Evidence reasoning rule-based classifier with uncertainty quantification

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 basic probability assignment generation and combination method for conflict data fusion in the evidence theory

Dempster-Shafer evidence theory is an effective method to deal with information fusion. However, how to deal with the fusion paradoxes while using the Dempster's combination rule is still an open issue. To address this issue, a new basic probability assignment (BPA) generation method based on the cosine similarity and the belief entropy was proposed in this paper. Firstly, Mahalanobis distance was used to measure the similarity between the test sample and BPA of each focal element in the frame of discernment. Then, cosine similarity and belief entropy were used respectively to measure the reliability and uncertainty of each BPA to make adjustments and generate a standard BPA. Finally, Dempster's combination rule was used for the fusion of new BPAs. Numerical examples were used to prove the effectiveness of the proposed method in solving the classical fusion paradoxes. Besides, the accuracy rates of the classification experiments on datasets were also calculated to verify the rationality and efficiency of the proposed method.

A new correlation belief function in Dempster-Shafer evidence theory and its application in classification

Uncertain information processing is a key problem in classification. Dempster-Shafer evidence theory (D-S evidence theory) is widely used in uncertain information modelling and fusion. For uncertain information fusion, the Dempster's combination rule in D-S evidence theory has limitation in some cases that it may cause counterintuitive fusion results. In this paper, a new correlation belief function is proposed to address this problem. The proposed method transfers the belief from a certain proposition to other related propositions to avoid the loss of information while doing information fusion, which can effectively solve the problem of conflict management in D-S evidence theory. The experimental results of classification on the UCI dataset show that the proposed method not only assigns a higher belief to the correct propositions than other methods, but also expresses the conflict among the data apparently. The robustness and superiority of the proposed method in classification are verified through experiments on different datasets with varying proportion of training set.

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.

Situation assessment in air combat considering incomplete frame of discernment in the generalized evidence theory

For situation assessment in air combat, there may be incomplete information because of new technologies and unknown or uncertain targets and threats. In this paper, an improved method of situation assessment for air combat environment considering incomplete frame of discernment in the evidence theory is proposed to get a more accurate fusion result for decision making in the battlefield environment. First, the situation in air combat is assessed with knowledge. Then, the incomplete frame of discernment in the generalized evidence theory, which is an extension of Dempster-Shafer evidence theory, is adopted to model the incomplete and unknown situation assessment. After that, the generalized combination rule in the generalized evidence theory is adopted for fusion of situations in intelligent air combat. Finally, real-time decision-making in situation assessment can be reached for actions to take. Experiments in situation assessment of air combat with incomplete and uncertain situations show the rationality and effectiveness of the proposed method.

A multimodal model fusing multiphase contrast-enhanced CT and clinical characteristics for predicting lymph node metastases of pancreatic cancer

Objective. To develop a multimodal model that combines multiphase contrast-enhanced computed tomography (CECT) imaging and clinical characteristics, including experts’ experience, to preoperatively predict lymph node metastasis (LNM) in pancreatic cancer patients. Methods. We proposed a new classifier fusion strategy (CFS) based on a new evidential reasoning (ER) rule (CFS-nER) by combining nomogram weights into a previous ER rule-based CFS. Three kernelled support tensor machine-based classifiers with plain, arterial, and venous phases of CECT as the inputs, respectively, were constructed. They were then fused based on the CFS-nER to construct a fusion model of multiphase CECT. The clinical characteristics were analyzed by univariate and multivariable logistic regression to screen risk factors, which were used to construct correspondent risk factor-based classifiers. Finally, the fusion model of the three phases of CECT and each risk factor-based classifier were fused further to construct the multimodal model based on our CFS-nER, named MMM-nER. This study consisted of 186 patients diagnosed with pancreatic cancer from four clinical centers in China, 88 (47.31%) of whom had LNM. Results. The fusion model of the three phases of CECT performed better overall than single and two-phase fusion models; this implies that the three considered phases of CECT were supplementary and complemented one another. The MMM-nER further improved the predictive performance, which implies that our MMM-nER can complement the supplementary information between CECT and clinical characteristics. The MMM-nER had better predictive performance than based on previous classifier fusion strategies, which presents the advantage of our CFS-nER. Conclusion. We proposed a new CFS-nER, based on which the fusion model of the three phases of CECT and MMM-nER were constructed and performed better than all compared methods. MMM-nER achieved an encouraging performance, implying that it can assist clinicians in noninvasively and preoperatively evaluating the lymph node status of pancreatic cancer.

