3种基于互反判断矩阵的互补判断矩阵排序法

Three Reciprocal Judgement Matrices-Based Methods for Priorities of Complementary Judgement Matrices

引进了互反判断矩阵与互补判断矩阵之间的转换公式 ,介绍了完全一致性互反判断矩阵和完全一致性互补判断矩阵之间的关系 .提出了 3种基于互反判断矩阵的互补判断矩阵排序方法 ,详细地研究了它们的一些优良性质 ,如 :强条件下保序性等 ,并进一步把这些方法推广到群体决策环境中 .从而弥补了互补判断矩阵排序理论和方法的不足 ,为解决互补判断矩阵排序问题提供了新的途径 .理论分析和数值结果均表明 :这些排序方法具有简洁、可行、且易于计算器或计算机上实施等优点 .

This paper introduces the transformation formulas of reciprocal judgement matrix and complementary judgement matrix, and presents the relationship between the perfectly consistent reciprocal judgement matrix and perfectly consistent complementary judgement matrix. Based on the priority methods of three reciprocal judgement matrices, three methods for priorities of complementary judgement matrices are proposed, and their desired properties such as rank preservation under strong condition, etc. are studied. These three priority methods are also extended to group decision-making. The methods supplement and develop the theory and methodology of priority of complementary judgement matrices. The theoretic analyses and numerical results show that the methods are simple, feasible, and can be performed on computer easily.