Uncertainty, Imprecision and Additivity in Data Fusion : Historical Point of View

and key words 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 wor k 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, no n 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 . History of sciences, Probability, Fuzzy sets, Dempster-Shafer evidence theory, Data fusion, Imprecision, Uncertainty, Additivity .