Dempster's Rule Of Combination Research Articles

Merging multi-level evidential observations for dynamic reliability assessment of hierarchical multi-state systems: A dynamic Bayesian network approach

Dynamic reliability assessment has offered a new paradigm for engineered systems to integrate multi-level observations to update the reliability measures of a specific running system. The existent work on dynamic reliability assessment can only leverage precise observations and cannot be straightforwardly implemented in scenarios where observations are imprecise. However, the observations are inevitably imprecise owing to the limited accuracy of inspection techniques and vague judgments of the system state. In engineering scenarios, multi-state systems (MSSs) with a hierarchical structure are commonly existent, and the imprecise observations can be collected across multiple physical levels of the system. In this article, the uncertainty associated with imprecise observations is characterized by the evidence theory, and it can be therefore regarded as an evidential form. A dynamic Bayesian network (DBN) model is utilized to evaluate the reliability of hierarchical MSSs with multi-level evidential observations. Subsequently, the evidence theory is implemented to quantify epistemic uncertainties associated with imprecise observations. These observations, sourced from multiple physical levels, are merged by the DBN model using the Dempster rule of combination (DRC) to update the reliability of a specific running system in a dynamic fashion. The feasibility and correctness of the proposed method have been demonstrated through a numerical case and a real engineering case of a kerosene filling control system (KFCS), and the result indicates that the proposed DBN-based algorithm methods have high applicability and generalizability.

Rolling bearing fault diagnosis based on multi-source data fusion

In this paper, a fault diagnosis method is proposed based on multi-source data fusion to address the inaccurate results caused by single evidence used for decision-making. First, empirical mode decomposition is performed using sensor data to extract fault features, and a fault feature matrix and a diagnostic matrix are established. Then the deviation vector is defined to obtain the difference between the diagnostic sample and the fault sample, and then the basic probability assignment is obtained for each diagnostic sample. Finally, the Dempster combination rule is used for fusion. The effectiveness and accuracy of this method in fault diagnosis of rolling bearings have been verified through examples of rolling bearings.

A novel quantum Dempster's rule of combination for pattern classification

Dempster's rule of combination (DRC) is widely used for uncertainty reasoning in intelligent information system, which is generalized to complex domain recently. However, as the increase of identification framework elements, the computational complexity of Dempster's rule of combination increases exponentially. To address this issue, we propose a novel quantum Dempster's rule of combination (QDRC) by means of Toffoli gate. The QDRC combination process is completely implemented using quantum circuits. To validate the efficiency of the proposed QDRC, we conduct simulation experiments on IBM and IonQ quantum cloud platforms. Besides, we implement the QDRC algorithm to the real quantum computer of IonQ Harmony. The experiment results show that the result of QDRC is getting more and more accurate as the number of measurements increases. In addition, we propose a quantum multisource information fusion method on the basis of QDRC. Finally, we demonstrate its effectiveness to solve pattern classification problem under several diverse real UCI datasets.

Research of ordinal model fusion based apple grading

Near infrared spectrum has been applied for the rapid non-destructive prediction and classification of the internal soluble solids content (SSC) of apples, due to its rapid, non-destructive and non-polluting nature. However, current apple grading methods do not make full use of the orderliness relationship existing in the apple grading labels. Therefore, ordinal model is introduced in the issue of apples grading based on the internal SSC. In details, the orderliness in the classification model is considered and ordinal regression is combined with apple classification model to establish ordered partition neural network and ordinal regression extreme learning machine, respectively. Meanwhile, to address the problems of poor applicability of single prediction model and the grading uncertainty associated with compulsory segmentation of grading boundaries, a Gaussian mass function generating method is proposed based on the distance between the predicted ordinal class labels and the real grading boundaries, and the multiple models can be fused through the Dempster combination rule, making a fuller description of the uncertainty problem on ordinal class labels prediction, providing a research basis for online non destructive testing grading of apples. Finally, the multiple model fusion process is fully demonstrated by simulation examples, the grading accuracy of Yantai Red Fuji apples is also improved than single ordinal model.

