Shafer theory ds theory of belief functions for managing uncertainties, specifically in the auditing and information systems domains. Engineering applications of artificial intelligence. The proposed method is composed essentially of two steps. Classic works of the dempstershafer theory of belief functions. Particularly appealing is the mathematical theory of evidence developed by arthur dempster. As a formal system, ds theory is distinguished from other uncertainty management approaches by dempster 1967, shafer 1976. Pdf download classic works of the dempster shafer theory. The dempstershafer theory, also known as the theory of belief functions, is a generalization of the bayesian theory of subjective probability. The dempster shafer ds theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. Pdf the dempstershafer theory of evidence researchgate. In particular, it provides explicit estimations of imprecision and con. Download classic works of the dempstershafer theory of. Student systems science and industrial engineering department thomas j. Dempstershafer evidence theory for image segmentation.
The ability to group complex data into a finite number of classes is. Data classification using the dempstershafer method arxiv. Dempster shafer theory dst or evidence theory is a general framework for reasoning with uncertainty, the role of dst is to combine evidences from the rules r1and r2 and compute an overall belief. Similarly to the ds theory, which is a generalisation of the classical probability theory, fuzzy logic provides an alternative reasoning apparatus as compared to boolean logic. For decades, dempster shafer evidence theory provides a solution for information fusion with reduced uncertainty and ambiguity.
Jun 27, 2019 dempster shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. The initial work introducing dempster shafer ds theory is found in dempster 1967 and shafer 1976. Watson school of engineering and applied science binghamton university p. Pellegrini a athe mitre corporation, burlington road, bedford, ma 01730.
This book brings together a collection of classic research papers on the dempstershafer theory of belief functions. The dempster shafer theory of evidence jean gordon and edward h. This research focuses on dempstershafers evidence theory and the different similarity measures used to compare two separate bodies of evidence boes. Unlike the probabilistic case, our axiomatic framework leads to intervalvalued utilities, and therefore, to a partial incomplete. Logistic regression, neural networks and dempstershafer theory. Classic works of the dempstershafer theory of belief. Handling of dependence in dempstershafer theory su. The dempstershafer theory owes its name to work by a. In this work we focus on the relationship between the dempster shafer. The main goal of this paper is to describe an axiomatic utility theory for dempster shafer belief function lotteries.
Pearl shows deficiencies of dempstershafer theory in dealing with several instances of commonsense reasoning in a processindependent manner. Dempstershafer theory and statistical inference with. Shafer theory to combine the results obtained from individual sources to find a final unified ranking. Information fusion with dempstershafer evidence theory. On the decision making problem in dempstershafer theory. In this present paper, which is an extended version of 4, we aim at formally comparing this extension and dempster shafer theory. With respect to polymatrix games with various link uncertainty, how do we deal with. If youre looking for a free download links of classic works of the dempstershafer theory of belief functions studies in fuzziness and soft computing pdf, epub, docx and torrent then this site is not for you. Shafer theory applied to regulatory decision process for selecting safer alternatives to toxic chemicals in consumer products. Indeed, probability theory may be seen as a limit of dempstershafer evidence theory when it is assumed. Section 2 gives the mathematical fundamentals of dempster shafer theory. The dempstershafer ds theory of belief functions 1, 2 is now wellestablished as a formalism for reasoning. However, it commonly has to suffer from the counterintuitive result.
Dempster shafer theory, with an example given of fusion using the cornerstone of the theory known as dempster s rule. The use of ds theory is illustrated by deriving a fraud risk assessment formula for a simplified version of a model developed by srivastava et al. A key feature of the theory is that propositions are represented as subsets of a set. The theory of belief functions, also referred to as evidence theory or dempster shafer theory dst, is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. We challenge the validity of dempstershafer theory by using an emblematic example to show that ds rule produces counterintuitive result. Pdf section 2 gives the mathematical fundamentals of dempstershafer theory. The dempster shafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. Dempster shafer theory is a mathematical theory of evidence for the representation of uncertainty. First, mass distributions in dempster shafer theory are obtained from the membership degrees of each pixel covering the three image components r, g and b. By bridging fuzzy logic and probabilistic reasoning, the theory of belief functions has become a primary tool for knowledge representation and uncertainty reasoning in expert systems. Software quality and reliability prediction using dempster.
