Extended Belief Rule-based System Research Articles

A novel extended rule-based system based on K-Nearest Neighbor graph

The Belief Rule-Based (BRB) system faces the rule combination explosion issue, making it challenging to construct the rule base efficiently. The Extended Belief Rule-Based (EBRB) system offers a solution to this problem by using data-driven methods. However, using EBRB system requires the traversal of the entire rule base, which can be time-consuming and result in the activation of many irrelevant rules, leading to an incorrect decision. Existing search optimization methods can somewhat solve this issue, but they have limitations. Moreover, the calculation of the rule activation weight only considers the similarity between input data and a single rule, ignoring the influence of the rule linkage. To address these problems, we propose a new EBRB system based on the K-Nearest Neighbor graph index (Graph-EBRB). We introduce the Hierarchical Navigable Small World (HNSW) algorithm to create the K-Nearest Neighbor graph index of the EBRB system. This index allows us to efficiently search and activate a set of key rules. We also propose a new activation weight calculation method based on the Graph Convolution Neural Network (GCN), and we optimize the system performance using a parameter learning strategy. We conduct a comprehensive experiment on 14 commonly used public data sets, and the results show that Graph-EBRB system significantly improves the reasoning efficiency and accuracy of the EBRB system. Finally, we apply the Graph-EBRB system to tree disease identification and achieve excellent classification performance, identifying over 90% of the diseased trees on the complete dataset.

An explainable decision model based on extended belief-rule-based systems to predict admission to the intensive care unit during COVID-19 breakout

Given the shortage of intensive care units (ICUs) due to the coronavirus disease (COVID-19), a prediction model is essential in ensuring the availability of ICU beds. However, several challenges, such as the importance of distinguishing indicators, efficiency of ICU admission records, and the explainability and effectiveness of the prediction model, hinder the effective prediction of ICU admissions. To mitigate these challenges, an explainable decision model that uses the extended belief rule-based system is introduced to predict ICU admission. First, an indicator extraction model is proposed to measure the importance of the various indicators and obtain representative indicators. Second, a Charnes, Cooper, and Rhodes (CCR) model is constructed to measure the efficiencies of the belief rules to achieve the compact structure of an extended belief rule base. Third, a new extended belief rule-based model, optimized by parameter optimization and domain division-based rule reduction, is developed to predict ICU admission. These procedures enable the explainable decision model to adapt to big data situation, offer explanations and realize high efficiency. Finally, a case study of ICU admission during a COVID-19 outbreak is conducted to demonstrate the implementation and effectiveness of the proposed model in a comparative analysis.

Ensemble extended belief rule-based systems with different similarity measures for classification problems

The extended belief rule-based (EBRB) system is shown to have the potential to handle both quantitative and qualitative information under uncertainty, and it has been used as an effective tool for decision support and classification problems. However, despite these advances, several drawbacks have emerged recently, and the most significant one is caused by its similarity measure using Euclidean distance, which could lead to counterintuitive individual matching degrees, while other widely used similarity measures have not been studied for their application in the EBRB system. To this end, seventeen similarity measures are investigated and applied in the EBRB system in this paper, and based on the analysis, an ensemble method for EBRB system with different similarity measures is proposed. Firstly, the problem of the similarity measure of the conventional EBRB system is investigated. Then, a variety of similarity measures are analyzed and their application in the EBRB system is studied. Next, the ensemble method for EBRB systems with different similarity measures is proposed, which consists of two parts, the adaptive weight learning method for determining the weight of each EBRB system with different similarity measures, and the evidential reasoning (ER)-based combination method for combining the inferential results of different methods. Finally, 25 classification datasets are studied to test the performance of EBRB systems with different similarity measures as well as the proposed method, and the results are compared with existing works. The comparison results show that the proposed method could not only achieve better results than any other EBRB systems with different similarity measures, but also outperform other conventional classifiers on some classification datasets, especially small-scale datasets.

