Dempster with extensions by glen shafer in 1987 shafer, 1976. Scalable clustering using the dempstershafer theory of. Dempstershafer theory introduction, connections with rough. Combination of evidence in dempster shafer theory sandia. In the context of dg transportation, risk refers to the likelihood of incurring the undesirable consequences of a possible accident. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. Pdf combination of evidence in dempstershafer theory. Using the dempstershafer theory of evidence to resolve.
Section 5 investigates the semigroup structure of dempster shafer and states the main results relating it to bayes. This theory offers an elegant theoretical framework for modeling uncertainty, and provides a method for combining distinct bodies of evidence collected. Distributed attack prevention using dempstershafer theory. Time series dempstershafer evidence theory trimmedwinsorized means power unit prices 20. The theory allows one to combine evidence from different sources and arrive at a degree of belief represented by a mathematical object called belief function that takes into account all the available evidence. Special issue on the dempstershafer theory of evidence. A python library for performing calculations in the dempstershafer theory of evidence. The dempster shafer theory of evidence jean gordon and edward h. Dempster shafer executes as a main fusion node, with the role to collect and fuse the information provided by the monitors, taking the final decision regarding a possible attack. 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. It is much newer theory, originating in the work of a. Dempster shafer theory does not require an assumption regarding the probability of the individual constituents of the set or interval.
A simple view of the dempstershafer theory of evidence. The theory of belief functions, also referred to as evidence theory or dempstershafer theory dst, is a general framework for reasoning with uncertainty, with. Particularly appealing is the mathematical theory of evidence developed by arthur dempster. In a narrow sense, the term dempstershafer theory refers to the original conception of the theory by dempster and shafer. A mathematical theory of evidence turns 40 glenn shafer. Dempstershafer theory for combining in silico evidence and.
Its capability to assign uncertainty or ignorance to propositions is a powerful tool for dealing with a large range of problems that otherwise would seem intractable. Assigning confidence degrees masses to sets of alternatives mtrue 0. When occurring or emerging it will support a set of propositions. 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. Fault proneness of ann under dempstershafer evidence theory and trimmedwinsorized means. Since the probability of an accident in a link of a route might depend on a variety of factors, it is necessary to find a way to combine the pieces of 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. The level of support for a hypothesis that is provided by the evidence is expressed as a numerical value per dempstershafer theory, implemented using the python programming language we calculate the belief and plausibility of a hypothesis. The dempstershafer theory dst is a mathematical theory of evidence. If an agent obtains a new piece a of evidence, he may update his belief with the. Dempstershafer theory dst, also known as the theory of evidence or the theory of belief functions, was introduced by shafer in 1976 1, based on dempsters previous works 24. In your case, it may be better to use bayesian approch instead of dempster shafer evidence theory.
Different theories have been proposed in multisource data fusion, such as the bayesian approach, dempstershafer evidence theory dset 6. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. The significant innovation of this framework is that it allows. 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. 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. Bell school of electronics, electrical engineering and computer science queens university belfast belfast bt7 1nn, uk fj. June 7, 2016 abstract the book that launched the dempster shafer theory of belief functions appeared 40 years ago. The foundations of ds have been laid out by dempster 24, 6 and shafer 18 22. A case of combination of evidence in the dempstershafer. Bayes theory is based on the classical ideas of probability, while dempstershafer theory is a recent attempt to allow more interpretation of what uncertainty is all about. This theory may be considered as a generalization of the probability theory.
For example, the widely used example in dempster shafer evidence theory is doctor dignosis, which doctor believe 60% the patient has disease a and 40% disease b. Approximations for decision making in the dempstershafer. Combining classifiers using the dempster shafer theory of. Dempstershafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. Situations and evidence for identity using dempstershafer theory. Dempster shafer theory and statistical inference with weak. Shafer, 1976 is one of the main points of criticism this formalism has to face. Combining evidence in the extended dempstershafer theory. 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 weight of evidence prediction by quantitatively accounting for the reliability of each of the sources being combined. The dempstershafer theory of evidence jean gordon and edward h. Safety case confidence propagation based on dempstershafer. In dempstershafer theory, it is this probability mass that is the focus, and it is the probability mass that constitutes the evidence. In particular, it provides explicit estimations of imprecision and con.
Note, there is no pior data here, just numbers from human experts. 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 paper presents a new classifier combination technique based on the dempstershafer theory of evidence. 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. Apr 01, 2002 dempster shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. Dempster in 1967 and his student glenn shafer in 1976. Different than the bayes rule, dempstershafer theory represents evidence as possibilistic belief. Distributed attack prevention using dempstershafer theory of. I came across the dempstershafer theory of evidence. Section 4 provides a resume of some elementary facts of group and semigroup theory. The application of dempstershafer theory demonstrated with. On the behavior of dempsters rule of combination and the. In ds theory, the degree of belief in evidence is analogous to the mass of a physical object mass of evidence supports a belief.
After combining the evidence, a threshold of guilt can be established based on belief, such as 0. The application of dempstershafer theory demonstrated. A new technique for combining multiple classifiers using. Dempstershafer theory does not require an assumption regarding the probability of the individual constituents of the set or interval. Combination of evidence in dempstershafer theory unt. Bayesian theory is only concerned about single evidences. Fundamental difference between ds theory and probability theory is the treatment of ignorance. May 10, 2017 transportation of dangerous goods dgs is generally associated with significant levels of risk. A new technique for combining multiple classifiers using the. The dempstershafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. The dempster shafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. Bayesian and dempstershafer reasoning for knowledgebased. It has since been extended by numerous authors and popularised, but only to a degree, in the literature on artificial intelligence ai and expert systems, as a technique for modelling reasoning under.
