Research on dependent evidence combination based on principal component analysis.

A novel decision-based fuzzy averaging filter consisting of a new Dempster-Shafer (D-S) noise detector and a two-pass noise filtering mechanism is proposed. Bodies of evidence are extracted, and the basic belief assignment is developed, avoiding the counter-intuitive problem of Dempster's combination rule. The combination belief value can be the decision rule for the D-S noise detector. A fuzzy averaging method where the weights are constructed using a predefined fuzzy set is developed to achieve noise cancellation. Besides that, a simple second-pass filter is also employed to improve the final filtering performance. Experimental results have confirmed the proposed filter outperforms other decision-based filters in terms of both noise suppression and detail preservation.

ABSTRACTThe main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.

Dempster-Shafer (DS) evidence theory is widely employed in the real world as a primary instrument for modeling uncertainty. However, when applying Dempster's combination rule, seemingly conflicting pieces of data could be merged to yield surprising results. There are a number of proposed scales for measuring the level of discrepancy between pieces of evidence. However, the presented methods only use a single metric to analyze the conflicting results. However, it is usually unwise to rely on a single criterion to measure the extent to which the facts conflict with one another. For the reason that flaws, differences, differences, and ambiguity all contribute to a higher level of conflict between the evidence. The objective of this study is to propose a novel data fusion method based on AHP for enhancing mathematical creativity education. This work stands out by effectively integrating multiple criteria to improve decision-making processes in educational settings. Given the efficacy of the approach proposed in this study in bringing together seemingly disparate data, we want to eventually extend its application to other forms of uncertainty theory, such as fuzzy set theory and imprecise probabilities. The concept of direct inquiry into the total ambiguity of evidence within the context of discernment will also be explored. Several criteria factors are used to determine the level of disagreement between the information presented here. A proposed analytic hierarchy technique uses multiple criteria to properly weight each piece of data. The initial stage is to assign a numerical value to each piece of evidence based on how well it satisfies each of the criteria. The criterion layer's covariance matrix can be derived by examining the relationship between the criteria's numerical values. After collecting data on each criterion's quantitative change, a fuzzy preference relation matrix can be built. The scheme layer makes use of a fuzzy preference relation matrix in place of a traditional pairwise comparison matrix. Each piece of evidence is given an overall weight based on its combined scheme weight and criteria weight. Two numerical experiments are offered to illustrate the effectiveness of the proposed method after the final weights have been applied to the primary evidence and the evidence has been combined using Dempster's rule. Results show that the proposed methodology outperforms alternative approaches to dealing with contradictory evidence discussed in the literature.

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

In the development of E-Commerce, security has always been the core and key issue. To aim at the assessment of E-Commerce security, in order to efficiently handle uncertain information in the process of decision making, a new fuzzy multi-criteria decision-making (MCDM) method is presented based on fuzzy sets theory (FST) and Dempster-Shafer evidence theory (DST). First, a hierarchical structure of E-Commerce security is established. Second, the ratings of the third level criteria and the importance weights of the first level criteria, given by the experts, are expressed in trapezoidal (or triangular) fuzzy numbers. The ratings can be transformed into basic probability assignments (BPA) based on an improved similarity measure of generalized fuzzy numbers we proposed, combining the BPAs from bottom to top using Dempster's combination rule. At last, the importance weights can be transformed into discounting coefficients and the BPAs of the first level criteria can be fused using the discounting rule to obtain the final assessment decision. An illustrative example is given to show that the proposed method can be applied to the security evaluation for the complex E-Commerce system and provides the scientific and consensus evaluated results as well.

Preoperative non-invasive histologic grading of breast cancer is essential. This study aimed to explore the effectiveness of a machine learning classification method based on Dempster-Shafer (D-S) evidence theory for the histologic grading of breast cancer. A total of 489 contrast-enhanced magnetic resonance imaging (MRI) slices with breast cancer lesions (including 171 grade Ⅰ, 140 grade Ⅱ, and 178 grade Ⅲ lesions) were used for analysis. All the lesions were segmented by two radiologists in consensus. For each slice, the quantitative pharmacokinetic parameters based on a modified Tofts model and the textural features of the segmented lesion on the image were extracted. Principal component analysis was then used to reduce feature dimensionality and obtain new features from the pharmacokinetic parameters and texture features. The basic confidence assignments of different classifiers were combined using D-S evidence theory based on the accuracy of three classifiers: support vector machine (SVM), Random Forest, and k-nearest neighbor (KNN). The performance of the machine learning techniques was evaluated in terms of accuracy, sensitivity, specificity, and the area under the curve. The three classifiers showed varying accuracy across different categories. The accuracy of using D-S evidence theory in combination with multiple classifiers reached 92.86%, which was higher than that of using SVM (82.76%), Random Forest (78.85%), or KNN (87.82%) individually. The average area under the curve of using the D-S evidence theory combined with multiple classifiers reached 0.896, which was larger than that of using SVM (0.829), Random Forest (0.727), or KNN (0.835) individually. Multiple classifiers can be effectively combined based on D-S evidence theory to improve the prediction of histologic grade in breast cancer.

Feature selection is one of the key processes in pattern classification. For the task of feature selection, an important problem is the evaluation of the classification capability or clarity of different feature spaces, which is related to their uncertainty. In the framework of Dempster-Shafer evidence theory (DST), the Basic Belief Assignment (BBA) can well describe the uncertainty. In this paper, Generative Adversarial Network (GAN) is used to generate BBAs in each feature space, and a novel feature selection approach based on ambiguity distribution is proposed, which uses the skewness and variance of the BBAs’ ambiguity values on each feature space. Experimental results of pattern classification on various UCI datasets show that our new proposed method is rational and can effectively improve the accuracy of pattern classification.

