Evidence Combination Rule Research Articles

A generalized weighted evidence fusion algorithm based on quantum modeling

In the field of evidence theory, the Dempster-Shafer framework is widely used for combining evidence. However, it often produces counterintuitive results when dealing with highly conflicting evidence. To mitigate this issue, the weighted evidence fusion method has gained popularity. However, with the generalization of the mass function from the perspective of quantum theory, the weighting of conflicting evidence under quantum effects remains an open issue. To address this issue, a generalized weighted evidence fusion algorithm based on quantum modeling is proposed in this study. First, when quantum interference effects are considered, Dempster's rule is generalized into a generalized evidence combination rule based on quantum modeling. Second, a generalized quantum evidence distance is proposed to measure the similarity of quantum evidence in the presence of phase-term interference. Third, a global and nonlinear quantum evidence weighting operator is designed to reduce the impact of conflicting quantum evidence. Then, based on this operator and the similarities between pieces of quantum evidence, the weighted quantum evidence is fused to yield the final conclusion using the proposed generalized combination rule. Finally, the rationality, reliability, and accuracy of the proposed method are effectively proven through experiments using a few numerical examples and applications.

The Multisensor Data Fusion Method Based on Improved Fuzzy Evidence Theory in the Coal Mine Environment

An enhanced evidence theory-based multisensor data fusion technique is presented to address the problem of poor data fusion caused by an unknown interference in the fully automated mining face multisensor system of a coal mine. Initially, the set of all measurement values is considered as the identification framework, and the principles of fuzzy mathematics are applied to introduce the membership function. This leads to the proposal of a novel method for calculating mutual support among multiple sensors. Furthermore, the basic belief assignment (BBA) in evidence theory is determined by measuring the confidence distance between sensors. Subsequently, a divergence measure is employed to assess the level of conflict and difference between BBA functions, which serves as an indicator of their credibility. The credibility of BBA functions is further adjusted by calculating their information volume using Shannon entropy. This adjustment aims to increase the weight of BBA functions that exhibit less conflict with other BBA functions. Ultimately, the fusion result is obtained through an evidence combination rule based on a conflict allocation. The numerical experimental results demonstrate that the proposed approach achieves higher accuracy, better robustness, and generality compared to the existing methods.

Enhanced Fuzzy Clustering for Incomplete Instance with Evidence Combination

Clustering incomplete instance is still a challenging task since missing values maybe make the cluster information ambiguous, leading to the uncertainty and imprecision in results. This article investigates an enhanced fuzzy clustering with evidence combination method based on Dempster-Shafer theory (DST) to address this problem. First, the dataset is divided into several subsets, and missing values are imputed by neighbors with different weights in each subset. It aims to model missing values locally to reduce the negative impact of the bad estimations. Second, an objective function of enhanced fuzzy clustering is designed and then optimized until the best membership and reliability matrices are found. Each subset has a membership matrix that contains all sub-instances’ membership to different clusters. The fuzzy reliability matrix is employed to characterize the reliability of each subset on different clusters. Third, an adaptive evidence combination rule based on the DST is developed to combine the discounted subresults (memberships) with different reliability to make the final decision for each instance. The proposed method can characterize uncertainty and imprecision by assigning instances to specific clusters or meta-clusters composed of several specific clusters. Once an instance is assigned to a meta-cluster, the cluster information of this instance is (locally) imprecise. The effectiveness of proposed method is demonstrated on several real-world datasets by comparing with existing techniques.

Water grade judgment of aquaculture based on IBES and evidence fusion

In aquaculture, water measuring data obtained by conventional multi-sensors often have some errors, therefore, a new water grade judgment method is proposed in the paper. First, by using the refractive learning strategy, an improved Bald Eagle Search algorithm (IBES) is studied. IBES can effectively overcome the problem of weak local search ability and slow convergence speed in traditional BES algorithm. Second, an aquaculture water grade judgment method based on IBES and evidence fusion is proposed. The interval number is used to represent the aquaculture water parameters, and the reliability coefficient Nk is optimized by IBES to complete the modification of the mass function. Then, the combination rule of interval evidence and the modified mass function are synthesized to obtain the comprehensive interval evidence. Finally, the water grade is judged according to the decision rule. In the experiments, three sensors (temperature, dissolved oxygen and pH) are used to obtain water data. The experimental results show that the median value of the fusion uncertainty obtained by the proposed method is reduced to 0.3769, its reliability is greatly improved compared with a single sensor. In addition, the performance of the proposed method is compared with other optimization algorithms, including GWO, ABC, PSO, WOA, BES, IBES, the experimental results show that the average probabilities of IBES in judgment of water grades for Excellent (I) and Poor (III) are all 93% which rank first. Therefore, the method can accurately determine the water grade from uncertain measurement data with inevitable error and random error, it can provide a new idea for aquaculture water grade judgment.

