Belief Rule-based System Research Articles

Evolutionary Optimization for the Belief-Rule-Based System: Method and Applications

Evolutionary optimization (EO) has been proven to be highly effective computation means in solving asymmetry problems in engineering practices. In this study, a novel evolutionary optimization approach for the belief rule base (BRB) system is proposed, namely EO-BRB, by constructing an optimization model and employing the Differential Evolutionary (DE) algorithm as its optimization engine due to its ability to locate an optimal solution for problems with nonlinear complexity. In the EO-BRB approach, the most representative referenced values of the attributes which are pre-determined in traditional learning approaches are to be optimized. In the optimization model, the mean squared error (MSE) between the actual and observed data is taken as the objective, while the initial weights of all the rules, the beliefs of the scales in the conclusion part, and the referenced values of the attributes are taken as the restraints. Compared with the traditional learning approaches for the BRB system, the EO-BRB approach (1) does not require transforming the numerical referenced values of the attributes into linguistic terms; (2) does not require identifying any initial solution; (3) does not require any mathematical deduction and/or case-specific information which verifies it as a general approach; and (4) can help downsize the BRB system while producing superior performances. Thus, the proposed EO-BRB approach can make the best use of the nonlinear modeling ability of BRB and the optimization superiority of the EO algorithms. Three asymmetry numerical and practical cases are studied to validate the efficiency of the proposed EO-BRB approach.

A novel rule generation and activation method for extended belief rule-based system based on improved decision tree

A novel rule generation and activation method for extended belief rule-based system based on improved decision tree

Machine learning with Belief Rule-Based Expert Systems to predict stock price movements

Price prediction of financial assets has been a key interest for researchers over the decades. Numerous techniques to predict the price movements have been developed by the researchers over the years. But a model loses its credibility once a large number of traders start using the same technique. Therefore, the traders are in continuous search of new and efficient prediction techniques. In this research, we propose a novel machine learning technique using technical analysis with Belief Rule-Based Expert System (BRBES), and incorporating the concept of Bollinger Band to forecast stock price in the next five days. A Bollinger Event is triggered when the closing price of the stock goes down the Lower Bollinger Band. The BRBES approach has never been applied to stock markets, despite its potential and the appetite of the financial markets for expert systems. We predict the price movement of the Swedish company TELIA as a proof of concept. The knowledge base of the initial BRBES is constructed by simulating the historical data and then the learning parameters are optimized using MATLAB’s fmincon function. We evaluate the performance of the trained BRBES in terms of Accuracy, Area Under ROC Curve, Root Mean Squared Error, type I error, type II error, R2 value, and profit/loss ratio. We compare our proposed model against a similar rule-based technique, Adaptive Neuro-Fuzzy Inference System (ANFIS), to understand the significance of the improved rule base of BRBES. We also compare the performance against Support Vector Machine (SVM), one of the most popular machine learning techniques, and a simple heuristic model. Finally, the trained BRBES is compared against recent state-of-the-art deep learning approaches to show how competitive the performance of our proposed model is. The results show that the trained BRBES produces better performance than the non-trained BRBES, ANFIS, SVM, and the heuristic approaches. Also, it indicates better or competitive performance against the deep learning approaches. Thus BRBES exhibits its potential in predicting financial asset price movement.

Micro-extended belief rule-based system with activation factor and parameter optimization for industrial cost prediction

Industrial cost is a comprehensive indicator to reflect industrial behaviors, whereas industrial data with annotation are rare because the annotation process is very expensive. Data increment transformation is a feasible solution to enrich annotated industrial data, but it bring a new challenge in system modeling because the size of transformational data is the quadratical relationship with that of collected data, and even turn into big data problem. Hence, a novel rule-based system proposed for handling big data problems, called micro-extended belief rule-based system (Micro-EBRBS), is introduced for industrial cost prediction. Firstly, the Micro-EBRBS is improved by (1) the use of activation factor to revise the calculation of individual matching degrees; (2) the use of parameter optimization to determine the optimal value of basic parameters. Afterwards, on the basis of data increment transformation, a novel industrial cost prediction model, called data increment-based Micro-EBRBS (DIME) model, is developed to accurately predict industrial costs. In case study, 13 state-own holding industries with historical data from 1999 to 2019 in China are used to illustrate the effectiveness of the DIME model. Comparative results show that the DIME model is more accurate than some existing models in industrial cost prediction.

