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Evidential reasoning (ER) rule has been widely used in addressing uncertainty, ignorance, and vagueness information. To explore its performance measure (PM), the perturbation analysis (PA) for the ER rule (ER rule-PA) is conducted, with perturbation taken into consideration. This article aims to analyze the robustness and stability of the ER rule, serving as theoretical basis and technical support for applied research and applications. The combination of two pieces of independent evidence is discussed, and perturbation is added to one piece of evidence. To represent the expected utility of evidence combination under perturbation, perturbation utility is introduced. The novel concept of perturbation coefficient is proposed to characterize the PM of the ER rule (ER rule-PM). The properties of perturbation coefficient are explored to demonstrate the impact of perturbation. The maximum permissible error (MPE) of perturbation coefficient is defined to characterize the acceptability of perturbation. A numerical study is examined to illustrate the implementation process of ER rule-PA. Moreover, a case study of reliability evaluation of aerospace relay is conducted to show the potential applications of ER rule-PA, which makes the proposed method more practical. [ABSTRACT FROM AUTHOR]

It is important to predict the hidden behavior of a complex system. In the existing models for predicting the hidden behavior, the hidden belief rule base (HBRB) is an effective model which can use qualitative knowledge and quantitative data. However, the frame of discernment (FoD) of HBRB which is composed of some states or propositions and the universal set including all states or propositions is not complete. The global ignorance and local ignorance cannot be considered at the same time, which may lead to the inaccurate forecasting results. To solve the problems, a new HBRB model named as PHBRB in which the hidden behavior is described on the FoD of the power set is proposed in this correspondence paper. Furthermore, by using the evidential reasoning rule as the inference tool of PHBRB, a new projection covariance matrix adaption evolution strategy is developed to optimize the parameters of PHBRB so that more accurate prediction results can be obtained. A case study of network security situation prediction is conducted to demonstrate the effectiveness of the newly proposed method. [ABSTRACT FROM AUTHOR]

Nonlinear complex system modeling has drawn attention from diverse fields and many approaches have been developed. Among those approaches, the advantages of the belief rule base (BRB) expert system have been shown for managing multiple types of information under uncertainty and modeling the nonlinearity present in many theoretical and practical complex systems. However, two challenges still need to be addressed. First, BRB needs to be downsized to conserve modeling and computational effort. For this challenge, a new disjunctive assumption is applied, which can significantly downsize BRB while maintaining its completeness. Second, the structure and parameters of BRB need to be jointly optimized. For this challenge, a new Akaike information criterion (AIC)-based optimization objective is derived to represent both modeling accuracy and modeling complexity. Moreover, a joint bi-level optimization model with an AIC-based objective is constructed for the BRB structure and parameters, and a bi-level optimization algorithm is proposed. Three evolutionary algorithms, namely, the genetic algorithm, particle swarm optimization algorithm, and differential evolutionary algorithm, are tested in a comparative fashion to determine the best fit for the optimization engine. The results of two practical case studies show that the joint optimization approach can identify an optimal configuration for both its structure and parameters, which is referred to as the best decision structure in this paper. [ABSTRACT FROM AUTHOR]