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Temporal Dempster-Shafer Theory

MU Ke-Dian LIN Zuo-Quan,

计算机科学 , 2003,
Abstract: In this paper,we propose temporal Dempster.Shafer theory to handle the combination of uncertainty and time. In temporal Dempster.Shafer theory,the element of the temporal frame of discernment is defined as an event that associates a hypothesis with corresponding time interval. And the assignment of belief to subset of the temporal frame of discernment is performed by the mass function. It is a representation and reasoning mechanism that combines uncertainty and time by the basic frame of Dempster.Shafer theory.
Dempster-Shafer for Anomaly Detection  [PDF]
Qi Chen,Uwe Aickelin
Computer Science , 2008,
Abstract: In this paper, we implement an anomaly detection system using the Dempster-Shafer method. Using two standard benchmark problems we show that by combining multiple signals it is possible to achieve better results than by using a single signal. We further show that by applying this approach to a real-world email dataset the algorithm works for email worm detection. Dempster-Shafer can be a promising method for anomaly detection problems with multiple features (data sources), and two or more classes.
On the Combinality of Evidence in the Dempster-Shafer Theory  [PDF]
Lotfi Zadeh,Anca Ralescu
Computer Science , 2013,
Abstract: In the current versions of the Dempster-Shafer theory, the only essential restriction on the validity of the rule of combination is that the sources of evidence must be statistically independent. Under this assumption, it is permissible to apply the Dempster-Shafer rule to two or mere distinct probability distributions.
Using Dempster-Shafer Theory in Knowledge Representation  [PDF]
Alessandro Saffiotti
Computer Science , 2013,
Abstract: In this paper, we suggest marrying Dempster-Shafer (DS) theory with Knowledge Representation (KR). Born out of this marriage is the definition of "Dempster-Shafer Belief Bases", abstract data types representing uncertain knowledge that use DS theory for representing strength of belief about our knowledge, and the linguistic structures of an arbitrary KR system for representing the knowledge itself. A formal result guarantees that both the properties of the given KR system and of DS theory are preserved. The general model is exemplified by defining DS Belief Bases where First Order Logic and (an extension of) KRYPTON are used as KR systems. The implementation problem is also touched upon.
A Defect in Dempster-Shafer Theory  [PDF]
Pei Wang
Computer Science , 2013,
Abstract: By analyzing the relationships among chance, weight of evidence and degree of beliefwe show that the assertion "probability functions are special cases of belief functions" and the assertion "Dempster's rule can be used to combine belief functions based on distinct bodies of evidence" together lead to an inconsistency in Dempster-Shafer theory. To solve this problem, we must reject some fundamental postulates of the theory. We introduce a new approach for uncertainty management that shares many intuitive ideas with D-S theory, while avoiding this problem.
Dempster-Shafer vs. Probabilistic Logic  [PDF]
Daniel Hunter
Computer Science , 2013,
Abstract: The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal in the sense that disagreement can occur when any one of them is removed. An example is given in which the traditional assumption of conditional independence of evidence on hypotheses holds and a uniform prior is assumed, but probabilistic logic and Dempster's rule give radically different results for the combination of two evidence events.
Can Evidence Be Combined in the Dempster-Shafer Theory  [PDF]
John Yen
Computer Science , 2013,
Abstract: Dempster's rule of combination has been the most controversial part of the Dempster-Shafer (D-S) theory. In particular, Zadeh has reached a conjecture on the noncombinability of evidence from a relational model of the D-S theory. In this paper, we will describe another relational model where D-S masses are represented as conditional granular distributions. By comparing it with Zadeh's relational model, we will show how Zadeh's conjecture on combinability does not affect the applicability of Dempster's rule in our model.
A Logical Interpretation of Dempster-Shafer Theory, with Application to Visual Recognition  [PDF]
Gregory M. Provan
Computer Science , 2013,
Abstract: We formulate Dempster Shafer Belief functions in terms of Propositional Logic using the implicit notion of provability underlying Dempster Shafer Theory. Given a set of propositional clauses, assigning weights to certain propositional literals enables the Belief functions to be explicitly computed using Network Reliability techniques. Also, the logical procedure corresponding to updating Belief functions using Dempster's Rule of Combination is shown. This analysis formalizes the implementation of Belief functions within an Assumption-based Truth Maintenance System (ATMS). We describe the extension of an ATMS-based visual recognition system, VICTORS, with this logical formulation of Dempster Shafer theory. Without Dempster Shafer theory, VICTORS computes all possible visual interpretations (i.e. all logical models) without determining the best interpretation(s). Incorporating Dempster Shafer theory enables optimal visual interpretations to be computed and a logical semantics to be maintained.
A Monte-Carlo Algorithm for Dempster-Shafer Belief  [PDF]
Nic Wilson
Computer Science , 2013,
Abstract: A very computationally-efficient Monte-Carlo algorithm for the calculation of Dempster-Shafer belief is described. If Bel is the combination using Dempster's Rule of belief functions Bel, ..., Bel,7, then, for subset b of the frame C), Bel(b) can be calculated in time linear in 1(31 and m (given that the weight of conflict is bounded). The algorithm can also be used to improve the complexity of the Shenoy-Shafer algorithms on Markov trees, and be generalised to calculate Dempster-Shafer Belief over other logics.
Data classification using the Dempster-Shafer method  [PDF]
Qi Chen,Amanda Whitbrook,Uwe Aickelin,Chris Roadknight
Computer Science , 2014, DOI: 10.1080/0952813X.2014.886301
Abstract: In this paper, the Dempster-Shafer method is employed as the theoretical basis for creating data classification systems. Testing is carried out using three popular (multiple attribute) benchmark datasets that have two, three and four classes. In each case, a subset of the available data is used for training to establish thresholds, limits or likelihoods of class membership for each attribute, and hence create mass functions that establish probability of class membership for each attribute of the test data. Classification of each data item is achieved by combination of these probabilities via Dempster's Rule of Combination. Results for the first two datasets show extremely high classification accuracy that is competitive with other popular methods. The third dataset is non-numerical and difficult to classify, but good results can be achieved provided the system and mass functions are designed carefully and the right attributes are chosen for combination. In all cases the Dempster-Shafer method provides comparable performance to other more popular algorithms, but the overhead of generating accurate mass functions increases the complexity with the addition of new attributes. Overall, the results suggest that the D-S approach provides a suitable framework for the design of classification systems and that automating the mass function design and calculation would increase the viability of the algorithm for complex classification problems.
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