Multi-Sensor Data Fusion Method Based on Improved Evidence Theory

To achieve autonomous navigation in complex marine environments, unmanned surface vehicles are equipped with a variety of sensors for sensing the surrounding environment and their own state. To address the issue of unsatisfactory multi-sensor information fusion in stochastic uncertain systems with unknown disturbances, an improved evidence theory multi-sensor data fusion method is proposed in this article. First, the affiliation function in fuzzy set theory is introduced as a support function to assign initial evidence for multi-sensor data, and the initial evidence is corrected according to the degree of data bias. Second, a divergence measure is employed to measure the degree of conflict and discrepancy among the evidence, and each piece of evidence is allocated proportional weight based on the conflict allocation principle. Finally, the evidence is synthesized through the evidence combination rule, and the data are weighted and summed to obtain the data fusion results. Since it is difficult to obtain dynamic information from multiple sensors carried by unmanned surface vehicles in practical applications, and considering that the proposed method has universal applicability, practical application experiments using previous research demonstrate that the proposed method has higher fusion accuracy than other existing data fusion methods.

BF-QC: Belief functions on quantum circuits

Dempster–Shafer Theory (DST) of belief function is a basic theory of artificial intelligence, which can represent the underlying knowledge more reasonably than Probability Theory (ProbT). Because of the computation complexity exploding exponentially with the increasing number of elements, the practical application scenarios of DST are limited. In this paper, we encode Basic Belief Assignments (BBA) into quantum superposition states and propose the implementation and operation methods of BBA on quantum circuits. We decrease the computation complexity of the Matrix Evolution on BBA (MEoB) on quantum circuits. Based on the MEoB, we realize the quantum belief functions’ implementation, the similarity measurements of BBAs, evidence Combination Rules (CR), and probability transformation on quantum circuits.

Flexible Risk Evidence Combination Rules in Breast Cancer Precision Therapy.

Evidence theory by Dempster-Shafer for determination of hormone receptor status in breast cancer samples was introduced in our previous paper. One major topic pointed out here is the link between pieces of evidence found from different origins. In this paper the challenge of selecting appropriate ways of fusing evidence, depending on the type and quality of data involved is addressed. A parameterized family of evidence combination rules, covering the full range of potential needs, from emphasizing discrepancies in the measurements to aspiring accordance, is covered. The consequences for real patient samples are shown by modeling different decision strategies.

A Data Classifier Based on Maximum Likelihood Evidential Reasoning Rule

In Dempster–Shafer evidence theory (DST), some classical evidence combination rules can be used to fuse the multiple pieces of evidence, respectively abstracted from different attributes (features) so as to increase the accuracy of multiattribute classification decision making. However, most of them have not yet considered the interdependence among multiple pieces of evidence. The newly proposed maximum likelihood evidential reasoning (MAKER) rule measures such ubiquitous interdependence by introducing correlation factors into evidence combination. Hence, this paper designs a MAKER‐based classifier to mine more correlation information for data classification. Finally, some numerical analysis (classification) experiments are carried out using five popular benchmark databases from the University of California, Irvine (UCI) to illustrate that the refined measure for evidence interdependence can aggregate the fused probability (belief degree) into real class label of a sample and further improve classification accuracy.

A novel evidence combination rule based on compromise conflict indicator and conflict focal element

The Dempster–Shafer evidence theory (DSET) has been commonly used in the fusion of multisource information in various fields. Owing to the normalization process based on the conflict measurement, the conclusion when fusing high conflict evidence is counter-intuitive when using Dempster’s Combination Rule (DCR). To solve the DCR issue, several combination rules have been developed. However, each of them has unreasonable behaviors in certain cases. In this study, the set of mathematical properties that must be satisfied by all the combinatorial rules is further refined. Under the framework of DSET, a novel combination rule is proposed by comprehensively considering the conflict focal elements and metrics. The conflict measurement is achieved through the newly proposed compromise conflict indicator. The advantages of the proposed combination rule over the existing methods are demonstrated by experiments on a few numerical examples and applications.

