Student systems science and industrial engineering department thomas j. The goal of the combination of imperfect information is to nd an accurate information, easily interpretable, which can resume the information set to be combined. An introduction to bayesian and dempster shafer data fusion. The dempstershafer theory is a mathematical theory of evidence, which allows one to combine evidences from different sources and arrive at a belief function by taking into account all the available evidences. As probabilistic, fuzzy, possibilistic and rough partitions are all special evidential partitions, our approach can be used to evaluate and compare the results of any soft clustering methods. Overview of dempstershafer and belief function tracking methods erik blasch1, jean dezert2, b pannetier2 1air force research laboratory, information directorate, rome, ny, 441 2the french aerospace lab, f91761 palaiseau, france. Combination of evidence in dempster shafer theory kari sentz ph. The complexity of manipulating and combining mass functions is then dras. Dempster shafer theory and statistical inference with weak. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. The complex formulation for combining belief functions shown. The conditioning as defined by the above rule is the foundation of reasoning in dempstershafer theory.
It is used to combine separate pieces of information evidence to calculate the probability of an event. Dempstershafer theory, data classification, dempsters rule of combination. Dempstershafer theory, with an example given of fusion using the cornerstone of the theory known as dempsters rule. Dempster shafer theory dst dst is a mathematical theory of evidence based on belief functions and plausible reasoning. In their approach, the distance between the output classification vector provided by each. Dempstershafer evidence combining for antihoneypot. Since then, nearly four h undred pap ers on the theory and practice of ds reasoning has b een.
Dempstershafer theory, which can be regarded as a generalisation of probability theory, is a widely used formalism for reasoning with uncertain information. Exploring the combination of dempstershafer theory and. The dempstershafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. In this thesis we have proposed three novel algorithms to combine di.
In, alani and deriche have proposed a new technique for combining classifiers using ds theory, in which different classifiers correspond to different feature sets. Dempster shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. Dempstershafer degrees of belief resemble the certainty factors in mycin, and this resemblance suggested that they might combine the rigor of probability theory. Most accurate prediction models require extensive testing e. In ds theory, the degree of belief in evidence is analogous to the mass of a physical object mass of evidence supports a belief. The ds theory offers provision for the representation of ignorance. Dempstershafer theory dst is a rigorous decisiontheory approach that provides a way to generate predictions, estimate the uncertainty associated with each prediction, and combine multiple sources of evidence to obtain a weightofevidence prediction by quantitatively accounting for the reliability of each of the sources being combined. Dempster shafer theory dst is a rigorous decision theory approach that provides a way to generate predictions, estimate the uncertainty associated with each prediction, and combine multiple sources of evidence to obtain a weightofevidence prediction by quantitatively accounting for the reliability of each of the sources being combined. The theory of belief functions, also referred to as evidence theory or dempstershafer theory dst, is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. This report surveys a number of possible combination rules for dempster shafer structures and provides examples of the implementation of these rules for discrete and intervalvalued data. Compared with bayesian theory, the dempstershafer theory of evidence feels closer to our human perception and reasoning processes.
Dempstershafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. Dempstershafer evidence theory for image segmentation. A new technique for combining multiple classifiers using the. The theory of belief functions, also referred to as evidence theory or dempstershafer theory. First, mass distributions in dempstershafer theory are obtained from the membership degrees of each pixel covering the three image components r, g and b. This paper presents a new classifier combination technique based on the dempster shafer theory of evidence. In glenn shafers book, a mathematical theory of evidence, the author offers a reinterpretation of arthur dempsters work, a reinterpretation that identifies his lower probabilities as epistemic probabilities or degrees of belief, takes the rule for combining such degrees of belief as fundamental, and abandons the idea that they arise as lower bounds over classes of bayesian probabilities. Particularly appealing is the mathematical theory of evidence developed by arthur dempster. The significant innovation of this framework is that it allows. The dempster shafer theory of evidence jean gordon and edward h. The following discussion within this section on dst has mostly been adopted from klir 11.