However, some conditions, such as exclusiveness hypothesis and completeness constraint, limit its development and application to a large extend. Shafer theory applied to regulatory decision process. In an earlier article 1 we derived a method, within the framework of dempster shafer theory 23, to handle evidences that are weakly speci. Dempster shafer theory is based on the nonclassical idea of mass as opposed to the wellunderstood probabilities of bayes theory. Dempster shafer theory dst 30 is a generalization of probability theory that allows for incomplete knowledge. Most accurate prediction models require extensive testing e. Since its introduction the very name causes confusion, a more general term often used is belief functions both used intermittently here. Dempstershafer theory an overview sciencedirect topics. A new failure mode and effects analysis model using. Information fusion with dempstershafer evidence theory for. Combining testimonial reports from independent and partially reliable information sources is an important problem of uncertain reasoning. Unlimited viewing of the articlechapter pdf and any associated supplements and figures.
Expert systemsdempstershafer theory wikibooks, open books. Pedersens model has been selected to estimate the probability of collision, using the information provided by the ais, and dempster shafer theory has been selected for the treatment of uncertainty. In this section brief information will be given to can comprehend combination technique. Support for normalized as well as unnormalized belief functions different montecarlo algorithms for combining belief functions various methods related to the generalized bayesian theorem measures of uncertainty methods for constructing belief functions from data both python 2. Shafer showed how jeffreys generalization of bayes rule of conditioning can be reinterpreted in terms of the theory of belief functions. Dempstershafer theory for combining in silico evidence and. 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. This site is like a library, use search box in the widget to get ebook that you want. The dempstershafer theory dst is a mathematical theory of evidence. The validity of dempstershafer belief functions core. Software quality and reliability prediction using dempstershafer theory lan guo dissertation submitted to the college of engineering and mineral resources at west virginia university in partial ful. Pdf algorithms for dempstershafer theory researchgate. Dempstershafer theory dst provides a way to take ignorance uncertainty due to reducible variability into account.
This set is referred as the frame of discernment, and its. Dempstershafer theory, data classification, dempsters rule of combination. Dempster shafer theory ds is an effective method to model uncertainties and combine multiple evidences. Dempster shafer theory is widely applied to uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. Shortliffe the drawbacks of pure probabilistic methods and of the certainty factor model have led us in recent years to consider alternate approaches. Nate blaylock, james allen, in plan, activity, and intent recognition, 2014. Logistic regression, neural networks and dempster shafer theory. Dempster 1968 and glenn shafer 1976, but the kind of reasoning the theory uses can be found as far back as the seventeenth century. School of electronics and information technology, shanghai jiao tong university, shanghai 200240, peoples republic of china.
The integrative risk analytic framework is grounded in the dempster shafer ds theory that allows the analyst to combine multiple pieces of evidence and judgments from independent sources of information. Special issue on the dempstershafer theory of evidence. The dempstershafer theory of evidence jean gordon and edward h. Dempstershafer theory and statistical inference with weak beliefs ryanmartin, jianchunzhangandchuanhailiu abstract. Section 4 provides a resume of some elementary facts of group and semigroup theory. Dempstershafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in. Ds theory has been widely used in computer science and engi. Dst originated when shafer extended the original work of dempster in 1976 10. Using a simple engineering example, i highlight sources of confusion in the dempster shafer literature, and some questions that arise in the course of applying the dempster shafer algorithm.
However, the existing evidence theory is insufficient to consider the situations where it has no capability to express the fluctuations of data at a given phase of time during their execution, and the. June 7, 2016 abstract the book that launched the dempster shafer theory. May 01, 2007 classic works of the dempster shafer theory of belief functions studies in fuzziness and soft computing yager, ronald r. Ahmadzadeh and petrou used theory for predicting risk of soil erosion 11. The dempstershafer theory, also known as the theory of belief functions, is a generalization of the. 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. The theory came to the attention of ai researchers in the early 1980s, when they were trying to adapt probability theory to expert systems. The dempster shafer theory dst, also referred to as evidence theory, is a mathematical theory of evidence based on belief functions and plausible reasoning. Combination of evidence in dempstershafer theory kari sentz ph. Dempstershafer theory, with an example given of fusion using the cornerstone of the theory known as dempsters rule. Section 5 investigates the semigroup structure of dempster shafer and states the main results relating it to bayes. The following discussion within this section on dst has mostly been adopted from klir 11. A library written in java for performing calculations in the dempstershafer theory of evidence. Xu and krzyzak applied theorem to handwriting recognition 9.