A complex Jensen–Shannon divergence in complex evidence theory with its application in multi-source information fusion

Multi-source information fusion has attracted considerable attention in the few past years and plays a great role in real applications. However, the uncertainty or conflict will make the fusion results unreasonable. Furthermore, the information may be collected in the form of complex number that cannot be processed by existing methods. In this article, to handle the above issues, the complex evidence theory (CET) is exploited. CET is the generalization of Dempster–Shafer evidence theory, where the mass function is modeled by complex number, called complex mass function (CMF). In order to deal with multi-source information fusion from the perspective of the complex plane, a new Complex Jensen–Shannon divergence (CJS divergence) is presented in this article. The proposed CJS divergence can effectively measure the conflict between two CMFs, and it satisfies the properties of boundedness, symmetry and nondegeneracy. In addition, for a better combination result, we have adjusted the complex Dempster’s rule of combination, which is called the reinforced complex evidence combination rule (RCECR). Then an algorithm for multi-source information fusion is proposed based on the CJS divergence and the RCECR. Some numerical examples and two applications in target identification and medical diagnosis illustrate the effectiveness of the new approach.

Improved Multiclassification of Schizophrenia Based on Xgboost and Information Fusion for Small Datasets.

To improve the performance in multiclass classification for small datasets, a new approach for schizophrenic classification is proposed in the present study. Firstly, the Xgboost classifier is introduced to discriminate the two subtypes of schizophrenia from health controls by analyzing the functional magnetic resonance imaging (fMRI) data, while the gray matter volume (GMV) and amplitude of low-frequency fluctuations (ALFF) are extracted as the features of classifiers. Then, the D-S combination rule of evidence is used to achieve fusion to determine the basic probability assignment based on the output of different classifiers. Finally, the algorithm is applied to classify 38 healthy controls, 16 deficit schizophrenic patients, and 31 nondeficit schizophrenic patients. 10-folds cross-validation method is used to assess classification performance. The results show the proposed algorithm with a sensitivity of 73.89%, which is higher than other classification algorithms, such as supported vector machine (SVM), logistic regression (LR), K-nearest neighbor (KNN) algorithm, random forest (RF), BP neural network (NN), classification and regression tree (CART), naive Bayes classifier (NB), extreme gradient boosting (Xgboost), and deep neural network (DNN). The accuracy of the fusion algorithm is higher than that of classifier based on the GMV or ALFF in the small datasets. The accuracy rate of the improved multiclassification method based on Xgboost and fusion algorithm is higher than that of other machine learning methods, which can further assist the diagnosis of clinical schizophrenia.

An evidence combination rule based on a new weight assignment scheme

In evidence theory, conflicting evidence and fuzzy evidence have a significant impact on the results of evidence combination. Nevertheless, the existing weight assignment methods can hardly reflect the significant influence of fuzzy evidence on the combination results. In this paper, we address this issue by proposing a new method for assigning evidence weights and the corresponding combination rule. The proposed weight assignment method strengthens the consideration of fuzzy evidence. We further incorporate the Wasserstein distance to compute the clarity degree of the evidence. This is an important reference index for the weight assignment in the proposed combination rule and effectively reduces the impact of ambiguous evidence. Using experiments, we illustrate the significant impact of fuzzy evidence on the results of combination. This justifies its integration in the weight assignment process. The proposed combination rule with the new weight assignment method is also examined on a set of numerical arithmetic and Iris datasets. Our results confirm that compared with the four existing methods, the proposed method improves decision accuracy, F1 score, computational convergence and achieves more reliable fusion results.

Application of Improved MFDFA and D-S Evidence Theory in Fault Diagnosis

To improve the accuracy of centrifugal pump fault diagnosis, a novel fault diagnosis method based on improved multiple fractal detrended fluctuation analysis (MFDFA), the fusion of multi-sensing information derived from the back propagation (BP) neural network and the Dempster–Shafter (D-S) evidence theory, is accordingly proposed. Firstly, the multifractal spectral parameters of four sensor signals under four different operating conditions were extracted as centrifugal pump fault feature vectors using improved MFDFA and input to the BP neural network. Then, the basic trust assignment function was constructed by calculating trustworthiness (both local and global) as priori information, which is based on the output results of the neural networks specific to of each group of sensors. Finally, the basic trust assignment function was fused with decision processing in accordance with the D-S evidence combination rule in order to effectively achieve the multi-sensor information fusion centrifugal pump fault diagnosis. The experimental results show the multiple fractal spectrum feature parameters extracted by the improved MFDFA can accurately reflect the signal essence, and can be used as the fault feature vector. On this basis, this multi-sensor fault diagnosis reduces the uncertainty of fault classification and demonstrates improved accuracy compared to the single-sensor fault diagnosis thanks to being based on a combination of the BP neural networks and D-S evidence theory. Thereby, this method can facilitate accurate diagnosis of the centrifugal pump fault type with high confidence, subsequently providing a novel and alternative method to existing methods of diagnosis.

