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17
Shedding new light on Zadeh’s criticism of Dempster’s rule of combination
 In Proc. 8th Int. Conf. Information Fusion, contribution No. C81
, 2005
"... Abstract – Shortly after proposing Dempster’s rule of combination as a general aggregation rule for evidence from independent sources, Zadeh formulated an annoying example for which Dempster’s rule seemed to produce counterintuitive results. Since then, many authors have used Zadeh’s example either ..."
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Abstract – Shortly after proposing Dempster’s rule of combination as a general aggregation rule for evidence from independent sources, Zadeh formulated an annoying example for which Dempster’s rule seemed to produce counterintuitive results. Since then, many authors have used Zadeh’s example either to criticize DemsterShafer theory as a whole, or as a motivation for constructing alternative combination rules. This paper shows that the counterintuition of Zadeh’s example is not a problem of Dempster’s rule, but a problem of Zadeh’s model that does not correspond to reality. Two different ways to fix the problem will be discussed, showing that Dempster’s rule of combination perfectly behaves as one would expect. 1,2
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.
Resourcebounded and anytime approximation of belief function computations
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2002
"... This papers proposes a new approximation method for DempsterShafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resourcebounded propa ..."
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This papers proposes a new approximation method for DempsterShafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resourcebounded propagation scheme, in which the user determines in advance the maximal time available for the computation. This leads then to convenient, interruptible anytime algorithms giving progressively better solutions as execution time goes on, thus offering to trade the quality of results against the costs of computation. The paper demonstrates the usefulness of these new methods and shows its advantages and drawbacks compared to existing techniques.
Minimizing communication costs of distributed local computation
, 2005
"... A valuation algebra offers a suitable framework to represent knowledge and information. Based on this framework, several algorithms to process knowledge and pooled under the name local computation were mapped out in recent years. This paper proposes an extension of the valuation algebra framework th ..."
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A valuation algebra offers a suitable framework to represent knowledge and information. Based on this framework, several algorithms to process knowledge and pooled under the name local computation were mapped out in recent years. This paper proposes an extension of the valuation algebra framework that allows to express the costs of transmitting valuations between network hosts. Based on this model, we estimate the total computation costs caused by the local computation architectures and observe under which constraints these costs can be minimized. Once a sufficient condition is identified, we present an
Probabilistic argumentation and decision system
, 2003
"... The concept of probabilistic argumentation systems PAS is restricted to two types of variables: assumptions, which model the uncertain part of the knowledge, and propositions, which model the rest of the information. Instantiations of PAS have been used for dealing with problems in different context ..."
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The concept of probabilistic argumentation systems PAS is restricted to two types of variables: assumptions, which model the uncertain part of the knowledge, and propositions, which model the rest of the information. Instantiations of PAS have been used for dealing with problems in different contexts. Here, we introduce a third kind of variables into PAS: socalled decision variables. This new kind allows to describe the decisions which a user can make to react on some state of the system. Consider that given a system state, the users can themselves set the values of some decision variables in order to guarantee the requirement. The interesting system states are now those for which the users can find at least one setting of “their ” variables under which the requirement imposed on the system can be fulfilled. This can be seen as a game with two players, say nature against a user. Nature makes the first move and the user the second. If the requirement is fulfilled, the user wins (as the system is up), otherwise the user looses. Note that we do not include a concept of utility here as we are only interested in possible settings of decision variables. Further, we present an algorithm for computing arguments which exploits the special structure of PAS with decision variables. This allows now to use this framework for example in modelbased reliability theory for computing structure functions.
Shared ordered binary decision diagrams for DempsterShafer theory
 in European Conference ECSQARU’07, Hammamet, ser. Lecture Notes in Computer Science
, 2007
"... Abstract. The binary representation is widely used for representing focal sets of DempsterShafer belief functions because it allows to compute efficiently all relevant operations. However, as its space requirement grows exponentially with the number of variables involved, computations may become pr ..."
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Abstract. The binary representation is widely used for representing focal sets of DempsterShafer belief functions because it allows to compute efficiently all relevant operations. However, as its space requirement grows exponentially with the number of variables involved, computations may become prohibitive or even impossible for belief functions with larger domains. This paper proposes shared ordered binary decision diagrams for representing focal sets. This not only allows to compute efficiently all relevant operations, but also turns out to be a compact representation of focal sets. 1
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"... (will be inserted by the editor) of applications such as automatic surveillance [1], video indexing and retrieval [2] and humancomputer interaction [3]. Human actions can be extremely various, e.g. facial expression, hand gesture, human pose and people interaction. The scientific challenge is to re ..."
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(will be inserted by the editor) of applications such as automatic surveillance [1], video indexing and retrieval [2] and humancomputer interaction [3]. Human actions can be extremely various, e.g. facial expression, hand gesture, human pose and people interaction. The scientific challenge is to recognize a behavior from observations coming from multimedia features such as video, audio and text [4,5]. The global problem is to link the real world which has intrinsically an analogue nature to the human interpreted world which is symbolic [6]. In the context of video indexing and monitoring applications, human motion analysis is a means to automatically analyze videos and to cope with the increasing number of videos in databases. Low level analysis is not
Maintenance policy performance assessment in presence of imprecision based on DempsterShafer Theory of Evidence
, 2012
"... Abstract: The aim of this work is to assess the performance of a maintenance policy when a stochastic model of the life of the component of interest is known, but relies on parameters that are imprecisely known, and only through information elicited from experts. The case in which the information us ..."
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Abstract: The aim of this work is to assess the performance of a maintenance policy when a stochastic model of the life of the component of interest is known, but relies on parameters that are imprecisely known, and only through information elicited from experts. The case in which the information used to feed the model comes from a single expert has been investigated by the authors in a previous work. This paper deals with the different situation in which a number of experts are involved in the elicitation of the uncertain parameters; in particular, each expert provides an interval he/she believes containing the unknown value of the parameter which he/she is knowledgeable about. The different type of available information calls for the development of a different method to represent and propagate the associated uncertainty. Resorting to Probability theory to address this issue is questionable. Then, a technique based on the DempsterShafer Theory of Evidence (DSTE) is embraced in this work, which allows facing a practical case study concerning the check valve of a turbopump lubricating system in a Nuclear Power Plant. The output of such method consists of couples of Lower and Upper cumulative distributions describing the uncertainty in the maintenance performance indicators of interest (i.e., unavailability and costs), which accounts for both the aleatory and epistemic contributions.