Catálogo de publicaciones - libros

When merging belief functions, Dempster rule of combination is justified only when information sources can be considered as independent. When this is not the case, one must find out a cautious merging rule that adds a minimal amount of information to the inputs. Such a rule is said to follow the principle of minimal commitment. Some conditions it should comply with are studied. A cautious merging rule based on maximizing expected cardinality of the resulting belief function is proposed. It recovers the minimum operation when specialized to possibility distributions. This form of the minimal commitment principle is discussed, in particular its discriminating power and its justification when some conflict is present between the belief functions.

A new method is proposed for building a predictive belief function from statistical data in the Transferable Belief Model framework. The starting point of this method is the assumption that, if the probability distribution ℙ of a random variable X is known, then the belief function quantifying our belief regarding a future realization of X should have its pignistic probability distribution equal to ℙ. When PX is unknown but a random sample of X is available, it is possible to build a set of probability distributions containing ℙ with some confidence level. Following the Least Commitment Principle, we then look for a belief function less committed than all belief functions with pignistic probability distribution in . Our method selects the most committed consonant belief function verifying this property. This general principle is applied to the case of the normal distribution.

In this paper we study a new probability associated with any given belief function , i.e. the orthogonal projection [] of onto the probability simplex . We provide an interpretation of [] in terms of a redistribution process in which the mass of each focal element is equally distributed among its subsets, establishing an interesting analogy with the pignistic transformation. We prove that orthogonal projection commutes with convex combination just as the pignistic function does, unveiling a decomposition of [] as convex combination of basis pignistic functions. Finally we discuss the norm of the difference between orthogonal projection and pignistic function in the case study of a quaternary frame, as a first step towards a more comprehensive picture of their relation.

Based on the canonical decomposition of belief functions, Smets introduced the concept of a latent belief structure (LBS). This concept is revisited in this article. The study of the combination of LBSs allows us to propose a less committed version of Dempster’s rule, resulting in a commutative, associative and idempotent rule of combination for LBSs. This latter property makes it suitable to combine non distinct bodies of evidence. A sound method based on the plausibility transformation is also given to infer decisions from LBSs. In addition, an extension of the new rule is proposed so that it may be used to optimize the combination of imperfect information with respect to the decisions inferred.

This contribution deals with a belief processing which enables managing of multiple and overlapping elements of a frame of discernment. An outline of the Dempster-Shafer theory for such cases is presented, including several types of constraints for simplification of its large computational complexity. DSmT – a new theory rapidly developing the last five years – is briefly introduced. Finally, it is shown that the DSmT is a special case of the general Dempster-Shafer approach.

Traditional Dempster Shafer belief theory does not provide a simple method for judging the effect of statistical and probabilistic data on belief functions and vice versa. This puts belief theory in isolation from probability theory and hinders fertile cross-disciplinary developments, both from a theoretic and an application point of view. It can be shown that a bijective mapping exists between Dirichlet distributions and Dempster-Shafer belief functions, and the purpose of this paper is to describe this correspondence. This has three main advantages; belief based reasoning can be applied to statistical data, statistical and probabilistic analysis can be applied to belief functions, and it provides a basis for interpreting and visualizing beliefs for the purpose of enhancing human cognition and the usability of belief based reasoning systems.

The Transferable Belief Model (TBM) relies on belief functions and enables one to represent and combine a variety of knowledge from certain up to ignorance as well as conflict inherent to imperfect data. A lot of applications have used this flexible framework however, in the context of temporal data analysis of belief functions, a few work have been proposed. Temporal aspect of data is essential for many applications such as surveillance (monitoring) and Human-Computer Interfaces. We propose algorithms based on the mechanisms of Hidden Markov Models usually used for state sequence analysis in probability theory. The proposed algorithms are the “credal forward”, “credal backward” and “credal Viterbi” procedures which allow to filter temporal belief functions and to assess state sequences in the TBM framework. Illustration of performance is provided on a human motion analysis problem.

In this paper we propose a new tool called OWL-CM (OWL Combining Matcher) that deals with uncertainty inherent to ontology mapping process. On the one hand, OWL-CM uses the technique of similarity metrics to assess the equivalence between ontology entities and on the other hand, it incorporates belief functions theory into the mapping process in order to improve the effectiveness of the results computed by different matchers and to provide a generic framework for combining them. Our experiments which are carried out with the benchmark of Ontology Alignment Evaluation Initiative 2006 demonstrate good results.

The paper deals with quality measures of rules extracted from data, more precisely with measures of the whole extracted rulesets. Three particular approaches to extending ruleset quality measures from classification to general rulesets are discussed, and one of them, capable to represent uncertain validity of rulesets for objects, is elaborated in some detail. In particular, a generalization of ROC curves is proposed. The approach is illustrated on rulesets extracted with four important methods from the well-known iris data.

TAN (Tree-augmented Naïve Bayes) classifier makes a compromise between the model complexity and classification rate, the study of which has now become a hot research issue. In this paper, we propose a discriminative method that is based on KL (Kullback-Leibler) divergence to learn TAN classifier. First, we use EAR (explaining away residual) method to learn the structure of TAN, and then optimize TAN parameters by an objective function based on KL divergence. The results of the experiments on benchmark datasets show that our approach produces better classification rate.