Belief Rule Research Articles

Belief-Rule-Based System with Self-organizing and Multi-temporal Modeling for Sensor-based Human Activity Recognition.

Smart environment is an efficient and cost- effective way to afford intelligent supports for the elderly people. Human activity recognition (HAR) is a crucial aspect of the research field of smart environments, and it has attracted widespread attention lately. The goal of this study is to develop an effective sensor-based HAR model based on the belief-rule-based system (BRBS), which is one of representative rule-based expert systems. Specially, a new belief rule base (BRB) modeling approach is proposed by taking into account the self- organizing rule generation method and the multi-temporal rule representation scheme, in order to address the problem of combination explosion that existed in the traditional BRB modelling procedure and the time correlation found in continuous sensor data in chronological order. The new BRB modeling approach is so called self-organizing and multi-temporal BRB (SOMT-BRB) modeling procedure. A case study is further deducted to validate the effectiveness of the SOMT-BRB modeling procedure. By comparing with some conventional BRBSs and classical activity recognition models, the results show a significant improvement of the BRBS in terms of the number of belief rules, modelling efficiency, and activity recognition accuracy.

A New Method Based on Belief Rule Base with Balanced Accuracy and Interpretability for Student Achievement Prediction

In the field of education, the accurate prediction of students’ future performance is essential for personalized instruction and efficient allocation of resources. Such predictions not only help education professionals develop targeted educational strategies but also identify students’ learning needs at an early stage so that timely interventions and support can be provided. To gain the trust of educational experts and ensure the practical application value of the prediction results, the prediction methods used must be highly interpretable. However, there are two problems with the current belief rule base (BRB) applied to student performance prediction. First, there is a current lack of effective strategies for enhancing the interpretability of the optimization process. Second, BRB models that overemphasize accuracy tend to exhibit characteristics of black-box models. To overcome these challenges, this paper proposes a new method based on BRB with balanced accuracy and interpretability (BRB-Bai) for student achievement prediction. First, an attribute selection method is proposed to filter out important features associated with student performance. Then, expert knowledge credibility is calculated, and four interpretability strategies are proposed to ensure the interpretability of the model and to achieve a balance between interpretability and accuracy on the basis of expert knowledge credibility. The effectiveness of the proposed model is demonstrated by conducting experiments on the student achievement dataset.

An algorithm for belief rule induction with partial ignorance

Belief rules are an extension of fuzzy rules that consider belief degrees. They are widely applied due to their traceability, interpretability, and flexibility. However, current belief rules only consider residual support and global ignorance while ignoring partial ignorance. In this paper, we proposed a novel belief rule-based classification system called partial ignorance belief rule induction algorithm (PIBRIA). The consequent part of belief rules takes into account not only the residual support and global ignorance but also partial ignorance of evidence. The belief degrees in the consequent part of each belief rule collectively form a genuine basic probability assignment (BPA). Based on fuzzy unordered rule induction algorithm (FURIA), we propose the learning algorithm for belief rules with partial ignorance, which helps the novel proposed PRIBIA achieve a balance between accuracy and complexity. The inference method employs the Dempster’s combination rule and Shafer’s discounting operation, where the discounting operation can resolve evidence conflicts in the combination rule. The effectiveness and superiority of PIBRIA in handling classification tasks have been validated by comparing it to some state-of-the-art rule-based models. The results of statistical tests show that PIBRIA outperforms all other methods in terms of classification accuracy. Whereas its computational complexity and model complexity are moderate.

A fuzzy evidential reasoning-based approach for assessing the navigation obstruction risk of shipwrecks in the Yangtze river

ABSTRACT This paper aims to evaluate the navigation obstruction risk represented by shipwrecks in shallow waters based on a fuzzy evidential reasoning approach. The purpose of this approach is to establish a hierarchical decision-making framework that considers ship conditions, traffic environment, distance from sensitive areas, and natural environment; to derive the belief rule base using the IF-THEN rule with a belief structure; and to obtain the crisp values of navigation obstruction risk of shipwrecks via evidential reasoning. This approach is applied to the navigation obstruction risk assessment of 10 historical shipwrecks in the Yangtze River, and the evaluation results are consistent with historical data. Consequently, this approach can be used for assisting in shipwreck salvage decision-making in navigable waters.

