Basic Belief Assignment Research Articles

A new computational measurement and optimization approach for DSmT

A great deal of interest has been paid to computation problem of Dezert-Smarandache theory (DSmT). But there are still problems on complex analysis and frequently search. The computational measurement of DSmT is presented in which the computation is generated in the search for focal elements, the combination of focal elements and basic belief assignment, the expression of focal elements.

Comparative Study on BBA Determination Using Different Distances of Interval Numbers

Dempster-Shafer theory (DST) is an important theory for information fusion. However, in DST how to determinate the basic belief assignment (BBA) is still an open issue. The interval number based BBA determination method is simple and effective, where the features of different classes’ samples are modeled using the interval numbers, i.e., an interval number model is constructed for each focal element.

A Reliability-Based Method to Sensor Data Fusion.

Multi-sensor data fusion technology based on Dempster–Shafer evidence theory is widely applied in many fields. However, how to determine basic belief assignment (BBA) is still an open issue. The existing BBA methods pay more attention to the uncertainty of information, but do not simultaneously consider the reliability of information sources. Real-world information is not only uncertain, but also partially reliable. Thus, uncertainty and partial reliability are strongly associated with each other. To take into account this fact, a new method to represent BBAs along with their associated reliabilities is proposed in this paper, which is named reliability-based BBA. Several examples are carried out to show the validity of the proposed method.

Evidence updating based on novel Jeffrey-like conditioning rules

Dempster–Shafer evidence theory (DST) is an important tool for uncertainty modeling and reasoning, where the uncertainty reasoning includes both the evidence combination and conditioning. New conditioning rules for evidence updating in DST are proposed in this paper. First, two new definitions, namely the weak conditional basic belief assignment (BBA) and strong conditional BBA, are proposed in the spirit of conditional probability in the probabilistic framework. Then, the corresponding Jeffrey-like conditioning rules are proposed to update evidence. The proposed methods have some desirable properties for the evidence updating. Some numerical examples are provided, where existing conditioning rules in DST are compared with newly proposed methods. Experimental results and related analyses show that the conditional BBAs and Jeffrey-like rules proposed in this paper are rational and effective.

Evidential Fusion Based Technique for Detecting Landslide Barrier Lakes From Cloud-Covered Remote Sensing Images

Landslide barrier lakes usually form quickly after disasters and require very timely remote sensing images to monitor the land-cover change. However, cloud-free images are not always available in emergency situations. This paper provides a method to fuse multitemporal cloud-covered images for change detection, based on the evidential fusion framework. First, the frame of discernment is defined by postclassification comparison results. Second, a way of measuring the basic belief assignment (BBA) is introduced based on the confusion matrixes. Next, a simple BBA redistribution process is proposed to deal with cloud coverage problems. Then, the complementary and redundant information from the input images can be fused following the evidence combination and decision making rules in the evidential fusion framework. Finally, the land-cover change map can be derived. Thanks to the Dempster–Shafer evidence theory, the proposed method can complete the change detection process—including data fusion and cloud removal—in an integrated manner. The proposed method is applied to detect the landslide barrier lake in a real case study, using a series of cloud-covered images from the GF-1 satellite. Result comparisons show that the proposed method is more effective than some basic fusion strategies that perform change detection and cloud removal in separate steps. Then, some approaches to improve the proposed method are discussed: introducing new evidence combination rule, improving the classification accuracy, and adding new evidences. All the results indicate the potential of evidential fusion for change detection from cloud-covered images.

Multiple Objects Fusion Tracker Using a Matching Network for Adaptively Represented Instance Pairs.

Multiple-object tracking is affected by various sources of distortion, such as occlusion, illumination variations and motion changes. Overcoming these distortions by tracking on RGB frames, such as shifting, has limitations because of material distortions caused by RGB frames. To overcome these distortions, we propose a multiple-object fusion tracker (MOFT), which uses a combination of 3D point clouds and corresponding RGB frames. The MOFT uses a matching function initialized on large-scale external sequences to determine which candidates in the current frame match with the target object in the previous frame. After conducting tracking on a few frames, the initialized matching function is fine-tuned according to the appearance models of target objects. The fine-tuning process of the matching function is constructed as a structured form with diverse matching function branches. In general multiple object tracking situations, scale variations for a scene occur depending on the distance between the target objects and the sensors. If the target objects in various scales are equally represented with the same strategy, information losses will occur for any representation of the target objects. In this paper, the output map of the convolutional layer obtained from a pre-trained convolutional neural network is used to adaptively represent instances without information loss. In addition, MOFT fuses the tracking results obtained from each modality at the decision level to compensate the tracking failures of each modality using basic belief assignment, rather than fusing modalities by selectively using the features of each modality. Experimental results indicate that the proposed tracker provides state-of-the-art performance considering multiple objects tracking (MOT) and KITTIbenchmarks.