Product innovation based on the host gene and target gene recombination under the technological parasitism framework

In the rapidly changeable market, product innovation is critical for enterprises to improve their product competitiveness. Product innovation can be described as an evolutionary process of technical systems where the relationship between technologies follows the evolution from parasitism to symbiosis in technological parasitism theory. The existing research on the technological parasitism theory mainly focuses on explaining and verifying the evolution law of product systems from parasitism to symbiosis in the product innovation process. However, these research activities are a post-hoc summary, which limits the guidance for enterprises to proactively realize the evolution of products from parasitism to symbiosis in an ex-ante perspective. For the development of innovative products in the engineering field, enterprises lack an effective ex-ante design method to proactively find the appropriate parasitic technology, and integrate it with the host technology for the product system evolving towards a symbiotic state. To fill this gap, this paper proposes a product innovation design process based on the recombination of host and target genes under the technological parasitism framework. Product scenario analysis is used to explore the potential function needs to determine the search direction of parasitic technologies. The min-complement distance measure method is introduced to identify the appropriate parasitic technology. Based on four recombination operations, the construction process of new product genome through the recombination of host and target genes is proposed. The concept of new product is formed through the transcription of the product genome. The final scheme is developed objectively by using the coefficient variation method and Dempster combination rule. The proposed method is applied in the ex-ante design of a Chinese medicine dispensing machine for its feasibility and effectiveness.

Research on dependent evidence combination based on principal component analysis.

Dempster-Shafer evidence theory, as a generalization of probability theory, is a powerful tool for dealing with a variety of uncertainties, such as incompleteness, ambiguity, and conflict. Because of its advantages in information fusion compared with traditional probability theory, it is widely used in various fields. However, the classic Dempster's combination rule assumes that evidences are independent of each other, which is difficult to satisfy in real life. Ignoring the dependence among the evidences will lead to unreasonable fusion results, and even wrong conclusions. Considering the limitations of D-S evidence theory, this paper proposed a new evidence fusion model based on principal component analysis (PCA) to deal with the dependence among evidences. First, the approximate independent principal components of each information source were obtained based on principal component analysis. Second, the principal component data set was used as a new information source for evidence theory. Third, the basic belief assignments (BBAs) were constructed. As the fundamental construct of evidence theory, a BBA is a probabilistic function corresponding to each hypothesis, quantifying the belief assigned based on the evidence at hand. This function facilitates the synthesis of disparate evidence sources into a mathematically coherent and unified belief structure. After constructing the BBAs, the BBAs were fused and a conclusion was drawn. The case study verified that the proposed method is more robust than several traditional methods and can deal with redundant information effectively to obtain more stable results.

Higher Order Fractal Belief Rényi Divergence With Its Applications in Pattern Classification.

Information can be quantified and expressed by uncertainty, and improving the decision level of uncertain information is vital in modeling and processing uncertain information. Dempster-Shafer evidence theory can model and process uncertain information effectively. However, the Dempster combination rule may provide counter-intuitive results when dealing with highly conflicting information, leading to a decline in decision level. Thus, measuring conflict is significant in the improvement of decision level. Motivated by this issue, this paper proposes a novel method to measure the discrepancy between bodies of evidence. First, the model of dynamic fractal probability transformation is proposed to effectively obtain more information about the non-specificity of basic belief assignments (BBAs). Then, we propose the higher-order fractal belief Rényi divergence (HOFBReD). HOFBReD can effectively measure the discrepancy between BBAs. Moreover, it is the first belief Rényi divergence that can measure the discrepancy between BBAs with dynamic fractal probability transformation. HoFBReD has several properties in terms of probability transformation as well as measurement. When the dynamic fractal probability transformation ends, HoFBReD is equivalent to measuring the Rényi divergence between the pignistic probability transformations of BBAs. When the BBAs degenerate to the probability distributions, HoFBReD will also degenerate to or be related to several well-known divergences. In addition, based on HoFBReD, a novel multisource information fusion algorithm is proposed. A pattern classification experiment with real-world datasets is presented to compare the proposed algorithm with other methods. The experiment results indicate that the proposed algorithm has a higher average pattern recognition accuracy with all datasets than other methods. The proposed discrepancy measurement method and multisource information algorithm contribute to the improvement of decision level.

