Modeling, Inference, and Robustness Analysis of Interval Evidential Reasoning Rule

The evidential reasoning (ER) has been widely used in engineering practice owing to its powerful ability in dealing with various uncertainties. Typical ER methods require that evidence should be independent and mainly focus on the uncertainty caused by crisp values. However, when the evidence is obtained in interval forms, how to describe the interval uncertainty, analyze the evidence dependence, and explore the performance of the reasoning rule remains to be studied. As such, the modeling, inference, and robustness analysis of interval evidential reasoning (IER) rule is investigated. Specifically, the interval uncertainty is modeled through interval belief degree, interval weight, and interval reliability, and several calculation methods of interval evidential parameters are designed. The IER rule is developed theoretically based on the ER rule, and a minmax-based parameter optimization model is established to alleviate the subjective uncertainty in referential values. A robustness analysis method is put forward to study the performance of IER rule, where the perturbation threshold estimation model is built through the robustness coefficient. The health evaluation of laser gyroscope is conducted to demonstrate the implementation of IER rule and validate its effectiveness.