Medical assisted decision-making plays a key role in providing accurate and reliable medical advice. But in medical decision-making, various uncertainties are often accompanied. The belief rule base (BRB) has a strong nonlinear modeling capability and can handle uncertainties well. However, BRB suffers from combinatorial explosion and tends to influence explainability during the optimization process. Therefore, an interval belief rule base with explainability (IBRB-e) is explored in this paper. Firstly, pre-processing using extreme gradient boosting (XGBoost) is performed to filter out features with lower importance. Secondly, based on the filtered features, explainability criterion is defined. Thirdly, evidence reasoning (ER) rule is chosen as an inference tool, while projection covariance matrix adaptive evolutionary strategy (P-CMA-ES) algorithm with explainability constraints is chosen as an optimization algorithm. Lastly, the validation of the model is performed through a breast cancer case. The experimental results show that IBRB-e has good explainability while maintaining high accuracy.

Fault diagnosis is crucial for mastering the operation status of complex equipment. However, due to the complexity of large-scale data-driven models, the process of fault diagnosis is difficult to comprehend and provide convincing results. In this paper, a transparent rule-based fault diagnosis method is proposed by introducing expert reliability, which covers three aspects: modeling, reasoning and optimization. Firstly, a transparent knowledge base is proposed using belief rule base and linguistic Z-number, namely LZ-BRB, in which the expert reliability is modeled. LZ-BRB characterizes the mapping relationship reflected by incompletely reliable knowledge between fault features and fault states. Secondly, a new evidential reasoning rule with the unreliable proposition (ER-UP) is developed to perform the reasoning of LZ-BRB and obtain the diagnosis result. The reliability of diagnosis results is acquired and measures the trustworthiness of the diagnosis result. Thirdly, to improve the diagnosis accuracy and maintain the transparent modeling process, expert reliability is considered in model optimization and a knowledge-data hybrid-driven gradient descent (KDGD) method is developed. Finally, a fault diagnosis case of the aerospace relay verifies the proposed method. The case results show that the diagnosis performance of the proposed method is competitive and maintains superb transparency.Note to Practitioners—Fault diagnosis holds paramount importance in the health management of industrial equipment. Nowadays, large-scale intelligent fault diagnosis methods have gained widespread application in the diagnosis of various mechanical and electronic equipment. Nevertheless, due to the complex structure and excessive parameters, it is hard for managers to make sense of the modeling, reasoning and optimization process of these models. Hence, there is an urgent need for a transparent fault diagnosis approach that can provide trustworthy diagnosis results. In this paper, based on BRB and linguistic Z-number, we present a transparent rule-based fault diagnosis method considering the knowledge reliability of human experts in engineering, including a transparent knowledge base, inference engine and model optimization. A fault diagnosis case of aerospace relay validates the effectiveness of the method and demonstrates the transparency of the fault diagnosis process. The proposed method can effectively model incompletely reliable expert knowledge and achieve transparent fault diagnosis, contributing to the health management of complex equipment.

The evidential reasoning (ER) rule has been widely applied in the multiple attribute decision making (MADM), which makes the decision-making process transparent and credible by using a belief structure. To improve the ability of the ER rule in dealing with the interval uncertainty, a new interval ER (IER) rule is proposed in this article. The interval uncertainty is described as the interval grade in the new frame of discernment (FoD) to model the local ignorance. It is proved that the IER rule is a generalization of the ER rule. To study the influence of perturbation on the IER rule, the perturbation is first introduced to the belief structure, and the perturbation analysis (PA) is conducted for the IER rule. An optimization model is established to estimate the perturbation threshold, which can measure the effectiveness of the inference result under perturbation. Two numerical examples and a case study are carried out, respectively, to show the implementation process of the proposed IER rule and validate its effectiveness in different decision-making scenarios.

