Jean Dezert

Information fusion based on new proportional conflict redistribution rules

In this paper we propose anew family of fusion rules for the combination of uncertainty and conflicting information. This family of rules is based on new Proportional Conflict Redistributions (PCR) allowing us to deal with highly conflicting sources for static and dynamic fusion applications. Here five PCR rules (PCR1-PCR5) are presented, analyzed and compared through several numerical examples. From PCR1 up to PCR5 one increases in one hand the complexity of the rules, but in other hand one improves the exactitude of the redistribution of conflicting masses. The basic common principle of PCR rules is to redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. Alongside of these new five PCR rules, there are infinitely many ways these redistributions (through the choice of the set of weighting factors) can be chosen. PCR1 is equivalent to the weighted average operator (WAO) on Shafers model only for static fusion problems but these two operators do not preserve the neutral impact of the vacuous belief assignment (VBA). The PCR2-PCR5 rules presented here, preserve the neutral impact of VBA and turn out to be what we consider as reasonable and can serve as alternatives to the hybrid DSm rule. PCR4 is an improvement of minC and Dempsters rules of combination and PCR5 is what we feel is the most exact PCR fusion rule developed up to now. The hybrid DSm rule manages the transfer of the belief committed to the conflict through a simple and direct way while the transfer used within PCR rules is more subtle and complex. The PCR rules can be used also and naturally as new efficient alternatives to the Dempsters rule and its other alternatives already proposed in the Dempster-Shafer theory (DST) over the last twenty years.

Combination of sources of evidence with different discounting factors based on a new dissimilarity measure

The sources of evidence may have different reliability and importance in real applications for decision making. The estimation of the discounting (weighting) factors when the prior knowledge is unknown have been regularly studied until recently. In the past, the determination of the weighting factors focused only on reliability discounting rule and it was mainly dependent on the dissimilarity measure between basic belief assignments (bbas) represented by an evidential distance. Nevertheless, it is very difficult to characterize efficiently the dissimilarity only through an evidential distance. Thus, both a distance and a conflict coefficient based on probabilistic transformations BetP are proposed to characterize the dissimilarity. The distance represents the difference between bbas, whereas the conflict coefficient reveals the divergence degree of the hypotheses that two belief functions strongly support. These two aspects of dissimilarity are complementary in a certain sense, and their fusion is used as the dissimilarity measure. Then, a new estimation method of weighting factors is presented by using the proposed dissimilarity measure. In the evaluation of weight of a source, both its dissimilarity with other sources and their weighting factors are considered. The weighting factors can be applied in the both importance and reliability discounting rules, but the selection of the adapted discounting rule should depend on the actual application. Simple numerical examples are given to illustrate the interest of the proposed approach.

A new belief-based K-nearest neighbor classification method

The K-nearest neighbor (K-NN) classification method originally developed in the probabilistic framework has serious difficulties to classify correctly the close data points (objects) originating from different classes. To cope with such difficult problem and make the classification result more robust to misclassification errors, we propose a new belief-based K-nearest neighbor (BK-NN) method that allows each object to belong both to the specific classes and to the sets of classes with different masses of belief. BK-NN is able to provide a hyper-credal classification on the specific classes, the rejection classes and the meta-classes as well. Thus, the objects hard to classify correctly are automatically committed to a meta-class or to a rejection class, which can reduce the misclassification errors. The basic belief assignment (bba) of each object is defined from the distance between the object and its neighbors and from the acceptance and rejection thresholds. The bbas are combined using a new combination method specially developed for the BK-NN. Several experiments based on simulated and real data sets have been carried out to evaluate the performances of the BK-NN method with respect to several classical K-NN approaches.