The dempster shafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. The dempster shafer ds theory of evidence generalizes bayesian probability theory, by providing a coherent representation for ignorance lack of evidence. Abstract a modal logic interpretation of dempstershafer theory is developed in the framework of multivalued models of modal logic, i. Dempster shafer theory of evidences in mathematics, the dempster shafer ds theory 14 is used to calculate the belief degree, within the range 0,1, for a. Combination of evidence in dempstershafer theory kari sentz ph. Dempstershafer theory for combining in silico evidence and. As a formal system, ds theory is distinguished from other uncertainty management approaches by dempster 1967, shafer 1976. Combining multiple query interface matchers using dempstershafer theory of evidence jun hong, zhongtian he and david a. The initial work introducing dempstershafer ds theory is found in dempster 1967 and shafer 1976. For example, in the search for the identity of an infecting organism.
The dempstershafer theory the dempstershafer theory 8 allows us to combine evidence from different experts or other sources and provides a measure of con. Shortliffe the drawbacks of pure probabilistic methods and of the certainty factor model have led us in recent years to consider alternate approaches. Dempstershafer theory dst provides a way to take ignorance uncertainty due to reducible variability into account. Data classification using the dempstershafer method arxiv. Abstract the dempstershafer theory of belief functions has proved to be a pow. Abstract over the years, there have been many proposed methods in setbased tracking. The dempstershafer theory of evidence jean gordon and edward h. Combining classifiers using the dempster shafer theory of evidence. Since its introduction the very name causes confusion, a more general term often used is belief functions both used intermittently here. We next apply the theory in an example of fusing data from multiple sensors. Pdf combination of evidence in dempstershafer theory.
Vying with the bayes theory is the dempstershafer theory, that deals with measures of belief as opposed to probability. In this section, we will describe the dempster shafer theory ds 14 in brief, and then introduce our dsbased model for detecting honeypots. Combining multiple query interface matchers using dempster. The dempstershafer ds theory of evidence generalizes bayesian probability theory, by providing a coherent representation for ignorance lack of evidence. Again, the analysis is very straightforward and shows the power of the bayesian approach. Dempstershafer theory 2 provides an ideal modeling tool to address this problem. Whereas the bayesian theory requires probabilities for each question of interest, belief functions allow us to base degrees of belief for one question on probabilities for a. The dempstershafer theory dst is a mathematical theory of evidence. For example, within the field of medical diagnosis, it is.
Available evidence, even if incomplete, can be used to find imprecise probabilities for events. Bell school of electronics, electrical engineering and computer science queens university belfast belfast bt7 1nn, uk fj. Introduction the ability to group complex data into a finite number of classes is important in data mining, and means that more useful decisions can be made based on the available information. Combining classifiers using the dempster shafer theory of. The dempster shafer theory is a mathematical theory of evidence based on belief functions and plausible reasoning, which is used to combine separate pieces of information evidence to calculate the probability of an event. Dempstershafer theory is a framework that can handle these various evidentiary types by combining a notion of probability with the traditional conception of sets. Expert systemsdempstershafer theory wikibooks, open books. Compared with bayesian theory, the dempster shafer theory of evidence feels closer to our human perception and reasoning processes. However, the ensemble approach depends on the assumption that single classi ers errors are uncorrelated, which is known as classi er diversity. Modified dempstershafer ds evidence theory can handle conflicting. Paradox elimination in dempstershafer combination rule with. Dempster shafer theory, which can be regarded as a generalisation of probability theory, is a widely used formalism for reasoning with uncertain information.
Using dempster shafer theory to fuse multiple information sources in regionbased segmentation tomasz adamek, noel e. Dst originated when shafer extended the original work of dempster in 1976 10. The dempstershafer theory, also known as the theory of belief functions, is a generalization of the bayesian theory of subjective probability. The dempster shafer theory is a mathematical theory of evidence, which allows one to combine evidences from different sources and arrive at a belief function by taking into account all the available evidences. On the validity of dempstershafer theory jean dezert, pei wang, albena tchamova to cite this version. An introduction to bayesian and dempstershafer data fusion. On the independence requirement in dempstershafer theory for.
Section 5 investigates the semigroup structure of dempster shafer and states the main results relating it to bayes. Combination of evidence in dempster shafer theory sandia. Pdf using dempstershafer theory to fuse multiple information. A verified matlab toolbox for the dempstershafer theory. This versatility to represent and combine different types of evidence obtained from multiple. The dempstershafer ds theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. One starts with a belief function defined in a multivariable space being ones knowledge, makes certain observations on the values taken by some observational variables, e.