Belief rule base (BRB) expert system has been widely used in complex system modeling. Robustness is crucial to the modeling performance and safety of BRB. For a better understanding and utility of BRB, there is thereby an urgent need to know what kind of influence each part of BRB may have when the disturbance occurs. Aiming at this, a more comprehensive analysis of BRB robustness is conducted in this article. First, the Lipschitz condition for BRB is defined. With the definitions, a new robustness analysis method of BRB is proposed, which is conducted from four aspects: 1) the input transformation; 2) the matching degree calculation; 3) the matching degree normalization; and 4) the rule aggregation. Moreover, five guidelines for BRB construction are proposed by analyzing its robustness, which can offer a practical guide for users to establish, adjust, and improve the BRB model for specific applications. The robustness analysis of the BRB expert system for the relay health-state evaluation is conducted to verify the effectiveness of the proposed method.

The evidential reasoning (ER) rule has been widely used in the data analysis, which provides a transparent and credible inference process and can effectively deal with various uncertainties. However, the traditional ER rule requires the evidence to be strictly independent of each other, which may not be easily satisfied in engineering practice. In addition, the perturbation can affect the sample data and cause unstable inference results. As such, in this article, a new ER rule with likelihood analysis and perturbation analysis (PA) is proposed based on the maximum likelihood ER (MAKER). The likelihood analysis is used to acquire probabilistic evidence from the sample data. The interdependence index of evidence is defined on the marginal probability and joint probability. A parameter optimization model is established based on the maximum likelihood (ML). The PA is conducted on the proposed ER rule to study its robustness, and a generalized PA method is explored to facilitate its potential applications. A case study of the performance evaluation of laser gyros is carried out to show the implementation of the proposed method and validate its effectiveness in reality.

In current studies of safety assessment for complex systems with the evidential reasoning (ER) rule, the evidence reliability is generally given by experts, which makes the observation data by sensors ignored. However, sensors are inevitably affected by such various uncertainties as perturbations in engineering practice, which can reduce their quality and tracking ability. As such, the observation data may become unreliable, and the modeling accuracy of the ER rule is decreased. In this article, a new ER rule-based safety assessment method with sensor reliability for complex systems is proposed, where sensor reliability and perturbation are considered. The coefficient of the variation-based weighting (CVBW) method is employed to obtain sensor weight. The sensor reliability is calculated by static reliability and dynamic reliability, which are determined by experts and the distance-based method, respectively. The perturbation is quantified as a bounded parameter defined as the perturbation factor, which is used to describe uncertainties and aggregate static reliability and dynamic reliability. The performance analysis of safety assessment is conducted to demonstrate the rationality of perturbation and position poor sensors, followed by a safety assessment algorithm. A case study is carried out to validate the effectiveness of the proposed method.

Evidential reasoning (ER) rule has been widely used in dealing with uncertainty. As an important parameter to measure the inherent property of evidence, the evidence reliability makes the ER rule constitute a generalized reasoning framework. In current research of the ER rule, the evidence reliability tends to be expressed in the form of quantitative value by certain methods or expert knowledge. The single quantitative value lacks the ability to describe the statistical property of reliability, which leads to unreasonable results. In this article, a new ER rule with continuous probability distribution of reliability denoted by ERr-CR is proposed. The combination of two pieces of evidence is discussed in detail, where the reliability is profiled as random variables with specific probability distribution. To characterize the output of ERr-CR, a novel concept of expectation of the expected utility is proposed. In addition, the ERr-CR is expanded to multiple pieces of evidence to show its universality. Further, the basic performances of the ERr-CR are explored to illustrate the rationality. Moreover, a case study of safety assessment of natural gas storage tanks (NGSTs) is conducted to show the potential applications of ERr-CR, which makes the proposed method more practical.

As the generalization of fuzzy systems, the belief rule base (BRB) expert system is transparent and interpretable. However, the interpretability of BRB has almost been ignored recently and leads to the decrease of model credibility. The main reason is the lack of unified guidelines for establishing an interpretable BRB expert system. In this article, the interpretability characteristics of BRB are summarized systematically, which can be used as the guideline of BRB establishment. Four interpretability criteria are proposed to ensure the interpretability of BRB in the optimization. A modified optimization algorithm with the interpretability constraints transformed from the interpretability criteria is further developed. As such, an interpretable BRB can be established. A case study for health state evaluation of the aerospace relay is conducted to verify the effectiveness of the proposed method.

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.