Dempster's Rule Research Articles

Random subspace evidence classifier

Although there exist a lot of k-nearest neighbor approaches and their variants, few of them consider how to make use of the information in both the whole feature space and subspaces. In order to address this limitation, we propose a new classifier named as the random subspace evidence classifier (RSEC). Specifically, RSEC first calculates the local hyperplane distance for each class as the evidences not only in the whole feature space, but also in randomly generated feature subspaces. Then, the basic belief assignment is computed according to these distances for the evidences of each class. In the following, all the evidences represented by basic belief assignments are pooled together by the Dempster's rule. Finally, RSEC assigns the class label to each test sample based on the combined belief assignment. The experiments in the datasets from UCI machine learning repository, artificial data and face image database illustrate that the proposed approach yields lower classification error in average comparing to 7 existing k-nearest neighbor approaches and variants when performing the classification task. In addition, RSEC has good performance in average on the high dimensional data and the minority class of the imbalanced data.

TOPPER: topology prediction of transmembrane protein based on evidential reasoning.

The topology prediction of transmembrane protein is a hot research field in bioinformatics and molecular biology. It is a typical pattern recognition problem. Various prediction algorithms are developed to predict the transmembrane protein topology since the experimental techniques have been restricted by many stringent conditions. Usually, these individual prediction algorithms depend on various principles such as the hydrophobicity or charges of residues. In this paper, an evidential topology prediction method for transmembrane protein is proposed based on evidential reasoning, which is called TOPPER (topology prediction of transmembrane protein based on evidential reasoning). In the proposed method, the prediction results of multiple individual prediction algorithms can be transformed into BPAs (basic probability assignments) according to the confusion matrix. Then, the final prediction result can be obtained by the combination of each individual prediction base on Dempster's rule of combination. The experimental results show that the proposed method is superior to the individual prediction algorithms, which illustrates the effectiveness of the proposed method.

Toward an Axiomatic Definition of Conflict Between Belief Functions

Recently, the problem of measuring the conflict between two bodies of evidence represented by belief functions has known a regain of interest. In most works related to this issue, Dempster's rule plays a central role. In this paper, we propose to study the notion of conflict from a different perspective. We start by examining consistency and conflict on sets and extract from this settings basic properties that measures of consistency and conflict should have. We then extend this basic scheme to belief functions in different ways. In particular, we do not make any a priori assumption about sources (in)dependence and only consider such assumptions as possible additional information.

Using the Dempster-Shafer theory of evidence to rank documents

Multi-source information can be utilized collaboratively to improve the performance of information retrieval. To make full use of the document and collection information, this paper introduces a new informa- tion retrieval model that relies on the Dempster-Shafer theory of evidence. Each query-document pair is taken as a piece of evidence for the relevance between a document and a query. The evidence is combined using Dempster's rule of combination, and the belief committed to the relevance is obtained. Retrieved documents are then ranked according to the belief committed to the relevance. Several basic probability as- signments are also proposed. Extensive experiments over the Text REtrieval Conference (TREC) test col- lection ClueWeb09 show that the proposed model provides performance similar to that of the Vector Space Model (VSM). Under certain probability assignments, the proposed model outperforms the VSM by 63% in terms of mean average precision.

Weighted evidence combination based on distance of evidence and uncertainty measure

Dempster-Shafer evidence theory is an important tool in the fields of information fusion.However Dempster's rule of combination cannot efficiently handle highly conflicting evidence combination for it can arouse counter-intuitive behaviors.To deal with such a problem,a novel weighted average evidence combination approach is proposed.Not only the distance of evidence but also the uncertainty measure is utilized to determine the weights of the bodies of evidence.Based on the weighted averaged BOE and Dempster's rule of combination,the rational combination results can be obtained.The experimental results show that the method proposed can effectively handle conflicting evidence combination with better convergence.