Interpretable large-scale belief rule base for complex industrial systems modeling with expert knowledge and limited data

Complex system modeling technology is a hot topic. Nowadays, many complex industrial systems present three characteristics: multiple input indicators, limited data and interpretability requirements. With good interpretability, belief rule base (BRB) serves as an efficient tool for modeling complex systems. However, as the number of input indicators of industrial systems increases, BRB suffers from the combinatorial explosion problem, which makes it hard to generate large-scale BRB and optimize it while maintaining its interpretability. For this purpose, an interpretable large-scale BRB is proposed for complex systems with limited data, where expert knowledge can be utilized effectively. First, a framework for generating an initial large-scale BRB using expert knowledge and limited data is developed, including the determination of attribute weight, basic belief degree and rule weight. Afterwards, a new parameter optimization model is designed to reduce the burden of parameter optimization and maintain the interpretability of BRB, where the Adaptive Moment Estimation (Adam) algorithm is adopted to further improve the efficiency of large-scale parameter optimization. Finally, a health assessment case of an inertial navigation system (INS) verifies the proposed method.

A Health State Prediction Model for Aeroengine Based on Multi-attribute Belief Rule Base with Considering Monitoring Error

A Health State Prediction Model for Aeroengine Based on Multi-attribute Belief Rule Base with Considering Monitoring Error

Belief rule learning and reasoning for classification based on fuzzy belief decision tree

The belief rules which extend the classical fuzzy IF-THEN rules with belief consequent parts have been widely used for classifier design due to their capabilities of building linguistic models interpretable to users and addressing various types of uncertainty. However, in the rule learning process, a high number of features generally results in a belief rule base with large size, which degrades both the classification accuracy and the model interpretability. Motivated by this challenge, the decision tree building technique which implements feature selection and model construction jointly is introduced in this paper to learn a compact and accurate belief rule base. To this end, a new fuzzy belief decision tree (FBDT) with fuzzy feature partitions and belief leaf nodes is designed: a fuzzy information gain ratio is first defined as the feature selection criterion for node fuzzy splitting and then the belief distributions are introduced to the leaf nodes to characterize the class uncertainty. Based on the initial rules extracted from the constructed FBDT, a joint optimization objective considering both classification accuracy and model interpretability is then designed to further reduce the rule redundancy. Experimental results based on real datasets show that the proposed FBDT-based classification method has much smaller rule base and better interpretability than other rule-based methods on the premise of competitive accuracy.

Lithium-Ion Battery Health Assessment Method Based on Double Optimization Belief Rule Base with Interpretability

Health assessment is necessary to ensure that lithium-ion batteries operate safely and dependably. Nonetheless, there are the following two common problems with the health assessment models for lithium-ion batteries that are currently in use: inability to comprehend the assessment results and the uncertainty around the chemical reactions occurring inside the battery. A rule-based modeling strategy that can handle ambiguous data in health state evaluation is the belief rule base (BRB). In existing BRB studies, experts often provide parameters such as the initial belief degree, but the parameters may not match the current data. In addition, random global optimization methods may undermine the interpretability of expert knowledge. Therefore, this paper proposes a lithium-ion battery health assessment method based on the double optimization belief rule base with interpretability (DO-BRB-I). First, the belief degree is optimized according to the data distribution. Then, to increase accuracy, belief degrees and other parameters are further optimized using the projection covariance matrix adaptive evolution strategy (P-CMA-ES). At the same time, four interpretability constraint strategies are suggested based on the features of lithium-ion batteries to preserve interpretability throughout the optimization process. Finally, to confirm the efficacy of the suggested approach, a sample of the health status assessment of the B0006 lithium-ion battery is provided.

