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.
2014
coherence; conditional probability; decision making; dp-conditional possibility; inference; likelihood function; likelihood functions; t-conditional possibility
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/525279
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