Dempster-shafer theory and linguistic intuitionistic fuzzy number-based framework for blending knowledge from knowledge repositories: An approach for knowledge management

Based on Dempster-Shafer Evidence Theory (DSET) and Linguistic Intuitionistic Fuzzy Numbers (LIFN), this study presents a paradigm for Knowledge Blending (KB) that supports the Knowledge Management (KM) process. The KB framework highlights and analyzes knowledge blending, the emergence of new insights, the ordering of knowledge repositories, and selected knowledge entities that are part of such a knowledge combination. The KB method enables the analysis of knowledge repositories using linguistic terms and quantitative variables and the identification of the ordering of knowledge repositories and specific entities. Ordering knowledge repositories and entities during KB is tricky since knowledge providers employ a range of adjectives, rankings, interpretations, and linguistic terms, rendering the KB process ambiguous. To address the issue, we leverage DSET to describe the LIFNs extracted from knowledge sources as Basic Probability Assignments (BPA). Then, we merge subjective and objective weights obtained from knowledge repositories. To amend evidence from knowledge repositories, we apply the combined weight. Finally, the comprehensive evaluation value of each option is quantified using the combination rule of evidence, which aids in the blending of knowledge repositories and entities acquired from the knowledge repositories. We discuss a case study to explain the proposed method and compare it to other approaches in order to demonstrate its viability and usefulness. The case study highlights the value of KM during the knowledge structuring and auditing stages of the KM process.

A q-rung orthopair basic probability assignment and its application in medical diagnosis

Dempster-Shafer theory is widely used in decision-making and considered as one of the potential mathematical tools in order to fuse the evidence. However, existing studies in this theory show disadvantage due to conflicting nature of standard evidence set and the combination rule of evidence. In this paper, we have constructed the framework of q-rung evidence set to address the issue of conflicts based on the q-rung fuzzy number due to its more comprehensive range of advantage compared to the other fuzzy or discrete numbers. The proposed q-rung evidence set has the flexibility in assessing a parameter through the q-rung orthopair basic probability assignment consisting of membership and non-membership belief degree. Moreover, as the proposed q-rung orthopair basic probability assignment consists of pair of belief degrees, the possibility of conflicts cannot be ignored entirely. In this regard, a new association coefficient measure is introduced where each component of the belief degrees is modified through the weighted average mass technique. This paper uses various concept such as fuzzy soft sets, Deng entropy, association coefficient measure and score function for decision-making problem. Firstly, to obtain the initial q-rung belief function, we have implemented the Intuitionistic fuzzy soft set to assess the parameter of the alternatives and Deng entropy to find the uncertainty of the parameters. Secondly, the association coefficient measure is used to avoid the conflict through the modified form of evidence. Finally, we combined the evidence and found the score value of the Intuitionistic fuzzy numbers for the ranking of the alternatives based on the score values of alternatives. This study is validated with the case study in the medical diagnosis problem from the existing paper and compared the ranking of alternatives based on the score function of belief measures of the alternatives.

Three-Dimensional Change Detection in Urban Areas Based on Complementary Evidence Fusion

With the acceleration of urbanization, it is essential to carry out change detection (CD) and obtain surface change information in urban areas. In the early stages, the spectral information of remote sensing images was used as a change index to capture the spectral and texture changes of ground objects in a two-dimensional plane. However, due to the dense buildings in urban areas, shadows and occlusions can be easily formed, and spectral information is sensitive to the imaging environment, such as the illumination, atmospheric conditions, and imaging angles, so that the detection results based on remote sensing images can often be incomplete. Most changes include not only 2-D plane changes but also 3-D elevation changes. Compared with spectral information, the elevation is more stable and more resistant to interference. Therefore, the fusion of remote sensing image and digital surface model (DSM) data has the potential to be used to detect the changes in urban areas. In this article, we propose a complementary evidence fusion 3-D CD framework based on the Dempster–Shafer theory (CDST). In this framework, DSM and normalized difference vegetation index (NDVI) data are combined using a complementary evidence combination rule. The DSM data can effectively overcome the impact of shadows, and the NDVI data can capture the relevant changes of height-insensitive ground objects, such as vegetation and water. When mapping the basic probability assignment (BPA) of the difference image (DI), prior knowledge is used to ensure that the BPA is not affected by the data distribution. Since DSM and remote sensing image data are heterogeneous data, there is a high degree of conflict when representing the change information characteristics of specific areas. For example, the change between grassland and road is small in elevation but significant in the spectral details, and the traditional Dempster’s combination rule no longer applies. The proposed CDST framework uses a complementary evidence combination rule, which can effectively alleviate the conflicts between the evidence sources and improve the integrity of the detected changes. The experimental results obtained on real datasets confirm that the proposed method does indeed perform well.