Health state assessment model for complex systems: Trade-off accuracy and robustness in belief rule base

In complex system, health state assessment can determine the state of the system and identify potential system problems. However, due to the numerous uncertainties and variations present in complex systems, it is difficult to effectively construct assessment models. Belief rule base (BRB) can use data-driven and knowledge-driven methods to effectively address uncertain information, and is widely used for modeling health state assessments of complex systems. The primary modeling and optimization goals of BRB is currently at accuracy, ignoring the impact of robustness on complex systems, and the reliability of the model is reduced. Therefore, this article introduces a novel method to balance the accuracy and robustness of BRB models. This method enhances the performance of the BRB model in assessing complex system health and provides valuable guidance for engineering applications. Firstly, the guidelines for BRB modeling are systematically summarized to address the trade-off between accuracy and robustness. This provides essential guidance for constructing BRB models during the model-building process. Secondly, four feasible domain criteria are proposed to enhance the reliability of the BRB during the model optimization process. A modified multi-objective optimization algorithm is proposed based on the feasible domain criteria. Finally, in the case studies of aerospace relay and lithium-ion battery health assessments, the MSE of the proposed model for aerospace relay health assessment is 0.0015 with a Lipschitz constant of 6.73, while for lithium-ion battery health assessment, the MSE is 0.0013 with a Lipschitz constant of 24.17. The experimental results demonstrate that the proposed model has an advantage in terms of the trade-offs between both robustness and accuracy.

Optimal scheduling of green heating systems in buildings considering economy and exergy efficiency

Green heating in buildings is of great significance to global energy conservation and emission reduction, and the design of optimal scheduling models is the key to achieve cost reduction and efficiency improvement in heating systems. For the building heating system containing multiple heterogeneous energy sources such as solar energy, air energy and electricity, a multi-objective optimal scheduling model is established with the goal of maximizing the exergy efficiency and minimizing the economic cost of the system, taking into account the quality difference of energy in the conversion process. Regarding the nonconvex and nonlinear constraints in the scheduling model, the incremental linearization method and Big-M method are used to linearize the transformation, and obtain the multi-objective mixed-integer linear programming model. Further, the ε-constraint method is used to solve the Pareto frontier of multi-objective optimization and the technique for order preference by similarity to ideal solution (TOPSIS) method is used to make decision. Finally, the simulation study of the model is carried out, and the results show that the proposed multi-objective optimal scheduling can balance the system operation economy and exergy efficiency compared with the belief rule base and evidential reasoning (BRB-ER) method, and the system’s daily economic cost are reduced by 9.66 %, 9.94 % and 17.24 %, respectively, and the system’s average daily coefficient of performance (COP) are improved by 4.66 %, 14.05 % and 13.22 %, respectively, on three typical days, it is verified that the proposed optimal scheduling model has better economy and exergy efficiency. The proposed multi-objective optimal scheduling model introduces exergy efficiency rather than energy efficiency as one of the optimization objectives of the heating system and reasonably solves the optimization model, which can provide a new idea and reference for the multi-objective optimal scheduling of the green heating system in buildings.

A new aeronautical relay health state assessment method based on generic belief rule base with attribute reliability

As a classical rule-based modeling approach, belief rule base (BRB) expert system can integrate expert knowledge and possesses good interpretability. BRB with attribute reliability (BRB-r), built upon BRB, provides an effective way to deal with the problems of model reliability and environmental disturbances. Moreover, robustness is an important measure of perturbation resistance, and a robust BRB-r can remain reliable and stable in various environments. Therefore, to improve the model's ability to resist perturbations and enhance the model's adaptability, a new generic BRB with attribute reliability (G-BRB-r) is developed. Specifically, the robustness of BRB-r is analyzed in this paper to explore the change of BRB-r robustness under different perturbations. In addition, combining the effects of different factors on robustness, the construction criteria and constraints of robust BRB-r are given to guide modeling. Then, considering the effects of attribute reliability and robustness on modeling performance, a new generic BRB with attribute reliability is developed. Finally, the effectiveness and adaptability of the proposed method are demonstrated through a case study for health state assessment of the aerospace relay.