A New Evidential Reasoning Rule With Continuous Probability Distribution of Reliability

Evidential reasoning (ER) rule has been widely used in dealing with uncertainty. As an important parameter to measure the inherent property of evidence, the evidence reliability makes the ER rule constitute a generalized reasoning framework. In current research of the ER rule, the evidence reliability tends to be expressed in the form of quantitative value by certain methods or expert knowledge. The single quantitative value lacks the ability to describe the statistical property of reliability, which leads to unreasonable results. In this article, a new ER rule with continuous probability distribution of reliability denoted by ERr-CR is proposed. The combination of two pieces of evidence is discussed in detail, where the reliability is profiled as random variables with specific probability distribution. To characterize the output of ERr-CR, a novel concept of expectation of the expected utility is proposed. In addition, the ERr-CR is expanded to multiple pieces of evidence to show its universality. Further, the basic performances of the ERr-CR are explored to illustrate the rationality. Moreover, a case study of safety assessment of natural gas storage tanks (NGSTs) is conducted to show the potential applications of ERr-CR, which makes the proposed method more practical.

Spammer detection using multi-classifier information fusion based on evidential reasoning rule

Spammer detection is essentially a process of judging the authenticity of users, and thus can be regarded as a classification problem. In order to improve the classification performance, multi-classifier information fusion is usually used to realize the automatic detection of spammers by utilizing the information from multiple classifiers. However, the existing fusion strategies do not reasonably take the uncertainty from the results of different classifiers (views) into account, and the relative importance and reliability of each classifier are not strictly distinguished. Therefore, in order to detect spammers effectively, this paper develops a novel multi-classifier information fusion model based on the evidential reasoning (ER) rule. Firstly, according to the user's characterization strategy, the base classifiers are constructed through the profile-based, content-based and behavior-based. Then, the idea of multi-classifier fusion is combined with the ER rule, and the results of base classifiers are aggregated by considering their weights and reliabilities. Extensive experimental results on the real-world dataset verify the effectiveness of the proposed model.

An improved measure for belief structure in the evidence theory

Dempster-Shafer evidence theory (D-S theory) is suitable for processing uncertain information under complex circumstances. However, how to measure the uncertainty of basic probability distribution (BPA) in D-S theory is still an open question. In this paper, a method of measuring total uncertainty based on belief interval distance is proposed. This method is directly defined in the D-S theoretical framework, without the need of converting BPA into probability distribution by Pignistic probability transformation. Thus, it avoids the loss of information. This paper analyzes the advantages and disadvantages of the previous total uncertainty of measurement, and the uncertainty measurement examples show the effectiveness of the new uncertainty measure. Finally, an information fusion method based on the new uncertainty measure is proposed. The validity and rationality of the proposed method are verified by two classification experiments from UCI data sets.

Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory

Due to the nature of the Dempster combination rule, it may produce results contrary to intuition. Therefore, an improved method for conflict evidence fusion is proposed. In this paper, the belief entropy in D–S theory is used to measure the uncertainty in each evidence. First, the initial belief degree is constructed by using an improved base belief function. Then, the information volume of each evidence group is obtained through calculating the belief entropy which can modify the belief degree to get the final evidence that is more reasonable. Using the Dempster combination rule can get the final result after evidence modification, which is helpful to solve the conflict data fusion problems. The rationality and validity of the proposed method are verified by numerical examples and applications of the proposed method in a classification data set.