A Novel Pythagorean Group Decision-Making Method Based on Evidence Theory and Interactive Power Averaging Operator

Since Pythagorean fuzzy sets can better reflect the cognition of the decision objects for experts, researchers have begun to pay increasingly more attention to them in recent years. The majority of the research on Pythagorean fuzzy environment assumes that the decision maker is completely rational and does not consider the correlation among the attribute variables. In view of the above, this paper proposes a method to solve the multiple attribute group decision-making problem based on D-S theory and interactive power averaging operator. First, the new Pythagorean fuzzy interactive weighted power average operator is designed to aggregate the attribute evaluation information given by experts one by one, and the comprehensive evaluation information of each expert is obtained. Then, the expert comprehensive evaluation information is aggregated by the rule of evidence combination to obtain the comprehensive evidence information and confidence interval of each candidate. Then, the decision-making method for candidate alternatives is performed by the possibility discriminant rule. The design method considers not only the decision makers’ bounded rationality but also the correlation among the attribute variables. Finally, the selection of the energy exploitation plan illustrates the feasibility and effectiveness of the proposed group decision method.

Combining conflicting evidence based on Pearson correlation coefficient and weighted graph

Dempster–Shafer evidence theory (evidence theory) has been widely used as an efficient method for dealing with uncertainty. In evidence theory, Dempster's rule is the most well-known evidence combination method but it does not work well when the evidence is in high conflict. To improve the performance of combining conflicting evidence, an original and novel evidence combination method is presented based on the Pearson correlation coefficient and weighted graph. The proposed method can correctly recognize the alternative situation with a high accuracy. Besides, the convergence performance of this method is better when compared with other combination rules. In addition, the weighted graph generated by the proposed method can directly represent the relationship between different evidence, which can help researchers estimate the reliability of different body of evidence. Our experimental results indicate the advantages of our proposed evidence combination rule over existing methods, and the results are analyzed and discussed.

A Multi-Attribute Group Decision-Making Method Based on Linguistic Intuitionistic Fuzzy Numbers and Dempster–Shafer Evidence Theory

In this paper, we propose a multi-attribute group decision-making (MAGDM) method based on Dempster–Shafer Evidence Theory (DST) and linguistic intuitionistic fuzzy numbers (LIFNs), in which both the expert weights and attribute weights are unknown. Firstly, we represent LIFNs as basic probability assignments (BPAs) by DST based on linguistic scale function (LSF), and a linear programming model is proposed to combine the objective weights and subjective weights of attributes to obtain the combined weights. At the same time, the experts’ weights are obtained through Jousselme distance. Secondly, we use the weights to correct the evidence, and the comprehensive evaluation value of each alternative is calculated by the combination rule of evidence. Further, a new MAGDM approach with DST and LIFNs is presented. Finally, we give an example to explain the proposed method and compare it with other methods to show the feasibility and superiority.

An Evidence Combination Rule Based on Transferable Belief Model and Application in Reliability Assessment With Multi-Source Data

Increasingly complex system environments have put forward higher requirements for information fusion. Under this background, the application prospects of evidence theory which can function well in uncertain information representation and information fusion is promising. The effect of evidence theory on information fusion is closely related to evidence distance measurement method and evidence combination rules. Considering the difference of evidence information in belief level and that in decision level, this paper redefines the evidence distance and puts forward the measurement method of evidence credibility, thus realizing the correction of the original basic probability assignment function (BPA). Based on the evidence credibility, the evidence weight is generated, which leads to an efficient distribution of evidence conflict in the process of evidence combination. So, a new evidence combination rule is generated. According to a series of examples, the evidence distance proposed in this paper can effectively measure the evidence differences, and the new combination rules can reasonably distribute evidence conflicts thus avoiding evidence paradox. At the end of this paper, the new evidence distance and combination rule, combing with the Transferable Belief Model (TBM), are used to fuse the multi-source reliability test information, then the life cycle evaluation of a product is obtained. In addition, through the comparative analysis of the results, the feasibility and validity of this method being applied to practice are verified.