确定加权平均(WA)算子普遍处理方法:一种是先确定不同专家的权重,如权威专家赋予较大的权重,其他专家赋予较小的权重;另一种是先将专家给予的得分进行排序,然后根据得分高低给予不同的权重赋值,即有序加权平均(OWA)算子.基于此,利用主成分方法确定WA算子的权重:首先把每位专家给出的相应得分视为一个向量,求出这些向量的相关矩阵M;然后求出矩阵M的特征值和特征向量;根据特征值贡献率确定主成分的个数以及比重;最后结合特征向量(主成分)给出每位专家的权重.
Weighted Average(WA)Operator is widely used in lots of areas.Most of the existing methods are:some researchers pre-define different weight for different experts,for example,the higher reputation expert get higher weight,lower reputation expert gets lower weight;some other researchers sort the scores of each expert,and give different expert different weight according to their scores,which is called Ordered Weight Average(OWA).In this article,the author uses Principal Component Analysis method to define the weight:Firstly,treat each expert's score as a vector,then define the according correlation matrix M;Secondly,define the number and weight of principal components according to the eigenvalues contribution rate;Finally,define the weight of each expert according to the Eigenvectors of principal components.