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Possibilistic and probabilistic likelihood functions and their extensions: common features and specific characteristics. (English) Zbl 1334.60004
Summary: We deal with conditional probability in the sense of de Finetti and with \(T\)-conditional possibility (with \(T\) a triangular norm). We prove that Dubois and Prade conditional possibility is a particular min-conditional possibility and then we compare the two notions of conditioning by an inferential point of view. Moreover, we study \(T\)-conditional possibilities as functions of the conditioning event, putting in evidence analogies and differences with conditional probabilities. This allows to characterize likelihood functions (and their aggregations) consistent either with a \(T\)-conditional possibility or a conditional probability. This analysis highlights many syntactical coincidences. Nevertheless the main difference is a weak form of monotonicity, which arises only in the possibilistic case.

MSC:
60A05 Axioms; other general questions in probability
60A86 Fuzzy probability
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