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Implementing general belief function framework with a practical codification for low complexity
 in <Advances and Applications of DSmT for Information Fusion
, 2009
"... In this chapter, we propose a new practical codification of the elements of the Venn diagram in order to easily manipulate the focal elements. In order to reduce the complexity, the eventual constraints must be integrated in the codification at the beginning. Hence, we only consider a reduced hyper ..."
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In this chapter, we propose a new practical codification of the elements of the Venn diagram in order to easily manipulate the focal elements. In order to reduce the complexity, the eventual constraints must be integrated in the codification at the beginning. Hence, we only consider a reduced hyper power set D Θ r that can be 2 Θ or D Θ. We describe all the steps of a general belief function framework. The step of decision is particularly studied, indeed, when we can decide on intersections of the singletons of the discernment space no actual decision functions are easily to use. Hence, two approaches are proposed, an extension of previous one and an approach based on the specificity of the elements on which to decide. The principal goal of this chapter is to provide practical codes of a general belief function framework for the researchers and users needing the belief function theory.
Hierarchical Proportional Redistribution principle for uncertainty reduction and bba approximation
 in Proceedings of the 10th World Congress on Intelligent Control and Automation (WCICA 2012
"... Abstract—DempsterShafer evidence theory is very important in the fields of information fusion and decision making. However, it always brings high computational cost when the frames of discernments to deal with become large. To reduce the heavy computational load involved in many rules of combinatio ..."
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Abstract—DempsterShafer evidence theory is very important in the fields of information fusion and decision making. However, it always brings high computational cost when the frames of discernments to deal with become large. To reduce the heavy computational load involved in many rules of combinations, the approximation of a general belief function is needed. In this paper we present a new general principle for uncertainty reduction based on hierarchical proportional redistribution (HPR) method which allows to approximate any general basic belief assignment (bba) at a given level of nonspecificity, up to the ultimate level 1 corresponding to a Bayesian bba. The level of nonspecificity can be adjusted by the users. Some experiments are provided to illustrate our proposed HPR method. Index Terms—Belief functions, hierarchical proportional redistribution (HPR), evidence combination, belief approximation. I.
Reliability
"... and combination rule in the theory of belief functions ..."
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and combination rule in the theory of belief functions
Université de Technologie de Compiègne
, 2009
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
unknown title
, 2009
"... State estimation using interval analysis and belief function theory: Application to dynamic vehicle localization ..."
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State estimation using interval analysis and belief function theory: Application to dynamic vehicle localization
Reliability and combination rule in the theory of belief functions
"... Abstract This paper presents a point of view to address an application with the theory of belief functions from a global approach. Indeed, in a belief application, the definition of the basic belief assignments and the tasks of reduction of focal elements number, discounting, combination and decis ..."
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Abstract This paper presents a point of view to address an application with the theory of belief functions from a global approach. Indeed, in a belief application, the definition of the basic belief assignments and the tasks of reduction of focal elements number, discounting, combination and decision, must be thought at the same time. Moreover these tasks can be seen as a general process of belief transfer. The second aspect of this paper involves the introduction of the reliability in the combination rule directly and not before. Indeed, in general, the discounting process is made with a discounting factor that is a reliability factor of the sources. Here we propose to include in the combination rule an estimation of the reliability based on a local conflict estimation.
Université de Picardie Jules Verne, IUT de l’Oise
, 2010
"... Abstract. In this paper, belief functions, defined on the lattice of partitions of a set of objects, are investigated as a suitable framework for combining multiple clusterings. We first show how to represent clustering results as masses of evidence allocated to partitions. Then a consensus belief f ..."
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Abstract. In this paper, belief functions, defined on the lattice of partitions of a set of objects, are investigated as a suitable framework for combining multiple clusterings. We first show how to represent clustering results as masses of evidence allocated to partitions. Then a consensus belief function is obtained using a suitable combination rule. Tools for synthesizing the results are also proposed. The approach is illustrated using two data sets. 1
New Basic belief assignment approximations based on optimization
"... Abstract—The theory of belief function, also called DempsterShafer evidence theory, has been proved to be a very useful representation scheme for expert and other knowledge based systems. However, the computational complexity of evidence combination will become large with the increasing of the fram ..."
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Abstract—The theory of belief function, also called DempsterShafer evidence theory, has been proved to be a very useful representation scheme for expert and other knowledge based systems. However, the computational complexity of evidence combination will become large with the increasing of the frame of discernment’s cardinality. To reduce the computational cost of evidence combination, the idea of basic belief assignment (bba) approximation was proposed, which can reduce the complexity of the given bba’s. To realize a good bba approximation, the approximated bba should be similar (in some sense) to the original bba. In this paper, we use the distance of evidence together with the difference between the uncertainty degree of approximated bba and that of the original one to construct a comprehensive measure, which can represent the similarity between the approximated bba and the original one. By using such a comprehensive measure as the objective function and by designing some constraints, the bba approximation is converted to an optimization problem. Comparative experiments are provided to show the rationality of the construction of comprehensive similarity measure and that of the constraints designed. Index Terms—Evidence theory, belief function, bba, bba approximation, optimization. I.