Expert knowledge holds a pivotal role in artificial intelligence models. Constrained by the subjectivity and ignorance of human cognition, it is imperfectly reliable. Modeling and decision-making driven by such knowledge may generate large risks. To this end, it is necessary to investigate a mechanism for handling such imperfectly reliable knowledge. In this paper, the reliability of knowledge is described as expert reliability. A novel rule-based modeling framework with expert reliability is proposed correspondingly, including the following four parts: modeling, reasoning, optimization and robustness analysis. The main works are: (1) Based on the transparent knowledge representation of belief rule base (BRB), a linguistic Z-number BRB (LZ-BRB) is proposed, where the linguistic Z-number quantitatively represents expert reliability. (2) An improved evidential reasoning (ER) rule is developed to obtain the inference result of the LZ-BRB model. (3) A data-driven parameter optimization model is designed to reduce modeling errors caused by imperfectly reliable knowledge. (4) The robustness analysis of expert reliability is performed to further analyze its influence on the inference result. Finally, a fiber optic gyro (FOG) health evaluation case verifies the proposed method.

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.