水质评价中熵权对指标极差变化的敏感性分析

Effects of index range variation on entropy weight in water quality assessment

水质评价中熵权反映了各项评价指标对评价结果的影响程度。为分析熵权对指标极差变化的敏感性,采用Visual Basic编程和曲线拟合的方法,对单指标和多指标极差变化对权重的影响进行了研究。结果表明:在指标最大值、最小值不变的情况下,随着样本数的增加,各指标权重虽有变化,但变幅较小,可见小样本求得的熵权可以反映指标的重要性。当样本数确定时,仅改变单项指标的最大值或最小值,越小越优型指标的权重对最大值变化的敏感性大于对最小值变化的敏感性。多项指标同倍数增大时,2倍最大值是权重变化的特征点。

Entropy weight has been successfully used to reflect the influence extent of different indexes to evaluation results in water quality assessment.In order to investigate the weights' sensitivity to range,the impacts of range on entropy weight are examined from two aspects by visual basic programming and curve fitting software.The results show that when the ranges of index values are fixed,the weights of indexes varies within a small range as the number of water samples increases,which means that the weight of every index cannot be impacted by the sample size under this circumstance.When the sample number is fixed,the maximum value has a larger effect on entropy than minimum value only by changing one of them.It is the demarcation point for weight variation when multi-indexes maximum increase by 2 times.