Toward a generalized theory of uncertainty (GTU)--an outline

Belief Functions: The Disjunctive Rule of Combination and the Generalized Bayesian Theorem

This book is devoted to an emerging branch of Information Fusion based on new approach for modelling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations.

Advances and Applications of DSmT for Information Fusion

https://isiarticles.com/bundles/Article/pre/pdf/26408.pdf

Belief function combination and conflict management

It is a deep-seated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU), which is outlined in this paper, breaks with this tradition and views uncertainty in a broader perspective. Uncertainty is an attribute of information. A fundamental premise of GTU is that information, whatever its form, may be represented as what is called a generalized constraint. The concept of a generalized constraint is the centerpiece of GTU.

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Toward a generalized theory of uncertainty (GTU) - an outline

The theory of evidence proposed by G Shafer is gaining more and more acceptance in the field of artificial intelligence, for the purpose of managing uncertainty in knowledge bases One of the crucial problems is combining uncertain pieces of evidence stemming from several sources, whether rules or physical sensors This paper examines the framework of belief functions in terms of expressive power for knowledge representation It is recalled that probability theory and Zadeh's theory of possibility are mathematically encompassed by the theory of evidence, as far as the evaluation of belief is concerned Empirical and axiomatic foundations of belief functions and possibility measures are investigated Then the general problem of combining uncertain evidence is addressed, with focus on Dempster rule of combination It is pointed out that this rule is not very well adapted to the pooling of conflicting information Alternative rules are proposed to cope with this problem and deal with specific cases such as nonreliable sources, nonexhaustive sources, inconsistent sources, and dependent sources It is also indicated that combination rules issued from fuzzy set and possibility theory look more flexible than Dempster rule because many variants exist, and their numerical stability seems to be better



La theorie des fonctions de credibilite proposee par G Shafer est de plus en plus reconnue, dans le domaine de l'intelligence artificielle, pour le traitement de l'incertitude dans les bases de connaissances Un des problemes cruciaux est la combinaison d'informations issues de plusieurs sources (regles ou capteurs) Cet article etudie le cadre propose par les fonctions de credibilite quant a son pouvoir expressif pour la representation de connaissances On rappelle que d'un point de vue mathematique la theorie des probabilites et la theorie des possibilites sont des cas particuliers de la theorie des fonctions de credibilite pour ce qui est de l'evaluation de l'incertitude Les fondements empiriques et axiomatiques des fonctions de credibilite et de possibilite sont discutes Puis le probleme general de la combinaison est aborde en mettant l'accent sur la regle de Dempster On met en evidence le fait que cette regle est peu adaptee a la combinaison d'informations conflictuelles D'autres regles sont proposees pour traiter ce probleme dans diverses situations telles que sources inegalement fiables, incompletes, incoherentes, dependantes On indique aussi que les regles de combinaison proposees par la theorie des ensembles flous et des possibilites semblent plus flexibles que la regle de Dempster, car de nombreuses variantes existent; de plus leur stabilite numerique semble meilleure

Didler Dubois

Papers

Representation and combination of uncertainty with belief functions and possibility measures