Modeling, Optimization, and Robustness Analysis of Evidential Reasoning Rule Under Multidiscernment Framework

Evidential reasoning (ER) rule has been widely used in the fields of information fusion, multiattribute decision making, and pattern recognition. In current studies of ER rule, there is a strict one-to-one correspondence between the framework of discernment (FoD) of evidence and the FoD of reasoning results. However, this may not be satisfied in engineering practice, making it difficult to conduct the reasoning. When the element of FoD is changed, how the reasoning result will change is also a focus that deserves attention. As such, in this article, the modeling, optimization, and robustness analysis method of ER rule under multidiscernment framework is proposed. Specifically, the ER rule with transformation matrix is proposed to unify the evidence with different FoDs into the same FoD as reasoning results. A parameter optimization model is established based on the expected utility and interpretable constraints. A robustness analysis method of the proposed ER rule is proposed in the context of perturbation to further explore its performance. Particularly, the generation and transmission rules of perturbation are described, and two robustness criteria are defined. A case study of health assessment of laser gyroscope, the mainstream navigation equipment in the aerospace field, is conducted to present the implementation of the proposed method and verify its effectiveness in engineering practice.