Highly explainable cumulative belief rule-based system with effective rule-base modeling and inference scheme

Advancement and application of rule-based expert systems have been a key research area in explainable artificial intelligence (XAI) because the rule-base is one of the most common and natural explainable frameworks for knowledge representation. The present work aims to design a novel rule-based system, called Cumulative Belief Rule-Based System (CBRBS), by establishing efficient rule-base modeling and inference procedures, where the rule-base modeling procedure includes the generation of cumulative belief rules via numeric data transformation and extended belief rule integration, and the rule-base inference procedure includes the inference of cumulative belief rules via consistent rule activation and activated rule integration. All these procedures enable CBRBS to better achieve the balance of explainability, high-efficiency (or computing complexity), and accuracy to fit with different application scenarios, as well as overcome the limitations of classical rule-based systems. Extensive experiments based on the well-known pipeline leak detection problem and open-source classification problems are conducted to illustrate the feature and advantage of the CBRBS over other classical rule-based systems and some commonly used classifiers.

Convolutional rule inference network based on belief rule-based system using an evidential reasoning approach

With the development of artificial intelligence, we pay widespread attention to the high reliability and interpretability of resulting architectures and algorithms. As one of the main methods of machine learning, the “black-box” mechanism of neural networks lacks interpretability. In order to alleviate the low interpretability, based on belief rule-based inference methodology using the evidential reasoning approach (RIMER), we propose a convolutional rule inference network (CRIN), which is interpretable by involving rules in belief rule base (BRB) under various types of uncertain knowledge representation. Considering the influence of global data distribution on attribute weights, the determination of each attribute may be affected by all other attributes, based on the sigmoid activation function, we determine optimized attribute weights to make sure that each attribute weight is formed by all attribute values. The derivation functions with optimized attribute weights based on evidential reasoning theory also showed to ensure the feasibility of the following learning algorithm. For expressing the influence of local rules input on final output in the network, the network framework and learning algorithm of CRIN based on convolution strategy are proposed. The inference process in RIMER is used as the feedforward mechanism to ensure the interpretability of the network. Meanwhile, the gradient descent method is used as back propagation algorithm to adjust the parameters of rule base to establish a more reasonable BRB. The experimental results and comparative analysis demonstrate that the proposed CRIN has advantages in terms of interpretability and learning capability. This study suggests new trends for interpretable network and uncertain classification issues in the reasoning approach.

Construction of EBRB classifier for imbalanced data based on Fuzzy C-Means clustering

The Extended Belief Rule-Based (EBRB) system has been widely used to solve the real-world problems concerning with incompleteness, uncertainty, and ambiguity. However, EBRB is essentially a data-driven method, in which each rule is obtained from training data. Therefore, the generated extended belief rules may be severely biased when dealing with data with imbalanced classes. In this case, the number of the rules generated by the samples of majority classes (i.e., negative samples) may be much larger than those of minority classes (i.e., positive samples). Thus, the class imbalance may lead to significant biases in system decision-making. In order to resolve this problem, this paper proposes a novel EBRB system based on fuzzy C-means clustering (FCM-EBRB). First, we adopt FCM clustering to oversample the positive samples and undersample the negative ones, so as to achieve the balance between them. Next, this paper improves the construction method of EBRB and optimizes the system through an efficient parameter learning strategy. Finally, this paper conducts comprehensive comparison experiments on a binary classification synthetic dataset and 11 commonly used KEEL public class imbalance datasets. Experimental results show that the proposed method can effectively reduce the scale of the rule base and achieve high inference accuracy, especially for imbalanced data.

Interpretability and accuracy trade-off in the modeling of belief rule-based systems

As a widely used rule-based system, one of the strongest advantages of belief rule-based (BRB) systems is good interpretability. Currently, most studies on BRB modeling focus on improving accuracy only but overlook interpretability. In this study, the definition of interpretability in a BRB system is first discussed, and the evaluation indicators are designed for measurement. On this basis, a single-objective optimization framework for the interpretability and accuracy trade-off in the modeling of BRB systems is proposed. The differential evolution (DE) algorithm is utilized as the optimization tool, and a new encoding method of chromosomes is proposed to realize the coding of rules with different structures. Two case studies are tested to validate the efficiency and feasibility of the proposed optimization framework for BRB modeling in both prediction and classification. The results show that the proposed optimization framework can ensure the interpretability and accuracy of BRB systems simultaneously, which is conducive to promoting the application of BRB systems in fields that require high interpretability and accuracy.

