Dempster's Rule Research Articles

Implementasi Metode Dempster Shafer Analytic Hierarchy Process Untuk Pemilihan Program Studi Calon Mahasiswa

Methods Dempster Shafer Analytic Hierarchy Process is used to rank or sort information based on a number of criteria. DS/AHP advantage of Pairwise Comparison, Consistency Ratio, and Dempster Rule's of Combination, which is used to generate information systems in the form of a sequence of courses as consideration for the selection of majors for prospective students. The sample used in this study were 29 students of five faculty at the University of Diponegoro. The data used is the standard minimum value of each faculty and the average value of the semester report card 1-5 Mathematics, Indonesian, English, Biology, Chemistry, and Physics. Results of this study was the software selection study program that gives students the value of trust in each department. Testing the validity of the value of the accuracy of the system is done by comparing the majors were chosen with the recommendation majors produced by the system, resulting accuracy of 79.33%.

A Soft Decision Rule for Sparse Signal Modeling via Dempster–Shafer Evidential Reasoning

Recently, the problem of recovering sparse linear representation of a query in terms of a redundant dictionary has received great interest. The query sample is represented as a linear combination of the atoms of the dictionary. The unique representation is obtained via sparsity constraint, and the decision is made in terms of the characteristics of representation on reconstruction. The decision rule for sparse signal modeling can be viewed as a typical application of Bayesian estimation, where the likelihood function is inversely proportional to the reconstruction error. Different from the conventional rule, where the decision is directly made according to the overall reconstruction error associated with each class, this letter proposes a soft decision via Dempster–Shafer theory of evidence. To model the imprecision on uncertainty measurement, we introduce the samplewise ambiguity and the classwise ambiguity during the quantification of probability mass. Each sample that participates in the recovery of the query is considered as an item of evidence that supports certain hypothesis in regard to the class membership of query. The amount of evidence is quantified by a function of the distance between the query and the weighted training sample, where the weights result from the sparse representation coefficient. Then, various pieces of evidence derived from the candidate samples are pooled by means of Dempster's rule of combination, from which a soft decision can be reached.

Conflicting evidence combination based on uncertainty measure and distance of evidence.

Dempster–Shafer evidence theory is widely used in many fields of information fusion. However, the counter-intuitive results may be obtained when combining with highly conflicting evidence. To deal with such a problem, we put forward a new method based on the distance of evidence and the uncertainty measure. First, based on the distance of evidence, the evidence is divided into two parts, the credible evidence and the incredible evidence. Then, a novel belief entropy is applied to measure the information volume of the evidence. Finally, the weight of each evidence is obtained and used to modify the evidence before using the Dempster’s combination rule. Numerical examples show that the proposed method can effectively handle conflicting evidence with better convergence.

A novel approach of collision assessment for coastal radar surveillance

For coastal radar surveillance, this paper proposes a data-driven approach to estimate a blip's collision probability preliminarily based on two factors: the probability of it being a moving vessel and the collision potential of its position. The first factor is determined by a Directed Acyclic Graph (DAG), whose nodes represent the blip's characteristics, including the velocity, direction and size. Additionally, the structure and conditional probability tables of the DAG can be learned from verified samples. Subsequently, obstacles in a waterway can be described as collision potential fields using an Artificial Potential Field model, and the corresponding coefficients can be trained in accordance with the historical vessel distribution. Then, the other factor, the positional collision potential of any position is obtained through overlapping all the collision potential fields. For simplicity, only static obstacles have been considered. Eventually, the two factors are characterised as evidence, and the collision probability of a blip is estimated by combining them with Dempster's rule. Through ranking blips on collision probabilities, those that pose high threat to safety can be picked up in advance to remind radar operators. Particularly, a good agreement between the proposed approach and the manual operation was found in a preliminary test.

The problem of dependent evidence

It is appropriate to use Dempster's rule for combining belief functions only if the belief functions combined are based on independent items of evidence. What can be done in the case of dependent evidence? Often the answer is to reframe the problem. Three examples are given: one from everyday experience, one from probabilistic relaxation, and one from expert systems.

Assessing forensic evidence by computing belief functions

We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.

A novel method to use fuzzy soft sets in decision making based on ambiguity measure and Dempster-Shafer theory of evidence: An application in medical diagnosis.

