基于语言判断矩阵的一致性及其排序方法

Consistency and Ranking Approach Based on Linguistic Judgment Matrices

研究语言判断矩阵的乘性一致性及方案排序问题。首先给出有关语言判断矩阵和互反判断矩阵的定义及其性质,提出语言判断矩阵一致性的定义;然后通过引进导出矩阵将语言判断矩阵转换为数值矩阵,得出语言判断矩阵具有完全一致性或弱一致性的充要条件是其转换后得到的导出矩阵也具有同样的结论。同时利用该转换公式,给出基于语言判断矩阵的方案排序方法。最后,通过一个算例说明文中提出的分析方法。

This paper has studied the consistency of multiplication and ranking problem based on linguistic judgment matrix. First, several concepts and characters of linguistic judgment matrices and multiplicative judgment matrices were introduced, a concept of the consistency for linguistic judgment matrix is proposed; furthermore, transforming judgment matrix with linguistic assessment information into digital matrix through introducing the educed matrices, a conclusion is obtained that the linguistic judgment matrix is complete consistent or weak consistent if and only if the educed matrix is same also. Meanwhile,a ranking approach to linguistic judgment matrix was also given based on the transforming formula. Finally ,a numerical example was given to illustrate the use of the proposed in this paper.