A new combination method based on Pearson coefficient and information entropy for multi-sensor data fusion

When confronted with greatly contradictory evidence, the Dempster-Shafer evidence theory may exhibit certain constraints that lead to fused results which are inconsistent with common understanding. Within the existing Internet of Things landscape, there are occasions when a small number of sensors may malfunction and contradict each other. This study addresses contradictory information by processing the bodies of evidence beforehand. Additionally, an enhanced fusion technique for conflicting evidence is introduced, which employs Pearson correlation coefficient and information entropy. We propose a novel combination approach for multi-sensor data fusion based on evidence theory. Firstly, the credibility for each piece of evidence is computed through amalgamating correlation measurements with evidence distance between two pieces of evidence. Next, based on the information volume, the credibility is adjusted, resulting in the final weighting factor for the evidence. The reasonable weighted average evidence is then created using the weighting factor of each piece of evidence. Finally, the combined result is obtained by applying Dempster's combination rule, which combines the weighted average evidence N−1 times. Upon comparing the fusion results, it has been observed that the performance of the proposed method surpasses that of other methods. Our method can effectively minimize the ramifications of profoundly conflicting evidence in the fusion process, resulting in more logical fusion results than other methods. The outcomes of numerical examples expose that the technique put forward in this manuscript can manage highly conflicting evidence, thereby yielding fusion results that are more precise and conducive to making sound decisions.

Multisensor fault diagnosis via Markov chain and Evidence theory

In multi-sensor fusion, the Dempster–Shafer theory is frequently used for fault diagnosis and other decision-making problems. However, if the information collected from various sensors exhibits uncertainty and high conflict, the classical Dempster’s Combination Rule may produce a counter-intuitive result. Various studies were conducted by Ghosh and other scholars to solve this problem, and good results were achieved. This work provides a novel idea which uses the Markov chain to model the uncertainty information in evidence theory, explore the ordered rules in random evidence, and then obtain the evidence support degree, thereby reducing the effect of high-conflict evidence. Considering the information amount of evidence combined with the evidence support degree, the final credibility of evidence is obtained, and the weighted summation is used to obtain new evidence. Finally, the classical Dempster combination rule is used to process new evidence and make the final decision. Through numerical examples and case studies, the proposed method’s superior efficiency and robustness over the existing multisensor fault diagnosis methods are illustrated.

A Novel Evidence Combination Method Based on Improved Pignistic Probability.

Evidence theory is widely used to deal with the fusion of uncertain information, but the fusion of conflicting evidence remains an open question. To solve the problem of conflicting evidence fusion in single target recognition, we proposed a novel evidence combination method based on an improved pignistic probability function. Firstly, the improved pignistic probability function could redistribute the probability of multi-subset proposition according to the weight of single subset propositions in a basic probability assignment (BPA), which reduces the computational complexity and information loss in the conversion process. The combination of the Manhattan distance and evidence angle measurements is proposed to extract evidence certainty and obtain mutual support information between each piece of evidence; then, entropy is used to calculate the uncertainty of the evidence and the weighted average method is used to correct and update the original evidence. Finally, the Dempster combination rule is used to fuse the updated evidence. Verified by the analysis results of single-subset proposition and multi-subset proposition highly conflicting evidence examples, compared to the Jousselme distance method, the Lance distance and reliability entropy combination method, and the Jousselme distance and uncertainty measure combination method, our approach achieved better convergence and the average accuracy was improved by 0.51% and 2.43%.

Failure Mode and Effects Analysis on the Air System of an Aero Turbofan Engine Using the Gaussian Model and Evidence Theory.

Failure mode and effects analysis (FMEA) is a proactive risk management approach. Risk management under uncertainty with the FMEA method has attracted a lot of attention. The Dempster-Shafer (D-S) evidence theory is a popular approximate reasoning theory for addressing uncertain information and it can be adopted in FMEA for uncertain information processing because of its flexibility and superiority in coping with uncertain and subjective assessments. The assessments coming from FMEA experts may include highly conflicting evidence for information fusion in the framework of D-S evidence theory. Therefore, in this paper, we propose an improved FMEA method based on the Gaussian model and D-S evidence theory to handle the subjective assessments of FMEA experts and apply it to deal with FMEA in the air system of an aero turbofan engine. First, we define three kinds of generalized scaling by Gaussian distribution characteristics to deal with potential highly conflicting evidence in the assessments. Then, we fuse expert assessments with the Dempster combination rule. Finally, we obtain the risk priority number to rank the risk level of the FMEA items. The experimental results show that the method is effective and reasonable in dealing with risk analysis in the air system of an aero turbofan engine.

A New Reliability Coefficient Using Betting Commitment Evidence Distance in Dempster-Shafer Evidence Theory for Uncertain Information Fusion.