Online updating extended belief rule-based system for sensor-based activity recognition

Sensor-based activity recognition (AR) is a core problem with the research domain of smart environments. It has, however, the potential to provide solutions to address the problems associated with the growing size and ageing profile of the global population. The work presented within this paper focuses on the extended belief rule-based system (EBRBS), which offered promising performance compared with popular benchmark AR models and exhibited a high robustness in the situation of sensor failure. Nevertheless, efficiency remains one of the major issues to be improved for determining and updating the extended belief rule base (EBRB) within the EBRBS. This is critical for further utilizing the EBRBS in AR situations within dynamic smart environments. An eigendecomposition-based sensor selection method is firstly proposed to select an effective subset of sensors and to also enable efficient implementation to facilitate online AR. A novel domain division-based rule generation method is also proposed to generate and update an EBRB efficiently when new sensor data are available or when some sensors should be included or excluded in the EBRB. The combination of these two methods leads to an enhanced EBRBS, called online updating EBRBS. Two datasets (in a balanced class situation) obtained from simulation and actual environments are studied to provide detailed experimental analysis as a preliminary study and basis to handle further the imbalanced situation of real AR. The experimental results demonstrate an enhanced performance of the online updating EBRBS compared with the original EBRBS and some benchmark AR models, in terms of efficiency and effectiveness.

An internet of things belief rule base smart system to predict earthquake

<p><span>An intelligent belief rule base (BRB) based system with internet of things (IoT) integration can evaluate earthquake prediction (EP). This ingenious and rational system can predict earthquake by aggregating changed animal behavior combined with environmental and chemical changes which are taken as real time inputs from sensors. The BRB expert system blends knowledge demonstration criterion like attribute weight, rule weight, belief degree. The intelligent BRB system with IoT predicts the probable occurrence of the earthquake in a region based on the sign and symptoms culled by the persistent sensors. The final result taken from Intelligent BRB system with IoT integration is compared with expert and fuzzy-based system. The projected method gives a better prediction than the up-to-date expert system and fuzzy system</span></p>

An Evolutionary Belief Rule-Based Clinical Decision Support System to Predict COVID-19 Severity under Uncertainty

Accurate and rapid identification of the severe and non-severe COVID-19 patients is necessary for reducing the risk of overloading the hospitals, effective hospital resource utilization, and minimizing the mortality rate in the pandemic. A conjunctive belief rule-based clinical decision support system is proposed in this paper to identify critical and non-critical COVID-19 patients in hospitals using only three blood test markers. The experts’ knowledge of COVID-19 is encoded in the form of belief rules in the proposed method. To fine-tune the initial belief rules provided by COVID-19 experts using the real patient’s data, a modified differential evolution algorithm that can solve the constraint optimization problem of the belief rule base is also proposed in this paper. Several experiments are performed using 485 COVID-19 patients’ data to evaluate the effectiveness of the proposed system. Experimental result shows that, after optimization, the conjunctive belief rule-based system achieved the accuracy, sensitivity, and specificity of 0.954, 0.923, and 0.959, respectively, while for disjunctive belief rule base, they are 0.927, 0.769, and 0.948. Moreover, with a 98.85% AUC value, our proposed method shows superior performance than the four traditional machine learning algorithms: LR, SVM, DT, and ANN. All these results validate the effectiveness of our proposed method. The proposed system will help the hospital authorities to identify severe and non-severe COVID-19 patients and adopt optimal treatment plans in pandemic situations.

Enhancing extended belief rule-based systems for classification problems using decomposition strategy and overlap function

Multi-class and multi-attribute are two important features of classification problems and have different effects on the requirements and performance of the classifier. Decomposition strategy and overlap function are two effective ways to enhance the performance of classifiers, because the former decomposes a complex multi-class problem into multiple simple sub-problems; the latter uses various functions to specify the conjunctive relationship of input variables in a multi-attribute problem. Extended belief rule-based system (EBRBS) is an advanced rule-based system that has been widely used in classification problems. In order to apply decomposition strategies and overlap functions to enhance the performance of EBRBSs, the present work focuses on the investigative research and comparative evaluation of the commonly used one-versus-one (OVO) decomposition strategy and five common overlap functions to improve the performance of EBRBSs on multi-class and multi-attribute problems. More specifically, three typical kinds of EBRBSs, namely original EBRBS (O-EBRBS), EBRBS with dynamic rule activation (DRA-EBRBS), and a latest EBRBS for big data (Micro-EBRBS), are selected to conduct extensive experimental studies on twenty classification problems. To best of our knowledge, this present work is the first time to provide a meaningful and useful study in revealing the potential capability of the EBRBSs with decomposition strategy and overlap function for multi-class and multi-attribute problems. Experimental results demonstrate that the square product overlap function and the OVO strategy can enhance the performance of EBRBSs over others for twenty classification problems.