Sensing Attribute Weights: A Novel Basic Belief Assignment Method.

Dempster–Shafer evidence theory is widely used in many soft sensors data fusion systems on account of its good performance for handling the uncertainty information of soft sensors. However, how to determine basic belief assignment (BBA) is still an open issue. The existing methods to determine BBA do not consider the reliability of each attribute; at the same time, they cannot effectively determine BBA in the open world. In this paper, based on attribute weights, a novel method to determine BBA is proposed not only in the closed world, but also in the open world. The Gaussian model of each attribute is built using the training samples firstly. Second, the similarity between the test sample and the attribute model is measured based on the Gaussian membership functions. Then, the attribute weights are generated using the overlap degree among the classes. Finally, BBA is determined according to the sensed attribute weights. Several examples with small datasets show the validity of the proposed method.

Evidential framework for robust localization using raw GNSS data

Global Navigation Satellite Systems (GNSS) positioning in constrained environments suffers from the presence of Non Line Of Sight and multipath receptions so that, in addition to contain imprecise measurements (e.g. due to atmospheric effects), the set of GNSS pseudo-range observations includes some outliers. In this study, we evaluate the interest of the belief function framework as an alternative to the Interval Analysis approach classically used in localization to deal with imprecise data and possibly outliers. Following the basic idea of the RANSAC (RANdom SAmpling Consensus) algorithm, we propose a new detection of the outliers based on an evidential measure of the consistency of the solution. Each pseudo-range (PR) observation generates a 2D basic belief assignment (bba) that quantifies, for any 2D set, the possibility (according to the observed PR) that it includes the GNSS receiver. Outlier detection is then performed by evaluating directly the consistency of subsets of bbas and the inlier PR information is aggregated through the combination of corresponding bbas. In the case of a dynamic receiver, filtering is performed by combining the bbas derived from the new observations to a bba predicted from estimation at previous time step. Proposed approach was evaluated on two actual datasets acquired in urban environment. Results are evaluated both in terms of precision of the localization and in terms of guarantee of the solution. They compared with former approaches either in belief function framework or using interval analysis, stating the interest of the proposed algorithm.

A Clustering-Based Evidence Reasoning Method

Aiming at the counterintuitive phenomena of the Dempster–Shafer method in combining the highly conflictive evidences, a combination method of evidences based on the clustering analysis is proposed in this paper. At first, the cause of conflicts is disclosed from the point of view of the internal and external contradiction. Andthen,a new similarity measure based on it is proposed by comprehensively considering the Pignistic distance and the sequence according to the size of the basic belief assignments over focal elements.

Toward Belief Function-Based Cooperative Sensing for Interference Resistant Industrial Wireless Sensor Networks

In harsh and heterogeneous wireless environments, the communication reliability and latency of industrial wireless sensor networks (IWSNs) seriously suffer from both intra- and interinterference. This paper presents an interference resistant approach for IWSNs by utilizing cognitive radio techniques. To improve the interference detection performance while uploading data as little as possible, we present a new computationally efficient and effective belief function (BF) theory-based reliability–probability decision fusion rule for cooperative sensing. A factor called reliability degree is introduced to characterize the imprecision of sensor observations, and the basic belief assignments are constructed by combining this reliability degree and local detection performance. Unlike the inefficient existing BF-based fusion schemes, the proposed rule has an explicit form and it is equivalent to the well-known Chair–Vashney (CV) rule in high signal-to-noise ratio conditions. We applied the proposed rule in interference resistant IWSNs to detect and avoid interference. Both numerical results and tests results demonstrate that the proposed rule has significant improvement in detection performance, diversity gains, and throughput compared with existing BF fusion schemes and CV rule.

An improved α-cut approach to transforming fuzzy membership function into basic belief assignment

In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster–Shafer evidence theory (DST) framework, transformations from the other type of uncertainty representation into the basic belief assignment are needed. α-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional α-cut approach caused by its normalization step are pointed out in this paper. An improved α-cut approach is proposed, which can counteract the drawbacks of the traditional α-cut approach and has good properties. Illustrative examples, experiments and related analyses are provided to show the rationality of the improved α-cut approach.