Ds is a mathematical theory of evidence based on belief functions and plausible reasoning. Dempstershafer theory introduction, connections with. Dempster in the context of statistical inference, the theory was later developed by glenn. A simple view of the dempstershafer theory of evidence and. A python library for performing calculations in the dempster shafer theory of evidence. 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. The dempstershafer theory dst of evidence originated in the work of dempster on the theory of probabilities with upper and lower bounds. Zadeh compufer science division, universify of california, berkeley, california 94720 the emergence of expert systems as one of the major ar eas of activity within ai has resulted in a rapid growth of. Time series forecasting using artificial neural networks. It sho wn that application of the dempstershafer rule com bination in this case leads to ev. Transportation of dangerous goods dgs is generally associated with significant levels of risk. Application of extended dempstershafer theory of evidence in. As a more flexible mathematical tool, dempstershafer theory not only combines with other mathematical frameworks 1518, but also combines with. Dst is an evidence theory, it combines all possible outcomes of the problem.
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. Dempster shafer theory application to clustering mass function belief and plausibility functions connection with rough sets interpretation. The degrees of belief of propositions are given by probabilities or beliefs. This paper presents a new classifier combination technique based on the dempster shafer theory of evidence. 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. An introduction to bayesian and dempstershafer data fusion. The dempstershafer theory of evidence is a formalism, which allows appropriate interpretation of extractors con.
Application of dempstershafer theory to the in silico prediction of chemical toxicity based on qsar models and rulebased structural alerts demonstrates the advantages of this approach. Dempstershafer theory of evidence2 dempstershafertheorydstheoryisderivedfromdempstersoriginalwork23,24that. A wellknown theory of uncertainty used in ir is probability theory see fuh92 for a survey of probabilistic ir models. Indeed, probability theory may be seen as a limit of dempstershafer evidence theory when it is assumed. This paper reports on a largescale experiment for the evaluation of a formal querybiased combination of evidence mechanism. Novel paradigm for constructing masses in dempstershafer. Towards argumentation with symbolic dempstershafer. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict.
This report surveys a number of possible combination rules for dempstershafer structures and provides examples of the implementation of these rules for discrete and intervalvalued data. The dempstershafer theory, also known as the theory of belief functions, is a. The dempster shafer ds theory of evidence generalizes bayesian probability theory, by providing a coherent representation for ignorance lack of evidence. Here, an alternative theory of uncertainty is used, the dempstershafer theory of evidence sha76, because it is more flexible in modelling the ir. Compared with bayesian theory, the dempstershafer theory of evidence feels closer to our human perception and reasoning processes. This theory offers an elegant theoretical framework for modeling uncertainty, and provides a method for combining distinct bodies of evidence collected from. In this report we will discuss the above two philosophies or paradigms that make up. Data classification using the dempstershafer method arxiv. A library written in java for performing calculations in the dempstershafer theory of evidence. 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. Exploring the combination of dempstershafer theory and. In this context the dempster shafer theory of evidence dst has shown some promising results. 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 simple view of the dempstershafer theory of evidence and its implication for the rule of combination lotfi a. An alternative to the bayesian theory of evidence is dempstershafer theory which produces results similar to bayesian theory. This theory is being released because of following reason. We use the dempstershafer theory of evidence to combine optimally results obtained by content and link analyses on the web. A simple view of the dempster shafer theory of evidence and its implication for the rule of combination lotfi a. Shortliffe the drawbacks of pure probabilistic methods and of the certainty factor model have led us in recent years to consider alternate approaches. In this work we have proposed three novel algorithms to combine different biometric systems using the dst.
Dempstershafers theory of evidence applied to structured. Compared with bayesian theory, the dempster shafer theory of evidence feels closer to our human perception and reasoning processes. However, uncertain relationships between evidence and hypotheses bearing on this evidence are difficult to represent in applications of the theory. Dempstershafer theory dst, also known as the theory of evidence or the theory of belief functions, was introduced by shafer in 1976 1 based on dempsters previous works 2, 3, 4. Zadeh compufer science division, universify of california, berkeley, california 94720 the emergence of expert systems as one of the major ar. The dempstershafer theory is both a successor of fishers. Using the dempstershafer theory of evidence to resolve abox. Dempstershafer theory for combining in silico evidence. Section 5 investigates the semigroup structure of dempstershafer and states the main results relating it to bayes. Jeffreylike rules of conditioning for the dempstershafer theory of.
Application of extended dempstershafer theory of evidence. The dempstershafer ds theory of evidence generalizes bayesian probability theory, by providing a coherent representation for ignorance lack of evidence. Central to dempstershafer theory is the rule of combination of beliefs. The application of dempstershafer theory demonstrated with justi. Combining multiple query interface matchers using dempstershafer theory of evidence jun hong, zhongtian he and david a.
Dempstershafer theory application to clustering mass function belief and plausibility functions connection with rough sets interpretation. Forecasting errors for ann under dempstershafer evidence theory and trimmedwinsorized means. This intellectual autobiography looks back on how i came to write the book and how its ideas played out in my later work. The paper presents an algorithm for translating the subontologies containing con. June 7, 2016 abstract the book that launched the dempstershafer theory of belief functions appeared 40 years ago.