Environmental investment prediction using extended belief rule-based system and evidential reasoning rule

A scientific environmental investment prediction plays a crucial role in controlling environmental pollution and avoiding the blind investment of environmental management. However effective environmental investment prediction usually has to fact three challenges about diversiform indicators, insufficient data, and the reliability of prediction models. In the present study, a new prediction model is proposed using the extended belief rule-based system (EBRBS) and evidential reasoning (ER) rule, called ensemble EBRBS model, with the aim to overcome the above challenges for better environmental investment prediction. The proposed ensemble EBRBS model consists of two components: 1) multiple EBRBSs, which are constructed on the basis of not only using various feature selection methods to select representative indicators but also data increment transformation to enrich the training data; 2) an ER rule-based combination method, which utilizes the ER rule to accommodate the weights and reliabilities of different EBRBSs with the predicted outputs of these EBRBSs to have an integrated environmental investment prediction. A detailed case study is then provided for validating the proposed model via extensive experimental and comparison analysis based on the real-world environmental data about 25 environmental indicators for 31 provinces in China ranged from 2005 to 2018. The results demonstrate that the ensemble EBRBS model can be used as an effective model to accurately predict environmental investments. More importantly, the ensemble EBRBS model not only obtains a high accuracy better than some existing prediction models, but also has an excellent robustness compared with others under the situations of excessive indicators and insufficient data.

Extended Belief Rule-Base Optimization Base on Clustering Tree and Parameter Optimization

Extended belief rule-based (EBRB) system has a better ability to model complex problems than belief rule-based (BRB) system. However, the storage of rules in EBRB system is out of order, which leads to the low efficiency of rule retrieval during the reasoning process. Therefore, to improve the efficiency of rule retrieval, this study introduces K-means clustering tree algorithm into the construction of rule base, then proposes a multi-layer weighted reasoning approach based on K-means clustering tree. The proposed approach seeks out a path on the tree during the rule retrieval process, and then figures out several reasoning results according to the nodes on the path. These results are weighted and aggregated to obtain the final conclusion of the system, thus ensure both the efficiency of reasoning and the sufficient utilization of information. In addition, the differential evolution (DE) algorithm is used to train the parameters of EBRB system in this study. Several experiments are conducted on commonly used classification datasets from UCI, and the results are compared with some existing works of EBRB system and conventional machine learning methods. The comparison results illustrate that the proposed method can make an obvious improvement in the performance of EBRB system.

Belief-Rule-Base Inference Method Based on Gradient Descent With Momentum

The belief-rule-base (BRB) inference methodology using the evidential reasoning (ER) approach is widely used in different fields, such as fault diagnosis, system identification, and decision analysis. However, the calculation characteristic of the conventional rule activation weight makes the inference system have the rule zero activation problem. The difficulty of constructing partial derivatives restricts the optimization of parameters using the gradient method. Hence, this paper proposes a new belief rule structure and its gradient training method to solve the rule zero activation problem during the inference process and improve inference accuracy. The Gaussian function is applied to calculate the activation weight of the rule with the new structure. Its characteristics avoid the zero activation problem caused by the attribute reference value set in the original method. Based on the newly proposed method, the corresponding distance-sensitive parameter is set for each attribute, and the weight parameter of each rule is discarded. It simplifies the calculation of rule activation weights in the inference process and enables the partial derivatives of the parameters of the inference system to be easily constructed. In the parameter optimization, the momentum optimization gradient stochastic descent method is used to train the new BRB system, which improves the training speed and accuracy compared with the conventional methods. Experiments with nonlinear function fitting, oil pipeline leak detection, and classification of several public datasets are carried out to verify whether the new BRB system trained with momentum stochastic gradient descent (SGDM-BRB) has better performance than other conventional methods. The experimental results show that in the case of complete data, SGDM-BRB has higher accuracy and faster training speed than the conventional methods.

