乘型模糊判断矩阵排序向量的递推方法

Recursive Ranking Method of Multiplicative Fuzzy Judgment Matrix

文章首先在模糊判断矩阵乘型一致性以及矩阵元素和权重之间关系的基础上,结合模糊判断矩阵的上三角矩阵元素,构建了一个关于权重和矩阵上三角元素的方程组,并证明了该方程组存在唯一的正解。随后指出方程组的证明过程就是模糊判断矩阵排序向量的求解过程,从而给出了乘型一致性模糊判断矩阵排序向量的一种递推方法。然后,在偏差函数基础上,通过构造并求解一个优化模型,求出了非乘型一致性模糊判断矩阵的排序向量,结果显示,其解的形式与采用乘型一致性模糊判断矩阵递推方法得到的排序向量完全一样。最后,通过实例以及相关方法对比说明排序向量递推方法是可行有效的。

Based on multiplicative consistency of fuzzy judgment matrix and the relationship between the matrix elements and weights,the equation set about the weights and the upper triangular elements of the matrix is obtained.It is proved that the equation set has a unique positive solution,and a recursive ranking method of multiplicative fuzzy judgment matrix is found from the proving process.Then,on the basis of the deviation function,the ranking vector of non-multiplicative fuzzy judgment matrix is obtained by building and solving a programming model,and the result indicates that this is a very interesting result,i.e.the ranking method of non-multiplicative fuzzy judgment matrix is the same to that of multiplicative fuzzy judgment matrix.Finally,two examples and comparisons with other methods are used to illustrate that the proposed recursive ranking method is feasible and effective.