Inference and analysis on the evidential reasoning rule with time-lagged dependencies

Evidential reasoning rule (ER rule), benefits by the advantage in dealing with various uncertainties, is widely applied for independent evidence aggregation and multi-attribute decision making. In engineering practice, however, time-lagged correlations among multiple attributes from complex systems are often encountered, causing time-lagged dependencies among evidences generated from these attributes. To aggregate multiple pieces of time-lagged dependent evidence, an evidential reasoning rule with time-lagged dependencies, called the ER-TLD, is developed in this paper. Firstly, the calculation algorithm for the relative total time-lagged dependence coefficient (RT-TLDC) and the delay time of each attribute is proposed based on the distance correlation (dCor) method, with which nonlinear time-lagged correlations among multiple attributes can be captured. On this basis, the ER-TLD model is constructed by introducing the RT-TLDCs and delay times into the ER rule, so that multiple pieces of time-lagged dependent evidence can be effectively aggregated. Then, sensitivity analyses are conducted, and the impact of delay time change on the aggregation results is explored. Finally, the effectiveness and potential application of the proposed method are verified by one numerical example and three practical experiments. The aggregation results obtained by the ER-TLD show more rationality according to the comparative studies.