Random clustering forest for extended belief rule-based system

Random clustering forest for extended belief rule-based system

A greedy belief rule base generation and learning method for classification problem

Among many rule-based systems employed in classification problems, the belief rule-based (BRB) system has been significant for its ability to deal with both quantitative and qualitative information under uncertainty. However, it may face excessive information and low accuracy in some applications due to the limitations of the conventional BRB generation method. To this end, a greedy-based BRB learning method is proposed in this paper. Firstly, the BRB is generated by selecting a reduced number of belief rules from a set of candidate rules. Then, the BRB learning process is conducted by exploiting a selection and reduction strategy, which searches and selects the optimal rules from candidate rules as well as removes noise and redundant rules. Moreover, the original procedures of the inference process and class estimation are retained from conventional BRB systems. Thirty standard classification benchmarks are tested to validate the effectiveness and efficiency of the proposed method, and the classification results are compared with existing rule-based systems, novel belief rule-based systems, and conventional machine learning methods. The comparison results show that the proposed method could achieve relatively satisfactory accuracy while having a significantly smaller BRB. Furthermore, the results derived from benchmarks with two or three classes show the superior performance of the proposed method compared with some state-of-the-art classification methods.

A framework for optimizing extended belief rule base systems with improved Ball trees

Decision support systems imposed a challenge for efficiently reasoning through utilizing stored unordered rules. The Extended Belief Rule-Base (EBRB) system, renowned for its capability of modeling data with vagueness, incompleteness, uncertainty and nonlinear features, requires to traverse over all the rules for the execution of reasoning and consequently suffers reduced inference accuracy and efficiency. To improve the performance, we propose a framework of storing and retrieving belief rules based on employing an optimized structure called improved Ball tree. The framework first constructs a Ball tree index according to the distance between different rules in the metric space, via using the k-means++ algorithm rather than traditionally employed k-centers. Then, through our proposed dynamic threshold radius adjusting method, our algorithm finds an appropriate dataset threshold and accordingly activates more related rules. Moreover, the number of retrieved and activated irrelevant rules is significantly reduced, resulting in consequently improved reasoning accuracy and efficiency. Lastly, three sets of experiments were carried out to validate our algorithm in comparison with the previous EBRB systems.

Evidential reasoning based decision system to select health care location

<span>The general public’s demand of Bangladesh for safe health is rising promptly with the improvement of the living standard. However, the allocation of limited and unbalanced medical resources is deteriorating the assurance of safe health of the people. Therefore, the new hospital construction with rational allocation of resources is imminent and significant. The site selection for establishing a hospital is one of the crucial policy-related decisions taken by planners and policy makers. The process of hospital site selection is inherently complicated because of this involves many factors to be measured and evaluated. These factors are expressed both in objective and subjective ways where as a hierarchical relationship exists among the factors. In addition, it is difficult to measure qualitative factors in a quantitative way, resulting incompleteness in data and hence, uncertainty. Besides it is essential to address the subject of uncertainty by using apt methodology; otherwise, the decision to choose a suitable site will become inapt. Therefore, this paper demonstrates the application of a novel method named belief rule-based inference methodology-RIMER base intelligent decision system(IDS), which is capable of addressing suitable site for hospital by taking account of large number of criteria, where there exist factors of both subjective and objective nature.</span>

Environmental Governance Cost Prediction of Transportation Industry by Considering the Technological Constraints

In order to solve the problem of environmental governance investment planning in the transportation industry, a cost prediction model is proposed under technological constraints, where the input output indictors emphasizes the flexibility of prediction and its characters are asymmetric, while the constructs of prediction model focuses on the standardization and its characters are symmetrical. The basic principle of the cost prediction model is based on an extended belief rule-based (EBRB) system to model the input-output relationship in investment planning, and a parameter learning model to improve the accuracy of the EBRB system. Additionally, the technological innovation factors are also embedded in the cost prediction model to investigate the influence of technology-related outcomes on investment planning. Finally, based on the data of environmental governance in China’s transportation industry from 2003 to 2016, the cost of transportation industry environmental management in China’s thirty provinces from 2017 to 2033 is predicted under the constraints of technological innovation. Results show that: (1) the accuracy of the proposed cost prediction model is higher than some existing cost prediction methods; (2) the predicted environmental governance costs have a significant regional difference; (3) the upgrading of technological innovation is conducive to saving the future environmental governance costs of the transportation industry in some provinces. In addition to the above results, the present study provides model supports and policy references for government decision makers in transportation industry-related environmental cost planning.