Recently, fuzzy soft sets-based decision making has attracted more and more interest. Although plenty of works have been done, they cannot provide the uncertainty or certainty of their results. To manage uncertainty is one of the most important and toughest tasks of decision making especially in medicine. In this study, we improve the performance of reducing uncertainty and raising the choice decision level in fuzzy soft set-based decision making. We make use of two appropriate tools (ambiguity measure and Dempster-Shafer theory of evidence) to improve fuzzy soft set-based decision making. Our proposed approach consists of three procedures: primarily, the uncertainty degree of each parameter is obtained by using ambiguity measure; next, the suitable basic probability assignment with respect to each parameter (or evidence) is constructed based on the uncertainty degree of each parameter obtained in the first step; in the end, the classical Dempster's combination rule is applied to aggregate independent evidences into the collective evidence, by which the candidate alternatives are ranked and the best alternative will be obtained. We compare the results of our proposed method with the recent relative works. Through employing our presented approach, in Example 5, the belief measure of the uncertainty falls to 0.0051 from 0.0751; in Example 6, the belief measure of the uncertainty drops to 0.0086 from 0.0547; in Example 7, the belief measure of the uncertainty falls to 0.0847 from 0.1647; in application, the belief measure of the uncertainty drops 0.0001 from 0.0069. Three numerical examples and an application in medical diagnosis are provided to demonstrate adequately that, on the one hand, our proposed method is feasible and efficient; on the other hand, our proposed method can reduce uncertainty caused by people's subjective cognition and raise the choice decision level with the best performance.

A risk assessment approach for failure mode and effects analysis based on intuitionistic fuzzy sets and evidence theory

Failure mode and effects analysis (FMEA) is an extensively used engineering technique for defining, identifying and prioritizing the potential failure modes. Traditionally the Risk Priority Number (RPN) is used to rank the potential failure modes. In this paper, a new risk assessment methodology which combines intuitionistic fuzzy sets (IFSs) with evidence theory is proposed to analyze the potential failure modes. The risk factors S, O, and D are evaluated by using linguistic variables and intuitionistic fuzzy numbers, which can be transformed into the basic probability assignment functions. The Jousselme distance is used to compute the weights of decision makers in order to efficiently combine highly conflicting evidence. The weighted average of evidence is obtained and the classical Dempster's combination rule is used to combine the mass functions modified. The proposed approach is applied thereafter to the prioritization of failure modes. A numerical example for risk assessment is given to illustrate the effectiveness and rationality of the proposed method finally.

A multicriteria approach for analysis of conflicts in evidence theory

Dempster–Shafer Theory (DST) or Evidence Theory is regarded as one of the leading theories for modeling uncertainty in imprecise situations. The main advantage of this theory arises from the possibility of combining different bodies of evidence originally developed by using Dempster's combination rule. However, this rule leads to counter-intuitive results when the bodies of evidence conflict with each other to a high degree. Thus, different combinations of conflict management rules have been developed over the years where, regardless of the method used, what should be identified first of all is the level of conflict between the bodies of evidence. Therefore, different metrics were used to classify or quantify the conflict but no single one of these was successful because it is impracticable to represent all situations of conflict in this theory by using only one metric. Therefore, the contribution of this article is to analyze conflict within DST by using a multi-criteria analysis, for which the Multi Criteria Decision Making (MCDM) method considered was ELECTRE TRI. On modeling the problem, three classes of conflict (low, medium and high), were considered. To validate the model, a numerical analysis was conducted that included the use of a method to point up conflict so as to infer parameters.

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.

Dempster's rule of combination

The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.

Combining dependent bodies of evidence

Dempster's combination rule can only be applied to independent bodies of evidence. One occurrence of dependence between two bodies of evidence is when they result from a common source. This paper proposes an improved method for combining dependent bodies of evidence which takes the significance of the common information sources into consideration. The method is based on the significance weighting operation and the "decombination" operation. A numerical example is illustrated to show the use and effectiveness of the proposed method.

Full diversity reception based on Dempster-Shafer theory for network coding with multiple-antennas relay

In this paper, a two-way relay system which achieves bi-directional communication via a multiple-antenna relay in two time slots is studied. In the multiple access (MA) phase, the novel receive schemes based on Dempster-Shafer (D-S) evidence theory are proposed at the relay node. Instead of traditional linear detection, the first proposed MIMO-DS NC scheme adopts D-S evidence theory to detect the signals of each source node before mapping them into network-coded signal. Moreover, different from traditional physical-layer network coding (PNC) based on virtual MIMO model, the further proposed MIMO-DS PNC comes from the vector space perspective and combines PNC mapping with D-S theory to obtain network-coded signal without estimating each source node signal. D-S theory can appropriately characterize uncertainty and make full use of multiple evidence source information by Dempster's combination rule to obtain reliable decisions. In the broadcast (BC) phase, the space-time coding (STC) and antenna selection (AS) schemes are adopted to achieve transmit diversity. Simulation results reveal that the STC and AS schemes both achieve full transmit diversity in the BC phase and the proposed MIMO-DS NC/PNC schemes obtain better end-to-end BER performance and throughputs compared with traditional schemes with a little complexity increasing and no matter which scheme is adopted in the BC phase, MIMO-DS PNC always achieves full end-to-end diversity gain as MIMO-ML NC but with a lower complexity and its throughput approaches the throughput of MIMO-ML NC in high SNR regime.

Belief Function Based Decision Fusion for Decentralized Target Classification in Wireless Sensor Networks.

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.

Evidence Combination From an Evolutionary Game Theory Perspective.