Extended belief rule-based system using bi-level joint optimization for environmental investment forecasting

Scientific investment forecasting can effectively avoid the blind investments of environmental management. Among existing studies in developing investment forecasting models, the extended belief rule-based system (EBRBS) showed its potential to accurately predict environment investments but also exposed two challenges to be further addressed: (1) how to select antecedent attributes from various environmental indicators for the EBRBS; (2) how to optimize basic parameters of the EBRBS based on the selected antecedent attributes. Since these two challenges are connected, a bi-level joint optimization model is proposed to improve the EBRBS for better environmental investment forecasting, in which the selection of antecedent attributes is described as an upper-level optimization model using Akaike information criterion (AIC) and the optimization of basic parameters is as a lower-level optimization model using mean absolute error (MAE). Moreover, a corresponding bi-level joint optimization algorithm is proposed to solve the bi-level joint optimization model, where ensemble feature selection and swarm intelligence optimization are regarded as the engine of upper-level and lower-level optimizations, respectively. The real environmental data collected from 2005 to 2020 of 30 Chinese provinces are studied to verify the effectiveness of the proposed approach. Experimental results show that the EBRBS with bi-level joint optimization not only can effectively predict environmental investments, but also is able to have desired accuracy better than previous investment forecasting models.

Extended Belief Rule-Based System With Accurate Rule Weights and Efficient Rule Activation for Diagnosis of Thyroid Nodules

Extended belief-rule-based (EBRB) system is a representative rule-based system and has attracted much attention due to its capability of solving the problems of combinatorial explosion and time-consuming optimization incurred by belief-rule-based system. Despite their advantages, the development of EBRB suffers from some shortcomings, such as the unreasonable calculation of similarity between input and antecedent belief distributions (BDs), inaccurate calculation of individual matching degrees and rule weights, and inefficient determination of activation rules. To address these shortcomings, this article proposes a new EBRB system, in which an existing similarity measure between two BDs is adopted to accurately calculate the individual matching degrees and rule weights. Furthermore, the activation weight of a rule is efficiently calculated within an activation group generated using the affinity propagation algorithm, which is utilized to determine whether the rule is activated. The activation rules are then integrated using their weights and the evidential reasoning algorithm to generate the inference result. To demonstrate its accuracy and efficiency, the proposed EBRB system is employed to help diagnose thyroid nodules based on the historical examination reports collected from a tertiary hospital located in Hefei, Anhui, China. The findings are highlighted by the comparison of the proposed EBRB system with existing EBRB systems based on the historical reports and datasets derived from the University of California at Irvine.

A data-driven rule-based system for China’s traffic accident prediction by considering the improvement of safety efficiency

Rapid traffic development brings convenience to social circulation, but the number of fatalities in traffic accidents has brought great pressure on traffic safety and social stability management. Therefore, traffic accidents prediction is being of great significance to alleviate the safety pressure of regional traffic management. Nevertheless, the existing studies has yet reached a consensus on the scientific and feasible modeling method for traffic safety management, the improvement of traffic safety efficiencies has also rarely discussed in traffic accidents prediction. This paper fills the gap by promoting a novel data-driven decision model for traffic accidents prediction, which is constructed by the extended belief rule-based system (EBRBS) with considering the improvement of traffic safety efficiencies. Hence, the new traffic accident prediction model consists of two components: 1) safety efficiencies evaluation modeling with considering meta-frontier and group-frontier to evaluate the current traffic safety management, which are also defined to improve safety efficiencies evaluation by the adjustment of inputs and outputs; 2) extended belief rule base (EBRB)-based modeling for traffic accidents prediction by considering the improvement of traffic safety efficiencies, where the effective efficiencies of traffic management inputs and outputs are utilized to predict the future number of traffic accidents. The effectiveness of the proposed model is verified by using traffic management data from 31 Chinese provinces during 2003–2020. Experimental results demonstrate that the model can offer powerful reference value in the traffic accidents prediction process, which help to achieve the relatively effective efficiencies of traffic safety.