This framework is based on dempstershafer ds theory of evidence and owa operators. The proposed method is composed essentially of two steps. Fundamental difference between ds theory and probability theory is the treatment of ignorance. Nguyen 1978 points out, soon after its introduction, t. Aside famous zadehs example on the validity of dempsters rule of combination, it is shown that. This paper presents a new classifier combination technique based on the dempstershafer theory of evidence. Using dempstershafer theory to fuse multiple information sources in regionbased segmentation tomasz adamek, noel e. The application of the theory hinges on the use of a rule for combining evidence from different sources. Classic works of the dempstershafer theory of belief functions. A case of combination of evidence in the dempstershafer. Logo recognition based on the dempstershafer fusion of.
Section 4 provides a resume of some elementary facts of group and semigroup theory. Pdf algorithms for dempstershafer theory researchgate. Ds theory has been widely used in computer science and engi. The theory allows one to combine evidence from different sources and arrive at a degree of. Its capability to assign uncertainty or ignorance to propositions is a powerful tool for dealing with. Pdf combining the results of several neural network classifiers. Combining classifiers using the dempster shafer theory of evidence naseem, imran on. Combining evidence in the extended dempstershafer theory.
However, uncertain relationships between evidence and hypotheses bearing on this evidence are difficult to represent in applications of the theory. Indeed, probability theory may be seen as a limit of dempstershafer evidence theory when it is assumed. Logo recognition based on the dempstershafer fusion of multiple classi ers 3 ing di erent classi ers, leading to better performance. On the independence requirement in dempstershafer theory for combining classifiers providing statistical evidence. An introduction liping liu college of business administration, university of akron, akron, oh 443254801 the notion of belief functions is a result of the seminar work of shafer1 and its conceptual forerunnerlower and upper probabilities. The theory of belief functions has an established nexus with probability theory, possibility theory, and, by extension, fuzzy set theory. The main contribution of this paper is a novel framework for integration of evidence from multiple sources with the region merging process based on the dempstershafer ds theory by p. The initial work introducing dempster shafer ds theory is found in dempster 1967 and shafer 1976. An improved dempstershafer algorithm using a partial con.
Software quality and reliability prediction using dempster. Fusion 2012 15th international conference on information fusion, jul 2012, singapour, singapore. Box 6000 binghamton, ny 9026000 scott ferson applied biomathematics 100 north country road setauket, ny 11733 abstract. Pdf section 2 gives the mathematical fundamentals of dempstershafer. Data classification using the dempstershafer method. An introduction liping liu college of business administration, university of akron, akron, oh 443254801 the notion of belief functions is a result of the seminar work of shafer1 and its conceptual. Software quality and reliability prediction using dempstershafer theory lan guo as software systems are increasingly deployed in mission critical applications, accurate quality and reliability predictions are becoming a necessity. The theory of belief functions, also referred to as evidence theory or dempster shafer theory. Dempstershafer theory and statistical inference with weak beliefs ryanmartin, jianchunzhangandchuanhailiu abstract.
In particular, it provides explicit estimations of imprecision and con. Dempstershafer theory for combining in silico evidence. O connor centre for digital video processing, dublin city university, dublin 9, ireland. The main contribution of this paper is a novel framework for integration of evidence from multiple sources with the region merging process based on the dempster shafer ds theory by p. Neural network combining classifier based on dempster shafer theory for semantic indexing in video content. By bridging fuzzy logic and probabilistic reasoning, the theory of belief functions. Combining classifiers for word sense disambiguation based on. Section 5 investigates the semigroup structure of dempstershafer and states the main results relating it to bayes. Pdf the dempstershafer theory of evidence researchgate. Overview of dempstershafer and belief function tracking. A special feature of this theory is the possibility to characterize uncer. Special issue on the dempstershafer theory of evidence. Dempstershafer theory is based on the nonclassical idea of mass as opposed to the wellunderstood probabilities of bayes theory. The dempstershafer theory assumes that there is a fixed set of mutually exclusive and exhaustive elements called hypotheses or propositions and symbolized by the greek letter.
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