Incertitude, imprécision et additivité en fusion de données : point de vue historique
Uncertainty, Imprecision and Additivity in Data Fusion : Historical Point of View
OPEN ACCESS
This paper presents an historical overview of the evolution of the notion of probability . The different kinds of probability and the opposition between objectivists (or frequencists) and subjectivists are presented . Then we show how some works, following the wok by Cox, aim at deducing what is called by others axioms of probabilities, from a given set of basic postulates which well fit intuition. These postulates may then be modified in order to face the limits of probability and give rise to other data fusion approaches, non probabilistic (fuzzy sets, possibility theory, Dempster-Shafer evidence theory for instance) . In Dempster-Shafer evidence theory, the orthogonal combination rule, originally presented without true justification, can also be deduced from postulates, as shown in the work by Smets . We establish links between his postulates and Cox's ones . At last, we illustrate by a simple example the different computation ways for combining evidences proposed in the history of probability.
Résumé
Cet article présente un aperçu historique de l'évolution de la notion de probabilité . Les différentes classes de probabilités et l'antagonisme entre objectivistes (ou fréquencistes) et subjectivistes sont présentés . On montre ensuite comment certains travaux, à la suite de ceux de Cox, s'attachent à déduire ce que d'autres appellent les axiomes des probabilités d'un certain nombre de postulats de base correspondant bien à l'intuition . Ces postulats peuvent ensuite être modifiés pour faire face aux limites des probabilités et donnent lieu à d'autres approches, non probabilistes, de la fusion de données (ensembles flous, possibilités, Dempster-Shafer par exemple) . Dans la théorie des croyances de Dempster-Shafer, la règle de combinaison, présentée à l'origine sans véritable justification, peut également être déduite de postulats, comme le montrent les travaux de Smets. Nous établissons les liens entre ses postulats et ceux de Cox. Enfin, un exemple de combinaison de témoignages vient illustrer les différences entre les résultats obtenus selon quelques unes des méthodes proposées dans l'histoire des probabilités pour combiner des informations.
History of sciences, Probability, Fuzzy sets, Dempster-Shafer evidence theory, Data fusion, Imprecision, Uncertainty, Additivity
Mots clés
Épistémologie, Probabilités, Ensembles flous, Théorie des croyances de Dempster-Shafer, Fusion de données, Imprécision, Incertitude, Additivité
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