This paper deals with conditional decisions on generalized Anscombe-Aumann acts mapping states of the world to finitely additive probabilities on the set of menus of consequences, the latter conveying a form of “objective” ambiguity. If the decision maker has a systematic pessimistic/optimistic attitude towards “objective” ambiguity, acts reduce to functions mapping states of the world to belief/plausibility functions on consequences. We provide a system of axioms assuring the representability of a family of conditional preference relations on such acts by a conditional functional in which “subjective” uncertainty is modeled through a conditional belief/plausibility function on the states of the world, obeying to a suitable axiomatic definition.

Conditional decisions under objective and subjective ambiguity in Dempster-Shafer theory / Petturiti, Davide; Vantaggi, Barbara. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - (2022). [10.1016/j.fss.2022.02.011]

Conditional decisions under objective and subjective ambiguity in Dempster-Shafer theory

Vantaggi, Barbara
2022

Abstract

This paper deals with conditional decisions on generalized Anscombe-Aumann acts mapping states of the world to finitely additive probabilities on the set of menus of consequences, the latter conveying a form of “objective” ambiguity. If the decision maker has a systematic pessimistic/optimistic attitude towards “objective” ambiguity, acts reduce to functions mapping states of the world to belief/plausibility functions on consequences. We provide a system of axioms assuring the representability of a family of conditional preference relations on such acts by a conditional functional in which “subjective” uncertainty is modeled through a conditional belief/plausibility function on the states of the world, obeying to a suitable axiomatic definition.
2022
Belief functions; Finitely additive probabilities; Ambiguity; Conditional preferences
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Conditional decisions under objective and subjective ambiguity in Dempster-Shafer theory / Petturiti, Davide; Vantaggi, Barbara. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - (2022). [10.1016/j.fss.2022.02.011]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1645629
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