Inference, Optimization, and Analysis of an Evidential Reasoning Rule-Based Modeling Approach

The evidential reasoning (ER) rule, with its strict probabilistic reasoning and superior uncertainty handling ability, has been widely used in the evaluation, diagnosis, and decision-making. Recently, a modeling approach based on the ER rule that combines the evidence constituted by a single attribute (SA_ER) has gradually attracted scholars’ attention due to its good scalability and flexibility. However, in the SA_ER, the frame of discernment (FoD) is composed of a series of singleton propositions and the universal set of these propositions. Since the SA_ER has a special form of evidence structure, its reflection on the system output is incomplete. The existing FoD is unable to quantify this incompleteness, which greatly limits the development of SA_ER. In this article, an improved SA_ER approach that extends the FoD to the power set (PSA_ER) is proposed. Meanwhile, combined with the physical meaning of the model parameters, the expressions of evidence weight and reliability are deduced, respectively. Then, an intelligent optimization algorithm is used to optimize partial parameters to enhance the performance of PSA_ER. Further, the basic properties of PSA_ER are analyzed in detail from the parameter level to promote its engineering application. Finally, an engineering example is intended to demonstrate the effectiveness of the proposed approach.