针对传统层次分析法(AHP)在构造判断矩阵过程中需要满足一致性条件问题,本文研究AHP方法需要进行一致性调整的原因,提出了一种基于流形学习的非一致性判断矩阵排序方法。在非一致性判断矩阵排序过程中,首先基于近邻距离的概念,构建出判断矩阵所对应数据集的近邻距离矩阵;然后以近邻点的线性表示为基础,将每个数据点映射到一个全局低维坐标系,并据此获得判断矩阵所对应的低维嵌入;根据各层求解出的低维嵌入对各层要素进行优劣排序,进而得到最终排序结论。最后,通过数值案例验证了所提方法的有效性和实用性。
To solve the problems of the traditional AHP method which needs to satisfy the consistency condition in constructing judgment matrixes, the reasons of consistency regulation from AHP are studied and an inconsistency judgment matrix ranking method based on manifold learning is proposed in this paper. In the ranking process of inconsistency judgment matrixes, on the basis of the neighbor distance, the neighbor distance matrixes of the data sets corresponding to judgment matrixes are constructed firstly. Next each data point is mapped to a low-dimensionally global coordinate system based on the linear representations of the neighbor points, and the low-dimensional embeddings that correspond to judgment matrixes are obtained. Then the ranking conclusion is gotten by analyzing the superiority and inferiority ranking of the elements according to the correspondingly calculated low-dimensional embeddings from each hierarchy. Finally, a numerical example illustrates that the proposed method has a higher level of effectiveness and practicability.
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