A New Safety Evaluation Model of Coal Mine Roof based on Multi-sensor Fusion in case of Information Confliction

Factors that affect the safety of coal mine roof is a multi-faceted, information fusion technology can take full advantage of multi-source information complementary and comprehensive, and improving information quality and credibility of coal mine roof safety. In analyzing the current monitoring means, a coal mine roof safety evaluation model is presented based on Dempster-Shafer evidence fusion theory , After normalizing the various sensor data, the model can acquire the basic probability assignment of the system judging the security situation of the roof, and then using the Dempster-Shafe synthesis rule to synthesize the multi-evidence, and acquiring the whole judgment of the security situation of the roof; as to the problem of the failure of Dempster evidence synthesis rule under the high conflict, establish similarity matrix through the evidence distance, determine the weight coefficient of the evidence, and use the Dempster rule to combine after the pretreatment of the evidence. Through the simulation and compared with other improved methods, the model is proved to decrease the influences that the conflict makes to the combination result, and at the same time improve the convergence rate of evidence combination and reduce the risk of decision-making under the high conflict evidence.

Mapping the health of mature deciduous forest stands by fusing multisource geospatial data with Dempster's combination rule

In Canada, forest companies and government are faced with the important challenge of monitoring forest stand health. This task is especially difficult when the objective is to monitor the health of mature deciduous stands. Mapping methods for tree health have been proposed using multispectral and hyperspectral airborne sensors; however, acquiring airborne data over large areas remains costly. In addition, some studies have pointed out that forest dieback is characterized by multi-causality. Therefore, we propose a large-scale mapping method which includes a model to parameterize several factors influencing forest vigour. A high-spatial resolution satellite image was fused with a series of biophysical parameters using the Dempster–Shafer theory (DST). The study was performed over mature deciduous forests in the province of Québec, Canada. The fusion of a Satellite Pour l’Observation de la Terre (SPOT)-5 high resolution geometric (HRG) image with a surface deposit map and an ice storm damage-intensity map provided the best results, improving the overall accuracy by 15.1%, when compared with a K‐nearest-neighbour (KNN) algorithm using the SPOT-5 image alone. Moreover, the DST improved the accuracy of the vigour class identification, halving the standard deviation when compared with the KNN method. This study shows how the DST can be used to model the influence of biophysical parameters when combined with multispectral information to better assess the health of mature deciduous stands.

A NEW ADAPTIVE CLASSIFICATION FUSION METHOD BASED ON DEMPSTER-SHAFER THEORY IN REMOTE SENSING IMAGE

In this paper, a new adaptive classification fusion method was proposed based on the Dempster-Shafer's theory of evidence and fuzzy Kohonen neural network in remote sensing image. The new method incorporates ideas from unsupervised neural network model and uses neighborhood information in the framework of the Dempster-Shafer theory of evidence. This approach mainly consists in considering each neighbor of a pattern to be classified as an item of evidence supporting certain hypotheses concerning the class membership of that pattern. This evidence is represented by basic probability assignment, with pooled utilization of the Dempster's rule of combination. Experiments with SPOT remote sensing image demonstrate the excellent performance of this classification scheme as compared with the existing neural network techniques.

BRIDGING JEFFREY'S RULE, AGM REVISION AND DEMPSTER CONDITIONING IN THE THEORY OF EVIDENCE

Belief revision characterizes the process of revising an agent's beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster rule of combination, just like revision in the sense of Alchourrón, Gärdenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey's rule of updating, Dempster rule of conditioning and a form of AGM revision.

Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory

When conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible redundancy of dependent sources. To study idempotent merging, different strategies can be followed. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to study, respectively, their particularization or extension to belief functions. In this paper, we study the feasibility of extending the idempotent fusion rule of possibility theory (the minimum) to belief functions. We first investigate how comparisons of information content, in the form of inclusion and least-commitment, can be exploited to relate idempotent merging in possibility theory to evidence theory. We reach the conclusion that unless we accept the idea that the result of the fusion process can be a family of belief functions, such an extension is not always possible. As handling such families seems impractical, we then turn our attention to a more quantitative criterion and consider those combinations that maximize the expected cardinality of the joint belief functions, among the least committed ones, taking advantage of the fact that the expected cardinality of a belief function only depends on its contour function.

