一种确定指标权重的新方法

针对如何客观地确定某一状态下指标权重这一问题,在给出向量相似度定义的基础上,提出了一种确定指标权重的新方法——向量相似度法。依据向量的两要素(大小和方向),把向量的相似度分解为范数相似度和方向相似度,从而使得向量相似度得以准确的表达。通过计算各指标特征向量与系统综合指标向量的相似度并将其归一化处理进而得出了指标权重。由于该方法直接从系统性能指标抽样数据入手,没有人为因素的干扰,因此具有很强的客观性。结合算例确定指标权重的结果符合客观实际,与其它客观赋权法确定的权重值也很吻合,充分说明了此方法的有效性和实用性,为确定指标权重提供了一种有效的方法和途径。

A New Method for Calculating Weights

In order to calculate the index weights, a new method is explained based on the vector resemblance-degree. According to two factors of the vector (length and angle), divide vector resemblance-degree into length resemblance-degree and angle resemblance-degree, thus the vector resemblance-degree can be expressed exactly. By calculating vector resemblance-degree of index vector and the system integrative vector then standardize it the index weight is obtained. Because this method makes a good use of the sample data directly without man-made factors, so it is very external. In the end, an example has been given and the result is very coincident with the fact and the other methods, all these prove its validity and practicability, it offers a very effectual way for calculating the index weights.