## 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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