CHANGE DETECTION WITH MULTI-SOURCE DEFECTIVE REMOTE SENSING IMAGES BASED ON EVIDENTIAL FUSION

Remote sensing images with clouds, shadows or stripes are usually considered as defective data which limit their application for change detection. This paper proposes a method to fuse a series of defective images as evidences for change detection. In the proposed method, post-classification comparison process is firstly performed on multi-source defective images. Then, the classification results of all the images, together with their corresponding confusion matrixes are used to calculate the Basic Belief Assignment (BBA) of each pixel. Further, based on the principle of Dempster-Shafer evidence theory, a BBA redistribution process is introduced to deal with the defective parts of multi-source data. At last, evidential fusion and decision making rules are applied on the pixel level, and the final map of change detection can be derived. The proposed method can finish change detection with data fusion and image completion in one integrated process, which makes use of the complementary and redundant information from the input images. The method is applied to a case study of landslide barrier lake formed in Aug. 3rd, 2014, with a series of multispectral images from different sensors of GF-1 satellite. Result shows that the proposed method can not only complete the defective parts of the input images, but also provide better change detection accuracy than post-classification comparison method with single pair of pre- and post-change images. Subsequent analysis indicates that high conflict degree between evidences is the main source of errors in the result. Finally, some possible reasons that result in evidence conflict on the pixel level are analysed.

CHANGE DETECTION WITH MULTI-SOURCE DEFECTIVE REMOTE SENSING IMAGES BASED ON EVIDENTIAL FUSION

Abstract. Remote sensing images with clouds, shadows or stripes are usually considered as defective data which limit their application for change detection. This paper proposes a method to fuse a series of defective images as evidences for change detection. In the proposed method, post-classification comparison process is firstly performed on multi-source defective images. Then, the classification results of all the images, together with their corresponding confusion matrixes are used to calculate the Basic Belief Assignment (BBA) of each pixel. Further, based on the principle of Dempster-Shafer evidence theory, a BBA redistribution process is introduced to deal with the defective parts of multi-source data. At last, evidential fusion and decision making rules are applied on the pixel level, and the final map of change detection can be derived. The proposed method can finish change detection with data fusion and image completion in one integrated process, which makes use of the complementary and redundant information from the input images. The method is applied to a case study of landslide barrier lake formed in Aug. 3rd, 2014, with a series of multispectral images from different sensors of GF-1 satellite. Result shows that the proposed method can not only complete the defective parts of the input images, but also provide better change detection accuracy than post-classification comparison method with single pair of pre- and post-change images. Subsequent analysis indicates that high conflict degree between evidences is the main source of errors in the result. Finally, some possible reasons that result in evidence conflict on the pixel level are analysed.

Belief AHP Method — AHP Method with the Belief Function Framework

In this paper, the analytic hierarchy process (AHP) method is extended to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the transferable belief model (TBM). Our proposed approach, called belief AHP, is developed to help the decision maker to determine what the best alternatives are, considering multiple conflicting criteria where both alternatives and criteria may be soiled with imperfection. The Belief AHP method aims at comparing subsets of criteria and groups of alternatives in order to reduce the pair-wise comparisons number. Furthermore, to handle uncertainty that may appear in the comparison procedure, we use basic belief assignments (BBA) instead of exact ratios to elicitate expert preferences. Finally, to illustrate the feasibility of our approach and to judge its performances, we have applied our proposed method on a real application problem: we have considered the polyvinyl chloride (PVC) life cycle assessment especially the end of life phase.

Iterative Approximation of Basic Belief Assignment Based on Distance of Evidence.

In the theory of belief functions, the approximation of a basic belief assignment (BBA) is for reducing the high computational cost especially when large number of focal elements are available. In traditional BBA approximation approaches, a focal element’s own characteristics such as the mass assignment and the cardinality, are usually used separately or jointly as criteria for the removal of focal elements. Besides the computational cost, the distance between the original BBA and the approximated one is also concerned, which represents the loss of information in BBA approximation. In this paper, an iterative approximation approach is proposed based on maximizing the closeness, i.e., minimizing the distance between the approximated BBA in current iteration and the BBA obtained in the previous iteration, where one focal element is removed in each iteration. The iteration stops when the desired number of focal elements is reached. The performance evaluation approaches for BBA approximations are also discussed and used to compare and evaluate traditional BBA approximations and the newly proposed one in this paper, which include traditional time-based way, closeness-based way and new proposed ones. Experimental results and related analyses are provided to show the rationality and efficiency of our proposed new BBA approximation.

