一种改进的行和归一化排序方法

提出了一种改进的行和归一化排序方法(INRAM), 从保序性、置换不变性、相容性和累积优势度等方面对该方法的合理性进行了研究, 并且利用互补判断矩阵和互反判断矩阵之间的转换公式, 给出了相应的求解互补判断矩阵排序向量的算法, 从而丰富和发展了互反和互补判断矩阵的排序理论. 最后,通过算例将NRAM法和INRAM法与特征根排序方法(EM)及对数最小二乘法(LLSM)作了对比分析. 数值结果表明: INRAM法不仅简洁易行, 而且与EM 法的排序结果完全一致, 故能较好地揭示方案的真实排序.

Improved normalizing rank aggregation method for priorities

An improved normalizing rank aggregation method (INRAM) for priorities of reciprocal judgment matrices is presented and some of its desirable properties, such as rank preservation, compatibility, cumulative dominance, are studied. By using the transformation formulas of reciprocal judgment matrix and complementary judgment matrix, the corresponding method for priorities of complementary judgment matrix is also given. The priority theory of reciprocal judgment matrices and complementary judgment matrices is thus developed. Finally, the normalizing rank aggregation method (NRAM) and the INRAM are compared with the eigenvector priority method (EM) and the logarithmic least squares method (LLSM) through some numerical examples. The numerical results show that the INRAM is simple, feasible and can get the same priorities as that of the EM. Thus it can get underlying priorities for alternatives.