Dempster-Shafer evidence theory is widely used to deal with uncertain information by evidence modeling and evidence reasoning. However, if there is a high contradiction between different pieces of evidence, the Dempster combination rule may give a fusion result that violates the intuitive result. Many methods have been proposed to solve conflict evidence fusion, and it is still an open issue. This paper proposes a new reliability coefficient using betting commitment evidence distance in Dempster-Shafer evidence theory for conflict and uncertain information fusion. The single belief function for belief assignment in the initial frame of discernment is defined. After evidence preprocessing with the proposed reliability coefficient and single belief function, the evidence fusion result can be calculated with the Dempster combination rule. To evaluate the effectiveness of the proposed uncertainty measure, a new method of uncertain information fusion based on the new evidence reliability coefficient is proposed. The experimental results on UCI machine learning data sets show the availability and effectiveness of the new reliability coefficient for uncertain information processing.

A conflict evidence fusion method based on the composite discount factor and the game theory

Dempster–Shafer (D–S) evidence theory is widely used in various fields of information fusion. However, it is still an open issue that the D–S evidence theory may produce the counter–intuitive results in fusing high–conflict evidences. Aim at this problem, a novel conflict evidence fusion method based on the composite discount factor and the game theory is proposed in this paper. Firstly, an improved Shafer's conflict measurement formula based on the Jaccard similarity coefficient is devised, and combined with the Jousselme distance into a novel binary function to measure the global conflict between evidences as the evidence falsity. Then, the local conflict between evidences and the information volume of evidences are measured by using the Jousselme distance and belief entropy to indicate the credibility and uncertainty of evidences. Next, based on the game theory, the falsity, credibility and uncertainty are weighted and combined into the composite discount factors to correct each body of evidence (BOE). Ultimately, all corrected evidences are fused by Dempster's combination rule to obtain the final result. Two numerical examples are given to verify that the proposed method is effective and feasible, which outperforms the previous methods in handling the conflict evidences.

Belief Evolution Network-based Probability Transformation and Fusion

Smets proposes the Pignistic Probability Transformation (PPT) as the decision layer in the Transferable Belief Model (TBM), which argues when there is no more information, we have to make a decision using a Probability Mass Function (PMF). In this paper, the Belief Evolution Network (BEN) and the full causality function are proposed by introducing causality in Hierarchical Hypothesis Space (HHS). Based on BEN, we interpret the PPT from an information fusion view and propose a new Probability Transformation (PT) method called Full Causality Probability Transformation (FCPT), which has better performance under Bi-Criteria evaluation. Besides, we heuristically propose a new probability fusion method based on FCPT. Compared with Dempster Rule of Combination (DRC), the proposed method has more reasonable result when fusing same evidence.

Research on driving behaviour assessment based on evidence theory in 5G‐VANET

With the rapid development of 5G and vehicular ad hoc network (VANET), the data fusion plays an increasingly important role in the driving behaviour assessment. However, the unreasonable distribution of conflicting evidence remains a significant issue for decision fusion based on evidence theory. By analysing the parameter information of driving behaviour recognition, this paper proposed a new weighted evidence combination approach to fuse the highly conflicting information. In short, the proposed combination method not only retains the excellent mathematical characteristics of Dempster's combination rule, but also fully considers the mutual relations between evidences and the influence of the characteristics of evidence body. Firstly, a new dissimilarity measure is put forward to quantify the conflict degree between the evidences. Furthermore, the uncertainty measure and internal conflict are adopted to determine the weight of each evidence. Based on the weighted averaging combination method, the reasonable combined results are obtained. According to the experimental results, the proposed method has better performance than the existing methods, and provides an effective solution for driving behaviour assessment.

A generalized divergence of information volume and its applications

Dempster–Shafer evidence theory provides a powerful method for the expression and fusion of uncertain information. When handling the high conflict information, traditional Dempster combination rule can produce counterintuitive results. Hence, the reasonable conflict measure is essential in information fusion. Inspired by this view, the paper propose the new method to measure conflict between bodies of evidence. Firstly, we define a new information volume of mass function for the perspective of information discord and non-specificity. Second, we propose a generalized divergence based on information volume of mass function, denoted as Jensen–Shannon divergence of information volume (IJS). IJS can effectively measure the conflict between bodies of evidence. IJS reflects the conflict between bodies of evidence in terms of the differences between the support of propositions and the elements. That is, compared to the current approach, IJS not only fully considers the differences between the support degree of propositions, but also the differences of elements in propositions from the perspective of information non-specificity. When the mass function degenerates to a probabilistic distribution, IJS also degenerates to the classical Jensen–Shannon divergence. Meanwhile, IJS also satisfies the axioms of distance measure, such as non-negativity, symmetry and etc. Further, we proved these axioms based on mathematical derivation, and some numerical examples are applied to explain axioms and advantages. Based on the proposed divergence measure, we propose a multi-source information fusion method in the real world, and several data sets can be used to show that the proposed fusion method is superior to current method under the framework of evidence theory.