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

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.

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.

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.

Random clustering forest for extended belief rule-based system

Random clustering forest for extended belief rule-based system

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.

A structure optimization method for extended belief-rule-based classification system

The widely applied belief-rule-based(BRB) system has demonstrated its advantages in handling both qualitative and quantitative information. As an extension of BRB system, the extended belief-rule-based(EBRB) system bridges the rule-based methods and data-driven methods by efficiently transforming data into extended belief rules(EBRs). Many works have been done to apply EBRB system in addressing classification problems. However, the problems of making use of all attributes indiscriminately and activating almost all EBRs still affect the accuracy and computational efficiency of EBRB system. In this paper, a structure optimization method for EBRB(SO-EBRB) system, including attribute optimization and rule activation, is proposed to address aforementioned problems. In the attribute optimization, a weighted minimum redundancy maximum relevance(MRMR) method is proposed, where the relevance between attributes and label as well as the redundancy among attributes are used to evaluate attributes. Afterwards, the proposed attribute weight calculation method is utilized to assign attribute weights for the EBRB system. In rule activation, an improved minimum centre distance rule activation(MCDRA) method, which considering the weights of attributes in distance calculation, is used to activate customized EBRs for input query data. 15 benchmark classification data sets are utilized to verify the effectiveness of the proposed SO-EBRB method. The results show that, compared with conventional EBRB system, the SO-EBRB system achieves higher classification accuracy, lower rule activation ratio and less response time. Additionally, comparison between the proposed method and some state-of-art machine learning algorithms demonstrates that the SO-EBRB system achieves prominent performance in addressing classification problems.

A minimum centre distance rule activation method for extended belief rule-based classification systems

Originating from the belief-rule-based (BRB) system, the extended belief rule-based (EBRB) system combined the advantages of the rule-based method and those of data-driven methods. By transforming the data set into extended belief rules and using evidential reasoning (ER), the EBRB system has expanded the application of BRB systems and demonstrated their capability in addressing classification problems. Nevertheless, the problem of activating nearly the entire rule base in every classification process is embedded in the EBRB scheme. There have been advances in rule activation for the EBRB system; however, the introduction of subjective information into the classification, high computational costs and long response times are common problems facing existing rule activation methods. To solve the problems facing rule activation for EBRB systems, a minimum centre distance rule activation (MCDRA) method for EBRB systems is proposed. In MCDRA, no subjective information is required, and no time-consuming iteration procedure is necessary. Two components of the proposed MCDRA, i.e., the filtering procedure and the selection procedure, are designed to eliminate unrelated samples of input query data and to select and activate the highly related samples to the input query data. A total of 12 benchmark data sets are used to test the performance of EBRB with MCDRA (M-EBRB). The experimental results show that compared with other rule activation methods, the proposed method obtains satisfactory rule activation ratios, accuracies and response times. Additionally, M-EBRB performs well on noisy data and comparatively with both the fuzzy-rule-based classification system (FRBCS) and several machine learning classification algorithms. In addition, MCDRA can be utilized as a generic rule activation method and can be used to optimize other rule-based classification systems.

Extended belief rule based system with joint learning for environmental governance cost prediction

Abstract Predicting the cost of environmental governance is an essential process in environmental protection. However, the existing cost prediction methods face several challenges, including the necessity of considering the causality of environmental governance, the importance of distinguishing environmental indicators, and the difficulty of collecting environmental data. In order to address these challenges, a novel rule-based system, called the extended belief rule-based (EBRB) system, is first introduced to establish the basic framework of cost prediction. Then, a combination of structure learning and parameter learning, or joint learning, is developed to improve the performance of the EBRB system. Finally, a new cost prediction method based on the improved EBRB system is proposed for environmental governance. To verify the effectiveness of the new cost prediction method, an experimental study is carried out to compare the predicted cost of environmental governance in 29 provinces of China. The comparative analyses demonstrate that the new cost prediction method can not only provide a desired level of accuracy, but also exhibit excellent robustness that makes it better than some existing cost prediction methods.