Adaptive imputation of missing values for incomplete pattern classification

In classification of incomplete pattern, the missing values can either play a crucial role in the class determination, or have only little influence (or eventually none) on the classification results according to the context. We propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory. At first, we try to classify the object (incomplete pattern) based only on the available attribute values. As underlying principle, we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information. In this case, the object is committed to this particular class. However, if the object cannot be classified without ambiguity, it means that the missing values play a main role for achieving an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and Self-Organizing Map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is classified according to each training class, and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (which are particular disjunctions of several single classes). The credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets. HighlightsMissing values are adaptively imputed in classification according to context.SOM and K-NN are used for the imputation with admissible computation burden.Ensemble classifier is introduced for credal classification.The imprecision of classification can be well captured using belief functions.The proposed method has been tested by artificial and real data sets.

Fusion of sources of evidence with different importances and reliabilities

This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafers discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. We also discuss the possibility for mixing them in a global fusion process.

Credal c-means clustering method based on belief functions

The recent credal partition approach allows the objects to belong to not only the singleton clusters but also the sets of clusters (i.e. meta-clusters) with different masses of belief. A new credal c-means (CCM) clustering method working with credal partition has been proposed in this work to effectively deal with the uncertain and imprecise data. In the clustering problem, one object simultaneously close to several clusters can be difficult to correctly classify, since these close clusters appear not very distinguishable for this object. In such case, the object will be cautiously committed by CCM to a meta-cluster (i.e. the disjunction of these close clusters), which can be considered as a transition cluster among these different close clusters. It can well characterize the imprecision of the class of the object and can also reduce the misclassification errors thanks to the use of meta-cluster. CCM is robust to the noisy data because of the outlier cluster. The clustering centers and the mass of belief on each cluster for any object are obtained by the optimization of a proper objective function in CCM. The effectiveness of CCM has been demonstrated by three experiments using synthetic and real data sets with respect to fuzzy c-means (FCM) and evidential c-means (ECM) clustering methods.

Land cover change prediction with a new theory of plausible and paradoxical reasoning

The spatial prediction of land cover ot the Jeld scale in winter appears useful for the issue of bare soils reduction in agricultural intensive regions. High variability of the factors that motivate the land cover changes between each winter involves integration of uncertainty in the modelling process. Fusion process with Dempster-Shafer Theoiy (DST) presents some limits in generating errors in decision making when the degree of conflict, between the sources of evidence that suppor? land cover hypotheses, becomes important. This paper focuses on the application of Dezeri-Smarandache Theory (DSmT) method to the fusion of multiple land-use attributes for land cover prediction purpose. Results are discussed and compared with prediction levels achieved with DST. Through this

Evidence Combination From an Evolutionary Game Theory Perspective

rst application of the Dezert- Smarandache Theory, we show an example of this new approach abiliry to solve some of practical problems where the Dempster-Shafer Theory usuolly foils.

Credal classification rule for uncertain data based on belief functions

Dempster-Shafer evidence theory is a primary methodology for multisource information fusion because it is good at dealing with uncertain information. This theory provides a Dempsters rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multievidence system. Within the proposed ECR, we develop a Jaccard matrix game to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solutions stability and convergence, have been mathematically proved as well.

On the Validity of Dempster's Fusion Rule and its Interpretation as a Generalization of Bayesian Fusion Rule

Abstract In this paper we present a new credal classification rule (CCR) based on belief functions to deal with the uncertain data. CCR allows the objects to belong (with different masses of belief) not only to the specific classes, but also to the sets of classes called meta-classes which correspond to the disjunction of several specific classes. Each specific class is characterized by a class center (i.e. prototype), and consists of all the objects that are sufficiently close to the center. The belief of the assignment of a given object to classify with a specific class is determined from the Mahalanobis distance between the object and the center of the corresponding class. The meta-classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes. The selection of meta-classes depends on the application and the context, and a measure of the degree of indistinguishability between classes is introduced. In this new CCR approach, the objects assigned to a meta-class should be close to the center of this meta-class having similar distances to all the involved specific classes׳ centers, and the objects too far from the others will be considered as outliers (noise). CCR provides robust credal classification results with a relatively low computational burden. Several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this CCR method with respect to other classification methods.