Inference and analysis of a new evidential reasoning rule-based performance evaluation model

In the current studies on the evidential reasoning (ER) rule, a performance evaluation model that utilizes the ER rule to combine evidence constituted by a single observation indicator (Single indicator-based ER rule, SER) has been developed with excellent scalability. However, the belief distribution (BD) of SER-based evaluation model is composed of a set of single grades that describe the system performance and the corresponding belief degrees. This makes some common uncertain judgments with local ignorance unable to be considered in the inference process, resulting in a decrease in the accuracy and validity of the evaluation results. In this paper, a new SER-based performance evaluation model with extended BD is proposed. Firstly, on the basis of the existing BD in SER, some new elements capable of describing local ignorance are introduced. Secondly, by calculating and optimizing the relevant parameters, the new evaluation model is formed. Thirdly, according to the Stone-Weierstrass theorem and information entropy theory, the approximation ability and uncertainty of the evaluation model are discussed respectively. Finally, a practical example is given to illustrate the potential applications of the proposed model in engineering practice.