On the evidential reasoning rule for dependent evidence combination

Evidential Reasoning (ER) rule, which can combine multiple pieces of independent evidence conjunctively, is widely applied in multiple attribute decision analysis. However, the assumption of independence among evidence is often not satisfied, resulting in ER rule inapplicable. In this paper, an Evidential Reasoning rule for Dependent Evidence combination (ERr-DE) is developed. Firstly, the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability. On this basis, a calculation method of evidence Relative Total Dependence Coefficient (RTDC) is proposed using the distance correlation method. Secondly, as a discounting factor, RTDC is introduced into the ER rule framework, and the ERr-DE model is formulated. The aggregation process of two pieces of dependent evidence by ERr-DE is investigated, which is then generalized to aggregate multiple pieces of non-independent evidence. Thirdly, sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC. The properties of sensitivity coefficient are explored and mathematically proofed. The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively. Finally, the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.