In this paper, we investigate the problem encountered by Dempster's combination rule in view of Dempster's original combination framework. We first show that the root of Dempster's combination rule (defined and named by Shafer) is Dempster's original idea on evidence combination. We then argue that Dempster's original idea on evidence combination is, in fact, richer than what has been formulated in the rule. We conclude that, by strictly following what Dempster has suggested, there should be no counterintuitive results when combining evidence.

Random subspace evidence classifier

The existing approaches for fuzzy soft sets decision-making are mainly based on different types of level soft sets. How to deal with such kinds of fuzzy soft sets decision-making problems via decreasing the uncertainty resulting from human's subjective cognition is still an open issue. To address this issue, a hybrid method for utilizing fuzzy soft sets in decision-making by integrating a fuzzy preference relations analysis based on the belief entropy with the Dempster-Shafer evidence theory is proposed. The proposed method is composed of four procedures. First, we measure the uncertainties of parameters by leveraging the belief entropy. Second, with the fuzzy preference relations analysis, the uncertainties of parameters are modulated by making use of the relative reliability preference of parameters. Third, an appropriate basic probability assignment in terms of each parameter is generated on the modulated uncertainty degrees of parameters basis. Finally, we adopt Dempster's combination rule to fuse the independent parameters into an integrated one; thus, the best one can be obtained based on the ranking candidate alternatives. In order to validate the feasibility and effectiveness of the proposed method, a numerical example and a medical diagnosis application are implemented. From the experimental results, it is demonstrated that the proposed method outperforms the related methods, because the uncertainty resulting from human's subjective cognition can be reduced; meanwhile, the decision-making level can also be improved with better performance.

The Dempster-Shafer theory is being applied for handling uncertainty in various domains. Many methods have been suggested in the literature for faster computation of belief which is otherwise exponentially complex. Bayesian approximation is one such method. In this paper, we first present some results on invariance of Bayesian belief functions under Dempster's combination rule. Based on this, we interpret Bayesian approximation and further show that it inherits these properties from the combination operator of Dempster's combination rule. Finally, we bring into focus the limitation of Bayesian approximation.

Classical probabilistic relaxation method has been widely used for solving optimisation problems in various fields, including image processing and pattern recognition. However we realize that there exist cases in which a probability theoretic model is not adequate, especially there exists incompleteness in available information by noises. In order to solve the problem, this paper proposes a relaxation matching method based on Dempster-Shafer theory. Then the update process in probabilistic relaxation method is derived as a special case of Dempster's combination rule (1967) in DS theory.

Decision fusion in sensor networks enables sensors to improve classification accuracy while reducing the energy consumption and bandwidth demand for data transmission. In this paper, we focus on the decentralized multi-class classification fusion problem in wireless sensor networks (WSNs) and a new simple but effective decision fusion rule based on belief function theory is proposed. Unlike existing belief function based decision fusion schemes, the proposed approach is compatible with any type of classifier because the basic belief assignments (BBAs) of each sensor are constructed on the basis of the classifier’s training output confusion matrix and real-time observations. We also derive explicit global BBA in the fusion center under Dempster’s combinational rule, making the decision making operation in the fusion center greatly simplified. Also, sending the whole BBA structure to the fusion center is avoided. Experimental results demonstrate that the proposed fusion rule has better performance in fusion accuracy compared with the naïve Bayes rule and weighted majority voting rule.

To solve the invalidation problem of Dempster-Shafer theory of evidence (DS) with high conflict in multisensor data fusion, this paper presents a novel combination approach of conflict evidence with different weighting factors using a new probabilistic dissimilarity measure. Firstly, an improved probabilistic transformation function is proposed to map basic belief assignments (BBAs) to probabilities. Then, a new dissimilarity measure integrating fuzzy nearness and introduced correlation coefficient is proposed to characterize not only the difference between basic belief functions (BBAs) but also the divergence degree of the hypothesis that two BBAs support. Finally, the weighting factors used to reassign conflicts on BBAs are developed and Dempster’s rule is chosen to combine the discounted sources. Simple numerical examples are employed to demonstrate the merit of the proposed method. Through analysis and comparison of the results, the new combination approach can effectively solve the problem of conflict management with better convergence performance and robustness.

Reliable deterioration models for forecasting the condition of bridge elements, systems, and networks are essential components of any bridge management system. Estimating deterioration transition probabilities is the basis of the popular Markov chain deterioration model. Transition probabilities ha ve been produced in the literature by statistical and probabilistic analysis performed on available bridge inspection and condition data. The available data may be limited or inconsistent with the Markov chain transition period. In addition, the conventional probability theory has limitations when applied to problems with a stochastic nature such as bridge deterioration. This paper introduces a novel method based on the theory of evidence for bridge deterioration modeling through expert judgment elicitation. The advantages of the theory of evidence over the traditional probability theory are discussed and the process for the theory implementation is demonstrated with a case study to validate the application of Dempster–Shafer theory of evidence to estimate the transition probabilities. Based on the results, the theory of evidence is proposed as a scientific expert judgement elicitation technique in the area of bridge condition rating and deterioration modeling. Expert judgment elicitation and theory of evidence application hold potential in the field of bridge management and require further investigation and research.