information granularity across the corresponding modifications of the reciprocal matrix. Based on the optimal granularity model, an interactive consistency improvement process is presented with the involvement of the decision maker. Then, an adaptive differential evolution algorithm is applied to optimize entries of the modified reciprocal matrix. Detailed experiments along with a thorough comparative analysis are completed to demonstrate the effectiveness of the proposed method.
在层次分析法（AHP）中，互反矩阵是基于对所有备选方案或所考虑属性之间完成的两两比较生成的。为确保决策解决方案的可靠性和有效性，通常需要对矩阵的元素进行一定修改，以提高互反矩阵的一致性。本研究旨在通过在评估过程中允许一定程度的信息粒度，提出一种一致性改进方法。这产生了一个粒度而非数值的两两比较矩阵。首先，在给定的平均信息粒度水平下，我们提出了一个以最大一致性为特征的最优粒度模型。通过在互反矩阵的相应修改中调用信息粒度分配过程，可以使一致性程度最大化。基于最优粒度模型，在决策者参与的情况下提出了一个交互式一致性改进过程。然后，应用自适应差分进化算法对修改后的互反矩阵的元素进行优化。完成了详细的实验以及全面的比较分析，以证明所提方法的有效性。
