基于熵函数与离差最大化的客观赋权法研究

针对大型机械设备安全评价中评价指标客观权重随加权方法的选择而变化的问题,提出一种基于熵和评价对象离差最大化的客观综合赋权模型。该模型将不同客观赋权法得到的权重向量视为指标真实客观权重向量的离散随机变量,将权重系数定义为权重系数的概率函数的随机变量,考虑不同客观加权方法得到的权向量的不确定性和实际目标权向量的一致性要求,基于熵函数获取权系数的约束方程;针对权重与对象评价值的关系,将评价对象离差的最大化作为上述权重系数约束函数的补充,构建客观综合赋权模型,使获取的指标客观权重仅与其携带的原始信息相关,极大的提高了大型机械设备安全评价的客观性。算例验证了该模型的合理性和有效性。

Research on objective weighting method based on entropy function and maximizing deviation

Considering the problem that the objective weight of evaluation indexes in safety evaluation of large-scale mechanical equipment changes with the selection of weighting methods,we proposed an objective comprehensive weighting model based on entropy and maximization of deviation of evaluation objects.In this model,the weight vectors obtained by different objective weighting methods are regarded as discrete random variables of the real objective weight vectors of the indexes,and the weight coefficients are defined as random variables of the probability function of the weight coefficients.Considering the uncertainty of the weight vectors obtained by different objective weighting methods and the consistency requirement of the actual target weight vectors,the constraint equations of the weight coefficients are obtained based on the entropy function;in view of the relationship between the weight and the evaluation value of the object,we took the maximization of deviation of the evaluation object as a supplement to the constraint function of the above-mentioned weight coefficient,and construct an objective comprehensive weighting model,so that the objective weight of the obtained index is only related to the original information it carries,thus greatly improving the objectivity of safety evaluation of large-scale mechanical equipment.The rationality and effectiveness of the model were verified by an example.