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. Nguyen 1978 points out, soon after its introduction, t. More precisely, we show that this extension can be reformulated in dempster shafer theory and thus, from an expressiveness point of view, it is equivalent to dempster shafer theory. Section 3 describes algorithms for performing the most important operations on mass functions, and gives their efficiency. Available evidence, even if incomplete, can be used to find imprecise probabilities for events. The dempster shafer ds theory of partial beliefs is one of the mostwell known formalisms to address the partial knowledge. Logistic regression, neural networks and dempstershafer. Classic works of the dempster shafer theory of belief functions book also available for read online, mobi, docx and mobile and kindle reading. A python library for performing calculations in the dempster shafer theory of evidence. Dempstershafer theory for combining in silico evidence. Download classic works of the dempster shafer theory of belief functions in pdf and epub formats for free. Dempster in the context of statistical inference, the theory was later developed by glenn. An approach to the dempster shafer theory of evidence.
Dec, 2019 the main goal of this paper is to describe an axiomatic utility theory for dempster shafer belief function lotteries. Oct 17, 2014 a python library for performing calculations in the dempster shafer theory of evidence. Dempster s rule of combination can only be used when the. Classic works of the dempster shafer theory of belief. Jeffreylike rules of conditioning for the dempstershafer theory of. Author links open overlay panel luyuan chen yong deng. Dempstershafer theory is based on the nonclassical idea of mass as opposed to the wellunderstood probabilities of bayes theory. Then, similar to the mutual information in the probability theory, these measures are used for computing the dependency of the variables of a social bliss problem on the persons happiness value. The basic idea is to first model the link uncertainty by using dempster shafer theory in a unified framework, and then analyze the equilibria of games in terms of specific requirements. This paper discusses the relationship between dempster shafer theory and the classical bayesian method, describes our sensor fusion research work using dempster shafer theory in comparison with the weighted sum of probability method. Download classic works of the dempster shafer theory of belief functions or read online books in pdf, epub, tuebl, and mobi format. The dempster shafer theory owes its name to work by a. In this paper, i discuss the basic notions of the dempster shafer theory.
The dempstershafer theory the dempstershafer theory 8 allows us to combine evidence from different experts or other sources and provides a measure of con. The dempster shafer theory the dempster shafer theory 8 allows us to combine evidence from different experts or other sources and provides a measure of con. 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. Box 6000 binghamton, ny 9026000 scott ferson applied biomathematics 100 north country road setauket, ny 11733 abstract. Dempster shafer evidence theory theory applied on several studies in computer science. Download pdf classic works of the dempster shafer theory. Within the framework of dempster shafer theory, we propose a general model of partially reliable sources which includes several previously known results as special cases. The two modified mappings are utilized in two ambiguity measures in dempster shafer theory.
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. Abstract a modal logic interpretation of dempster shafer theory is developed in the framework of multivalued models of modal logic, i. A mathematical theory of evidence turns 40 glenn shafer. The dempster shafer theory gives a solid ba sis for reasoning applications characterized by uncertainty. Shafer theory was presented in 22, although the proposed algorithm lacked a full formal justi. A verified matlab toolbox for the dempstershafer theory. Click download or read online button to get classic works of the dempster shafer theory of belief functions book now. This methodology has been applied to maritime traffic in the canary islands and has been validated using the kullbackleibler divergence.
First, mass distributions in dempstershafer theory are obtained from the membership degrees of each pixel covering the three image components r, g and b. View dempster shafer theory research papers on academia. 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. A new failure mode and effects analysis model using dempster shafer evidence theory and grey relational projection method. Combination of evidence in dempster shafer theory kari sentz ph. Fault recognition using an ensemble classifier based on. An introduction to bayesian and dempstershafer data fusion. Dempster shafer theory and statistical inference with weak. This naturally leads us to choose the dempster shafer approach as our first sensor fusion implementation algorithm.
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