An interpretable capacity prediction method for lithium-ion battery considering environmental interference

Predicting the capacity of lithium-ion battery (LIB) plays a crucial role in ensuring the safe operation of LIBs and prolonging their lifespan. However, LIBs are easily affected by environmental interference, which may impact the precision of predictions. Furthermore, interpretability in the process of predicting LIB capacity is also important for users to understand the model, identify issues, and make decisions. In this study, an interpretable method considering environmental interference (IM-EI) for predicting LIB capacity is introduced. Spearman correlation coefficients, interpretability principles, belief rule base (BRB), and interpretability constraints are used to improve the prediction precision and interpretability of IM-EI. Dynamic attribute reliability is introduced to minimize the effect of environmental interference. The experimental results show that IM-EI model has good interpretability and high precision compared to the other models. Under interference conditions, the model still has good precision and robustness.

A New Student Performance Prediction Method Based on Belief Rule Base with Automated Construction

Student performance prediction (SPP) is a pivotal task in educational analytics, enabling proactive interventions and optimized resource allocation by educators. Traditional SPP models are often hindered by their complexity and lack of interpretability. This study introduces a novel SPP framework, the Belief Rule Base with automated construction (Auto–BRB), designed to address these issues. Firstly, reference values are derived through data mining techniques. The model employs an IF–THEN rule-based system integrated with evidential reasoning to ensure both transparency and interpretability. Secondly, parameter optimization is achieved using the Projected Covariance Matrix Adaptive Evolution Strategy (P–CMA–ES), significantly enhancing model accuracy. Moreover, the Akaike Information Criterion (AIC) is then applied to fine-tune the balance between model accuracy and complexity. Finally, case studies on SPP have shown that the Auto–BRB model has an advantage over traditional models in terms of accuracy, while maintaining good interpretability. Therefore, Auto–BRB has excellent application effects in educational data analysis.

Heterogeneous Information Fusion Recognition Method Based on Belief Rule Structure

Heterogeneous Information Fusion Recognition Method Based on Belief Rule Structure

A health assessment method with attribute importance modeling for complex systems using belief rule base

In the health assessment for complex systems, system attributes refer to the indicators or components having an impact on the health state of the system. When assessing the health state of complex systems, the relative importance of system attributes should be accurately modeled, otherwise incorrect results may occur. Especially for some complex systems with small samples, data-driven methods are prone to overfitting. In this article, a new method using belief rule base (BRB) is proposed to model the relative importance of system attributes while assessing the health state. As an interpretable modeling tool, BRB constructs nonlinear mapping relationships between system attributes and health state. A data-knowledge hybrid-driven ensemble feature selection (DKH-EFS) method is developed to calculate the relative importance of the system attributes, namely attribute importance (AM). A random sensitivity analysis (RSA) method of the model output to the input of BRB is proposed to calculate the feature importance (FI) of BRB. A new parameter optimization model considering the consistency between the AM and FI is introduced to improve the modeling ability of BRB for the AM. A case study on the health assessment of the fiber optic gyroscope (FOG) validates the proposed method.

On the continuous probability distribution attribute weight of belief rule base model

On the continuous probability distribution attribute weight of belief rule base model

A Student Performance Prediction Model Based on Hierarchical Belief Rule Base with Interpretability

Predicting student performance in the future is a crucial behavior prediction problem in education. By predicting student performance, educational experts can provide individualized instruction, optimize the allocation of resources, and develop educational strategies. If the prediction results are unreliable, it is difficult to earn the trust of educational experts. Therefore, prediction methods need to satisfy the requirement of interpretability. For this reason, the prediction model is constructed in this paper using belief rule base (BRB). BRB not only combines expert knowledge, but also has good interpretability. There are two problems in applying BRB to student performance prediction: first, in the modeling process, the system is too complex due to the large number of indicators involved. Secondly, the interpretability of the model can be compromised during the optimization process. To overcome these challenges, this paper introduces a hierarchical belief rule base with interpretability (HBRB-I) for student performance prediction. First, it analyzes how the HBRB-I model achieves interpretability. Then, an attribute grouping method is proposed to construct a hierarchical structure by reasonably organizing the indicators, so as to effectively reduce the complexity of the model. Finally, an objective function considering interpretability is designed and the projected covariance matrix adaptive evolution strategy (P-CMA-ES) optimization algorithm is improved. The aim is to ensure that the model remains interpretable after optimization. By conducting experiments on the student performance dataset, it is demonstrated that the proposed model performs well in terms of both accuracy and interpretability.

