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. (C) 2013 Elsevier B.V. All rights reserved.
Possibilistic and probabilistic likelihood functions and their extensions: Common features and specific characteristics / Giulianella, Coletti; Davide, Petturiti; Vantaggi, Barbara. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 250:250(2014), pp. 25-51. [10.1016/j.fss.2013.09.010]
Possibilistic and probabilistic likelihood functions and their extensions: Common features and specific characteristics
VANTAGGI, Barbara
2014
Abstract
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. (C) 2013 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.