Interval-valued Evidence Updating with Reliability and Sensitivity Analysis for Fault Diagnosis

AbstractInformation fusion methods based on Dempster-Shafer evidence theory (DST) have been widely used in fault diagnosis. In DST-based methods, the monitoring information collected from sensors is modeled as multiple pieces of diagnosis evidence in the form of basic belief assignment (BBA), and Dempster’s rule is then used to combine these BBAs to obtain the fused BBA for diagnosis decision making. However, the belief structure with crisp singlevalued belief degrees in BBA may be too coarse to truthfully represent detailed fault information. Moreover, Dempster’s rule only uses a static combination process, which is unsuitable for dynamically fusing information collected at different time steps. In order to address these issues, the paper proposes a dynamic diagnosis method based on interval-valued evidential updating. First of all, the diagnosis evidence is constructed as an interval-valued belief structure (IBS), which provides a more informative scheme than BBA to model fault information. Secondly, th...

A New Probabilistic Transformation of Belief Mass Assignment

In this paper, we propose in Dezert-Smarandache Theory (DSmT) framework, a new probabilistic transformation, called DSmP, in order to build a subjective probability measure from any basic belief assignment defined on any model of the frame of discernment. Several examples are given to show how the DSmP transformation works and we compare it to main existing transformations proposed in the literature so far. We show the advantages of DSmP over classical transformations in term of Probabilistic Information Content (PIC). The direct extension of this transformation for dealing with qualitative belief assignments is also presented.

A Clustering-Based Evidence Reasoning Method

Aiming at the counterintuitive phenomena of the Dempster–Shafer method in combining the highly conflictive evidences, a combination method of evidences based on the clustering analysis is proposed in this paper. At first, the cause of conflicts is disclosed from the point of view of the internal and external contradiction. And then, a new similarity measure based on it is proposed by comprehensively considering the Pignistic distance and the sequence according to the size of the basic belief assignments over focal elements. This measure is used to calculate the commonality function of evidences to amend the evidence sources; Meanwhile, the Iterative Self-organizing Data Analysis Techniques Algorithm (ISODATA) method based on the new measure is used for clustering according to the clustering characters of the original evidences. The Dempster rule is applied to combining all the evidences in each clustering into an evidential representative, and the reliability is calculated based on the commonality and the occurrence frequency of the evidences in the clustering. At last, Murphy's method is used to combine these evidential representatives of the different clusterings. The experimental results through a series of numeric examples show that the method proposed in this paper is more effective and superior to others.

Adaptive imputation of missing values for incomplete pattern classification

In classification of incomplete pattern, the missing values can either play a crucial role in the class determination, or have only little influence (or eventually none) on the classification results according to the context. We propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory. At first, we try to classify the object (incomplete pattern) based only on the available attribute values. As underlying principle, we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information. In this case, the object is committed to this particular class. However, if the object cannot be classified without ambiguity, it means that the missing values play a main role for achieving an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and Self-Organizing Map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is classified according to each training class, and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (which are particular disjunctions of several single classes). The credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets.

Kohonen's Map Approach for the Belief Mass Modeling.

In the framework of the evidence theory, several approaches for estimating belief functions are proposed. However, they generally suffer from the problem of masses attribution in the case of compound hypotheses that lose much conceptual contribution of the theory. In this paper, an original method for estimating mass functions using Kohonen's map derived from the initial feature space and an initial classifier is proposed. Our approach allows a smart mass belief assignment, not only for simple hypotheses but also for disjunctions and conjunctions of hypotheses. Thus, it can model at the same time ignorance, imprecision, and paradox. The proposed method for a basic belief assignment (BBA) is of interest for solving estimation mass functions problems where a large quantity of multivariate data is available. Indeed, the use of Kohonen's map simplifies the process of assigning mass functions. The proposed method has been compared with the state-of-the-art BBA technique on benchmark database and applied on remote sensing data for image classification purpose. Experimentation shows that our approach gives similar or better results than other methods presented in the literature so far, with an ability to handle a large amount of data.