A Novel Method for Conflict Data Fusion Using an Improved Belief Divergence Measure in Dempster–Shafer Evidence Theory

Dempster–Shafer (D-S) evidence theory plays an important role in multisource data fusion. Due to the nature of the Dempster combination rule, there can be counterintuitive results when fusing highly conflicting evidence data. To date, conflict management in D-S evidence theory is still an open issue. Inspired by evidence modification considering internal indeterminacy and external support, a novel method for conflict data fusion is proposed based on an improved belief divergence, evidence distance, and belief entropy. First, an improved belief divergence measure is defined to characterize the discrepancy and conflict between bodies of evidence (BOEs). Second, evidence credibility is generated to describe the external support based on the complementary advantages of the improved belief divergence and evidence distance. Third, belief entropy is utilized to quantify the internal indeterminacy and further determine evidence weight. Lastly, the classical Dempster combination rule is applied to fuse the BOEs modified by their credibility degrees and weights. As the results of numerical examples and an application show, the proposed divergence measure can overcome the invalidity of the existing measures in some special cases. Additionally, the proposed fusion method recognizes the correct target with the highest belief value of 98.96%, which outperforms other related methods in conflict management. The proposed fusion method also displays better convergence, validity, and robustness.

Reliability evaluation of weighted voting system based on D–S evidence theory

In classic weighted voting systems (WVSs), a voting unit (VU) is subjected to a three-failure mode, and the VU's decision result is represented as a definite one-dimensional variable, which causes the loss of the decision information of the VU. The VU's decision result is not fully utilized because of the use of the majority rule. In this study, we improve the WVS model and propose two new models. We analyze the failure mode of the VU in the new model and provide a method for calculating the probability of the occurrence of a VU failure. To avoid the loss of the VUs’ decision information, we use the basic probability assignment (BPA) function to characterize the decision results in the new models and propose four rules for generating the BPA. Three theorems are proved for combining different types of decision results of the VUs. We also replace the majority rule in the WVS with the Dempster combination rule to fully utilize the decision results of the VUs. We devise two algorithms to evaluate the reliability of the two new WVS models and conduct two experiments to test the utility of the proposed algorithms and analyze the effects of system parameters on the system reliability.

A fast evidential approach for stock forecasting

Within the framework of evidence theory, the confidence functions of different information can be combined into a combined confidence function to solve uncertain problems. The Dempster combination rule is a classic method of fusing different information. This paper proposes a similar confidence function for the time point in the time series. The Dempster combination rule can be used to fuse the growth rate of the last time point, and finally a relatively accurate forecast data can be obtained. Stock price forecasting is a concern of economics. The stock price data is large in volume, and more accurate forecasts are required at the same time. The classic methods of time series, such as ARIMA, cannot balance forecasting efficiency and forecasting accuracy at the same time. In this paper, the fusion method of evidence theory is applied to stock price prediction. Evidence theory deals with the uncertainty of stock price prediction and improves the accuracy of prediction. At the same time, the fusion method of evidence theory has low time complexity and fast prediction processing speed.

Conflict Data Fusion in a Multi-Agent System Premised on the Base Basic Probability Assignment and Evidence Distance.

The multi-agent information fusion (MAIF) system can alleviate the limitations of a single expert system in dealing with complex situations, as it allows multiple agents to cooperate in order to solve problems in complex environments. Dempster–Shafer (D-S) evidence theory has important applications in multi-source data fusion, pattern recognition, and other fields. However, the traditional Dempster combination rules may produce counterintuitive results when dealing with highly conflicting data. A conflict data fusion method in a multi-agent system based on the base basic probability assignment (bBPA) and evidence distance is proposed in this paper. Firstly, the new bBPA and reconstructed BPA are used to construct the initial belief degree of each agent. Then, the information volume of each evidence group is obtained by calculating the evidence distance so as to modify the reliability and obtain more reasonable evidence. Lastly, the final evidence is fused with the Dempster combination rule to obtain the result. Numerical examples show the effectiveness and availability of the proposed method, which improves the accuracy of the identification process of the MAIF system.