Combination rule of D–S evidence theory based on the strategy of cross merging between evidences

Recent studies on the combination rule of D–S evidence theory can be summarized as two categories, i.e. the methods based on modification for Dempster rule, and the methods based on correction to original evidence sources. However, both of them fail to deal with the role of cardinality of focal elements in process of combination, leading generally to the imperfect final results which are hard to show the inherent differences between different bodies of evidence. In this paper, we propose a combination rule based on the strategy of cross merging between evidences, a newly developed methodology which can better reflect the focusing degree of focal elements between bodies of evidence, and make final combination results more succinct, reasonable and valid. Throughout the process of combination, such global information as reliability, focusing weights, and expected support of evidences is thoroughly taken into account. In addition, an effort is made to allocate evidential conflict in proportion only among combination propositions in order to refine combination results and reduce their decision range. A numerical example and its modified version demonstrate that the presented approach has good adaptability to the evidences in accord or with high conflict, and significantly outperforms other combination methods of a similar kind.

Study on Extenics Information Fusion Method and It's Application

This paper makes analysis on theories of D-S evidential reasoning, rough sets, and extenic sets; and indicates that there are some similarities among the three theories in defining uncertainty sets. Therefore, it's feasible to introduce relevant theories and methods of extenics into information fusion and a method of extenics fusion (MEF) is presented as well. The method combines extenic correlation function with Dempster rule and is considered a good solution for problems of evidence collision and BPA function in information fusion method based on D-S evidential reasoning. The simulation test shows that MEF is better than the traditional D-S evidential reasoning and is applicable to assess all kinds of problems. Using the method of this paper to evaluate surface water in one area of Northern China, the results were consistent with the fact.

On the fusion of imprecise uncertainty measures using belief structures

Our interest is in the fusion of information from multiple sources when the information provided by the individual sources is expressed in terms of an imprecise uncertainty measure. We observe that the Dempster–Shafer belief structure provides a framework for the representation of a wide class of imprecise uncertainty measures. We then discuss the fusion of multiple Dempster–Shafer belief structures using the Dempster rule and note the problems that can arise when using this fusion method because of the required normalization in the face of conflicting focal elements. We then suggest some alternative approaches fusing multiple belief structures that avoid the need for normalization.

Measuring Conflict Functions in Generalized Power Space

One of the most important open issues is that the classical conflict coefficient in D-S evidence theory (DST) cannot correctly determine the conflict degree between two pieces of evidence. This drawback greatly limits the use of DST in real application systems. Early researches mainly focused on the improvement of Dempster's rule of combination (DRC). However, the current research shows it is very important to define new conflict coefficients to determine the conflict degree between two or more pieces of evidence. The evidential sources of information are considered in this work and the definition of a conflict measure function (CMF) is proposed for selecting some useful CMFs in the next fusion work when sources are available at each instant. Firstly, the definition and theorems of CMF are put forward. Secondly, some typical CMFs are extended and then new CMFs are put forward. Finally, experiments illustrate that the CMF based on Jousselme and its similar ones are the best suited ones.

Two-level combination approach for solving conflict evidences

Considering that the combination of Dempster rule in Dempster-Shafer Theory (DST) has disadvantages while dealing with highly conflict evidences,a new two-level combination method for fusing conflict evidences was proposed.Distinguishing between highly conflict evidence and lowly conflict evidence,the method adopted the PCR6 rule based on Dezert-Smarandache Theory (DSmT) on the first level of combination to solve high conflict and used Dempster rule to keep fast convergence speed and good calculation capability on the second level,which could manage conflict evidence with various degrees effectively and reasonably.The validity of the proposed method was demonstrated by calculation examples.

A new linguistic MCDM method based on multiple-criterion data fusion

Multiple-criteria decision-making (MCDM) is concerned with the ranking of decision alternatives based on preference judgements made on decision alternatives over a number of criteria. First, taking advantage of data fusion technology to comprehensively consider each criterion data is a reasonable idea to solve the MCDM problem. Second, in order to efficiently handle uncertain information in the process of decision making, some well developed mathematical tools, such as fuzzy sets theory and Dempster Shafer theory of evidence, are used to deal with MCDM. Based on the two main reasons above, a new fuzzy evidential MCDM method under uncertain environments is proposed. The rating of the criteria and the importance weight of the criteria are given by experts’ judgments, represented by triangular fuzzy numbers. Then, the weights are transformed into discounting coefficients and the ratings are transformed into basic probability assignments. The final results can be obtained through the Dempster rule of combination in a simple and straight way. A numerical example to select plant location is used to illustrate the efficiency of the proposed method.

