面向复杂评价模型的证据推理方法

Evidential Reasoning Approach for Solving Complex Evaluation Models

证据推理方法针对多层结构的属性合成采用递归方式,其合成次数为评价属性树的分支结点个数,合成计算量较大.为减少计算量,文中提出一种非递归方式的合成方法,并对比两种合成方式的时间复杂度.为探究非递归方式处理各类不同置信结构分布的准确性和非线性特性,文中在三层结构的评价模型中,按照置信结构分布为和谐、准和谐和冲突分别计算综合属性的置信度和效用值,从公式推导和实验结果对比的角度分析两种合成方式的非线性特性,从相对误差的角度分析非递归方式计算结果的准确性.实验结果与算例证明文中方法的有效性.

Since the attribute aggregation of the evidential reasoning approach with multiple-level hierarchical structures is implemented in a recursive way, the aggregation times are the number of the branch nodes of attribute tree, which results in a large amount of calculation. To reduce the amount of calculation, a non-recursive aggregation approach is proposed and its time complexity is compared with that of the recursive approach. To explore the accuracy and the nonlinear characteristics of the non-recursive approach to dealing with different belief distributions, the belief degrees and the utilities of the aggregated attribute are calculated in terms of the belief structures of harmony, quasi-harmony and conflict, respectively. The nonlinear characteristics of the two aggregation approaches are analyzed based on the comparison of formula derivation and experimental results, and the accuracy of the non-recursive approach is examined from the angle of relative errors. The experimental results and the numeric example show the effectiveness of the proposed approach.