Hawala in criminal court: the role of law and commercial culture in informal financial exchange

A historically informed understanding of ḥawāla and other varieties of informal value transfer systems (IVTS) requires consideration of the normative and cultural elements which structure and facilitate transactions in globalized financial markets. This paper argues that the Sharia-based normative and cultural framework of ḥawāla is created in the social relations of Muslim networks and that, in a criminal law context, this normativity can be used as a tool to discern between legitimate and illegitimate transactions. The new institutional economists’ (NIE) explanation of ḥawāla, which predominates in scholarly work, neglects this common frame of reference built on community, shared belief, and normative rules and expectations. The NIE views economic institutions through the lens of profitmaking and self-interest centred institutional development. Moreover, in a criminal law context, the profit-oriented perspective of law overlooks the normative characteristics that sometimes appear in the transactional characteristics of these transactions. When evidence of these characteristics is presented to the court, they offer a useful tool to differentiate legitimate from illegitimate transfers of value. Legitimate transfers will frequently be facilitated through dense networks in which the normativity and culture of ḥawāla frame the rules and expectations of parties to the transaction. Criminal transactions, on the other hand, typically involve fewer participants, sometimes from different ethnic and linguistic backgrounds, are profit-orientated, and involve means of enforcement such as the use of violence which traditional networks do not employ. The NIE perspective does not fully account for non-western legal orders or for commercial practices in which exchange remains culturally, historically, and socially embedded.

Network Security Prediction of Industrial Control Based on Projection Equalization Optimization Algorithm.

This paper predicts the network security posture of an ICS, focusing on the reliability of Industrial Control Systems (ICSs). Evidence reasoning (ER) and belief rule base (BRB) techniques are employed to establish an ICS network security posture prediction model, ensuring the secure operation and prediction of the ICS. This model first integrates various information from the ICS to determine its network security posture value. Subsequently, through ER iteration, information fusion occurs and serves as an input for the BRB prediction model, which necessitates initial parameter setting by relevant experts. External factors may influence the experts' predictions; therefore, this paper proposes the Projection Equalization Optimization (P-EO) algorithm. This optimization algorithm updates the initial parameters to enhance the prediction of the ICS network security posture through the model. Finally, industrial datasets are used as experimental data to improve the credibility of the prediction experiments and validate the model's predictive performance in the ICS. Compared with other methods, this paper's prediction model demonstrates a superior prediction accuracy. By further comparing with other algorithms, this paper has a certain advantage when using less historical data to make predictions.

Data-and knowledge-driven belief rule learning for hybrid classification

In hybrid classification problems, apart from labeled data, some related expert knowledge may also be obtained. If the partial information from these two sources can be jointly used well, the performance may be effectively improved. To this end, we develop a new framework for hybrid classification by modeling the uncertain data and knowledge in the form of belief rules under the framework of belief function theory. First, a data-driven belief rule learning algorithm is proposed to learn a compact and interpretable belief rule model from labeled training data. Then, a knowledge-driven belief rule learning algorithm is proposed to learn a model which is complementary to that learned from data via active learning strategy. Finally, the genetic integration of belief rules is developed in order to integrate data-driven belief rules with knowledge-driven ones to reduce the rule redundancy and rule conflict by considering both classification accuracy and model interpretability. Experiments based on both simulated and real data sets demonstrate the superiority of the proposed model for integrating data and knowledge.