Multi-model strategy based evidential soft sensor model for predicting evaluation of variables with uncertainty

The traditional soft sensor methods cannot be applied in the cases where uncertainty exists. To predict evaluation of variable with uncertainty, a novel method, called multi-evidential soft sensor model, was proposed based on evidence theory and multi-model strategy. In such method, the overall multi-model on the whole data space is established by weight sum of the multiple local models on local data spaces. For arbitrary given input vector x, each local model provides a prediction regarding the value of the output variable y, in the form of fuzzy belief assignment (FBA), defined as a collection of fuzzy sets of values with associated masses of belief. The output FBA is computed using a parametric, instance-based approach: imprecise training samples in the neighbourhood of x are considered as sources of partial information on the response variable y, and provide pieces of evidence reflecting the values taken by the response y; the pieces of evidences are pooled by using Dempster's rule of combination. To identify the parameters involved in the overall and local models, the so-called imprecise training samples are constructed from running data by means of data analysis and expertise knowledge.To validate the proposed method, a numerical experiment was designed based on a UCI dataset, and the experimental results suggest its power for predicting evaluation of variables with uncertainty. Finally, the prediction of unmeasured parameter level of coal powder filling in tubular ball mill was taken as the engineering example to validate the proposed method. The predicting results are in line with the experts’ analysis. The two validations suggest that the proposed method is applicable for predicting variables with uncertainty in process industry.

Analyzing the applicability of Dempster’s rule to the combination of interval-valued belief structures

To combine interval-valued belief structures (IBSs), it is necessary to investigate the applicability of Dempster's rule to know whether Dempster's rule is adequate to be used and whether other alternatives are needed. This makes it significant to investigate IBSs' pairwise relationships (IPRs) since they have an important impact on the applicability of Dempster's rule to the combination of two IBSs. IPRs can be constructed based on beliefs' pairwise relationships (BPRs), so this paper proposes a consistency measure to quantitatively divide BPRs into three categories. Using a consistency interval between two IBSs that is obtained by solving a pair of optimization problems constructed based on the consistency measure, IPRs are quantified and divided into six categories on the basis of BPRs. According to IPRs, the applicability of Dempster's rule to the combination of two IBSs is recommended. Finally, the applicability of Dempster's rule to the combination of multiple IBSs is investigated.

Evidence combination approach based on uncertainty measure

Focusing on the problem that the Dempster's combination rule cannot effectively combine conflict evidences and the high computational complexity of the present solution method based on distance between evidences, a weighted average evidence combination approach was proposed. First, the computational complexity of combination rule proposed by Deng Yong, taken as an instance of combination rules based on distance between evidences, was calculated and analyzed. Then the concept of uncertainty measure of evidence was used to describe the uncertainty of evidence body and as a basis of determining the weight of evidence. The numerical example shows that the evidence combination approach based on uncertainty measure can efficiently combine evidences, whether they conflict with each other or not, with faster convergence speed as well as lower computational complexity compared with those based on the distance between the evidences.

Representation of Uncertainty and Integration of PGIS‐based Grazing Intensity Maps Using Evidential Belief Functions

AbstractIn a project to classify livestock grazing intensity using participatory geographic information systems (PGIS), we encountered the problem of how to synthesize PGIS‐based maps of livestock grazing intensity that were prepared separately by local experts. We investigated the utility of evidential belief functions (EBFs) and Dempster's rule of combination to represent classification uncertainty and integrate the PGIS‐based grazing intensity maps. These maps were used as individual sets of evidence in the application of EBFs to evaluate the proposition that “This area or pixel belongs to the high, medium, or low grazing intensity class because the local expert(s) says (say) so”. The class‐area‐weighted averages of EBFs based on each of the PGIS‐based maps show that the lowest degree of classification uncertainty is associated with maps in which “vegetation species” was used as the mapping criterion. This criterion, together with local landscape attributes of livestock use may be considered as an appropriate standard measure for grazing intensity. The maps of integrated EBFs of grazing intensity show that classification uncertainty is high when the local experts apply at least two mapping criteria together. This study demonstrates the usefulness of EBFs to represent classification uncertainty and the possibility to use the EBF values in identifying and using criteria for PGIS‐based mapping of livestock grazing intensity.