强一致性区间数判断矩阵性质和排序

Properties and Priority Method of Strong Consistent Interval Judgment Matrix

研究了区间数判断矩阵的性质及排序问题。介绍了强一致性区间数判断矩阵、标准化区间数向量等概念;提出求解强一致性区间数判断矩阵排序向量的线性规划模型,并证明了所求排序向量是标准化区间数排序向量。在此基础上给出强一致性区间数判断矩阵的等价条件,进一步提出基于非线性规划模型的强一致性区间数判断矩阵的排序方法,最后通过实例验证了所提出的方法也适用于一致性区间数判断矩阵及满意一致性区间数判断矩阵。

The properties of strong consistent interval judgment matrix in literatures are not well studied both at home and abroad,so the priority method research lacks a theoretical basis.The properties and priority problems of strong consistent interval judgment matrix are studied in this paper.First,some concepts including the interval judgment matrix,the strong consistent interval judgment matrix and the normalized interval vector are explained.Then,a linear programming model is used to derive the normalized interval weights from the strong consistent judgment matrix.On that basis,an equivalent condition of strong consistency for interval judgment matrix is put forward.A nonlinear programming model is developed to generate interval weights for the interval comparison matrix with satisfactory consistency.Finally,two numerical examples are provided to illustrate the validity of the proposed method,and it is shown that the nonlinear programming model can also be applyied to consistent interval judgment matrix and satisfactory consistent interval judgment matrix.The properties and the ranking method may further improve the consistency theories of interval judgment matrix.