A Balance Adjusting Approach of Extended Belief-Rule-Based System for Imbalanced Classification Problem

The extended belief-rule-based (EBRB) system has become a widely recognized and effective rule-based system in decision-making. The system uses a data-driven method to generate the rule base by transforming each training sample into a rule. Hence, when an EBRB system is applied in an imbalanced classification dataset, the imbalance of training dataset will retain in the generated rule base. More specifically, the number of rules transformed from majority classes will be far greater than the rules transformed from minority classes. This issue usually leads to a sharp decrease in the accuracies of minority classes. This study analyses how the imbalance of training dataset exists in the generated EBRB and then proposes a Balance Adjusting (BA) approach to eliminate the influence of imbalance in the rule base. The BA approach adjusts rule activation weights of all activated rules, and further enhances the competitiveness of rules with higher activation weight during the rule aggregation process of the EBRB system. Several case studies in imbalanced benchmark classification datasets from UCI demonstrate how the use of the BA approach improves the performance of the EBRB system. This study also conducts a series of experiments to validate the improvement of the proposed approach compared with some conventional and recent existing works. The comparison results illustrate that the BA approach is feasible, effective and robust, and it performs well especially in large scale datasets. Moreover, the BA approach can also combine with various rule activation weight calculation methods, which means it might worth to be applied as a generic process before the rule aggregation process of the EBRB system.

A Micro-Extended Belief Rule-Based System for Big Data Multiclass Classification Problems

Big data classification problems have drawn great attention from diverse fields, and many classifiers have been developed. Among those classifiers, the extended belief rule-based system (EBRBS) has shown its potential in both big data and multiclass situations, while the time complexity and computing efficiency are two challenging issues to be handled in EBRBS. As such, three improvements of EBRBS are proposed first in this paper to decrease the time complexity and computing efficiency of EBRBS for multiclass classification under the assumption of large amount of data, including the strategy to skip rule weight calculation, a simplified evidential reasoning algorithm, and the domain division-based rule reduction method. This turns out to be a micro version of the EBRBS, called Micro-EBRBS. Moreover, one of commonly used cluster computing, named Apache Spark , is then applied to implement the parallel rule generation and inference schemes of the Micro-EBRBS for big data multiclass classification problems. The comparative analyses of experimental studies demonstrate that the Micro-EBRBS not only can obtain a desired accuracy but also has the comparatively better time complexity and computing efficiency than some popular classifiers, especially for multiclass classification problems.

Extended belief-rule-based system with new activation rule determination and weight calculation for classification problems

Among many rule-based systems employed to deal with classification problems, the extended belief-rule-based (EBRB) system is an effective and efficient tool and also has potentials in handing both quantitative and qualitative information under uncertainty. Despite many advantages, several drawbacks must be overcome for better applying the conventional EBRB system, including counterintuitive individual matching degrees, insensitivity to the calculation of individual matching degrees, and the inconsistency problem. Accordingly, by constructing the activation region of extended belief rules and revising the calculation formula of activation weights, the new procedures of activation rule determination and weight calculation are proposed to improve the conventional EBRB system, while the original procedures of rule inference and class estimation are retained from the conventional EBRB system. Nineteen classification datasets with different numbers of classes are studied to validate the efficiency and effectiveness of the proposed EBRB classification system compared with existing works. The comparison results demonstrate that the proposed EBRB classification system not only obtains a high accuracy better than the conventional EBRB system, but also has an excellent response time for classification. More importantly, the results derived from multi-class datasets show the significant performance of the proposed EBRB classification system compared with some state of art classification tools.