基于转换的混合判断矩阵排序方法及比较研究

Prioritization methods and comparative study of hybrid judgement matrix based on transformations

介绍加型一致性和积型一致性混合判断矩阵的概念,相应的定义了加型转换和积型转换。基于这两种转换,分别给出了将混合判断矩阵转换为互反判断矩阵的特征向量法和对数最小二乘法以及转换为互补判断矩阵的改进的最小方差法。通过算例说明了所给算法的可行性和有效性。从方法的难易,区分度及客观性三方面对现有方法做了对比分析。结果表明所给方法比较简洁和有效,具有很好的可靠性和实用性。

The concepts of additive and multiplicative perfectly consistent hybrid judgment matrix are introduced. Additive transformation and multiplicative transformation are defined. Based on these two transformations, three prioritization methods for hybrid judgement matrix are put forward which are eigenvector method and logarithmic least-squares method for transformed reciprocal judgement matrix and improved least-variance method for transformed complementary judgement matrix. A numerical example is presented to illustrate the effectiveness of the developed methods. The comparative study between these methods and the existing methods is also given in terms of difficulty, differentiability and objectivity. The advantages of the proposed methods are obtained.