Dempster-Shafer evidence theory is a primary methodology for multisource information fusion because it is good at dealing with uncertain information. This theory provides a Dempster's rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multievidence system. Within the proposed ECR, we develop a Jaccard matrix game to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solution's stability and convergence, have been mathematically proved as well.

Target Recognition via Information Aggregation Through Dempster–Shafer's Evidence Theory

In this letter, a novel classification via information aggregation through Dempster-Shafer's (DS) evidence theory has been presented to target recognition in a SAR image. Although the DS theory of evidence has been widely studied over the decades, less attention has been paid to its application for target recognition. To capture the characteristics of a SAR image, this letter exploits a new multidimensional analytic signal named monogenic signal. Since the components of the monogenic signal are of a high dimension, it is unrealistic to be directly used. To solve the problem, an intuitive idea is to derive a single feature by these components. However, this strategy usually results in some information loss. To boost the performance, this letter presents a classification framework via information aggregation. The monogenic components are individually fed into a recently developed algorithm, i.e., sparse representation-based classification, from which the residual with respect to each target class can be produced. Since the residual from a query sample reflects the distance to the manifold formed by the training samples of a certain class, it is reasonable to be used to define the probability mass. Then, the information provided by the monogenic signal can be aggregated via Dempster's rule; hence, the inference can be reached.

A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence

This paper proposes a novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence. First, the uncertain degrees of various parameters are determined via grey relational analysis, which is applied to calculate the grey mean relational degree. Second, suitable mass functions of different independent alternatives with different parameters are given according to the uncertain degree. Third, to aggregate the alternatives into a collective alternative, Dempster's rule of evidence combination is applied. Finally, the alternatives are ranked and the best alternatives are obtained. The effectiveness and feasibility of this approach are demonstrated by comparing with the mean potentiality approach because the measure of performance of this approach is the same as the mean potentiality approach's, the belief measure of the whole uncertainty falls from 0.4723 to 0.0782 (resp. 0.3821 to 0.0069) in the example of Section 5 (resp. Section 6).

Grey Clustering Evaluation Model Based on D-S Evidence Theory to Evaluate the Scheme of Basin Initial Water Rights Allocation

In view of the characteristics of the randomness and uncertainty of basin initial water rights allocation scheme evaluation, this paper, integrating the Dempster-Shafer (D-S) evidence theory and the grey clustering evaluation method, researches on the evaluation method of allocation scheme. Taking advantages of D-S evidence theory and the compact- center-point triangular whitenization weight function (CCTWF) in processing and integrating the uncomplete information, the grey clustering evaluation model based on D-S evidence theory is proposed. The integrated clustering coeffi- cients matrix is obtained by using the grey clustering evaluation method based on CCTWF, and we look each clustering object as an evidence. Then, D-S evidence theory is used to obtain the belief function of every evidence with application of Dempster's combination rule, and the result of scheme evaluation in terms of the principle of selecting maximum value of belief functions. Finally, we take the evaluation of basin initial water rights allocation scheme of Dalinghe River in China for instance to demonstrate the practicability and effectiveness of this model.

Combining various types of belief structures

We first discuss the basic ideas of the Dempster–Shafer belief structure. We particularly emphasize the associated measures of plausibility and belief. We discuss the cumulative distribution function associated with a belief structure. We next turn to the issue of combining multiple belief structures. Two different types of combination of belief structures are investigated. The first, which we refer to as the fusion of belief structures, occurs when the belief structures being combined are providing information about the same variable. Here we make use of the Dempster rule. The second type, which we refer to as the joining of belief structures, occurs when the belief structures being combined are providing information about different variables. Here we make use of a belief structures cumulative distribution function and the Sklar theorem. The classic belief structures typically have a finite number of focal elements; here we began to look at belief structures which have a continuum of focal elements.

A Novel Robust MM Filter against Outliers

AbstractAn Interacting Multiple Model (IMM) filter suppresses outliers by integrating model‐conditioned estimation and model mode recognition through adaptive mode switches based on a Bayesian probability update. However, it may face significant outlier‐caused peak errors, which are undesirable or even impermissible in many applications, for example, target tracking. This paper considers that, from the view of the Dempster‐Shafer Theory, the IMM filter actually fuses the Bayesian beliefs of the model mode with Dempster's Rule of Combination, which can deal with uncertainties instead of the evidence conflicts that may exist as outliers appear. Therefore, we propose the adaptive robust multiple model (RMM) filter through introducing practical expert knowledge in the belief function framework, which runs online to reduce outlier‐caused peak errors. In RMM, the Likelihood Temporal Ratio (LTR) is incorporated to provide extra information on the tendency of mode switching. Moreover, expert rules are introduced to construct adaptive belief functions using discount techniques and to select the combination rule that better deals with evidence conflicts when outliers appear. The simulations in target tracking scenarios show that the proposed RMM filter significantly reduces outlier‐caused peak errors and hence obtains a lower rate of track loss in the cluttered environment.