We use imprecise probabilities, based on a concept of generalized coherence, for the management of uncertainty in artificial intelligence. With the aim of reducing the computational difficulties, in the checking of generalized coherence we propose a method which exploits, in the framework of the betting criterion, suitable subsets of the sets of values of the random gains. We give an algorithm in each step of which a linear system with a reduced number of unknowns can be used. Our method improves a procedure already existing in literature and could be integrated with recent approaches of other authors, who exploit suitable logical conditions with the aim of splitting the problem into subproblems. We remark that our approach could be also used in combination with efficient methods like column generation techniques. Finally, to illustrate our method, we give some examples.

On the linear structure of betting criterion and the checking of coherence / V., Biazzo; Gilio, Angelo. - In: ANNALS OF MATHEMATICS AND OF ARTIFICIAL INTELLIGENCE. - ISSN 1012-2443. - STAMPA. - 35:1-4(2002), pp. 83-106. [10.1023/a:1014570831884]

On the linear structure of betting criterion and the checking of coherence

GILIO, ANGELO
2002

Abstract

We use imprecise probabilities, based on a concept of generalized coherence, for the management of uncertainty in artificial intelligence. With the aim of reducing the computational difficulties, in the checking of generalized coherence we propose a method which exploits, in the framework of the betting criterion, suitable subsets of the sets of values of the random gains. We give an algorithm in each step of which a linear system with a reduced number of unknowns can be used. Our method improves a procedure already existing in literature and could be integrated with recent approaches of other authors, who exploit suitable logical conditions with the aim of splitting the problem into subproblems. We remark that our approach could be also used in combination with efficient methods like column generation techniques. Finally, to illustrate our method, we give some examples.
2002
algorithms; alternative theorems; basic sets; betting criterion; computational aspects; computational aspects.; conditional probability bounds; g-coherence checking; non relevant gains; not relevant gains; random gain
01 Pubblicazione su rivista::01a Articolo in rivista
On the linear structure of betting criterion and the checking of coherence / V., Biazzo; Gilio, Angelo. - In: ANNALS OF MATHEMATICS AND OF ARTIFICIAL INTELLIGENCE. - ISSN 1012-2443. - STAMPA. - 35:1-4(2002), pp. 83-106. [10.1023/a:1014570831884]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/94314
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