TY - CONF

T1 - Some results on generalized coherence ofconditional probability bounds

AU - Sanfilippo, Giuseppe

PY - 2003

Y1 - 2003

N2 - Based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of g-coherence is equivalent to the 'avoiding uniform loss' property for lower and upper probabilities (a la Walley). Moreover, given a g-coherent imprecise assessment by our algorithms we can correct it obtaining the associated coherent assessment (in the sense of Walley and Williams). As is well known, the problems of checking g-coherence and propagating tight g-coherent intervals are NP and FP^NP complete, respectively, and thus NP-hard. Two notions which may be helpful to reduce computational effort are those of non relevant gain and basic set. Exploiting them, our algorithms can use linear systems with reduced sets of variables and/or linear constraints. In this paper we give some insights on the notions of non relevant gain and basic set. We consider several families with three conditional events, obtaining some results characterizing g-coherence in such cases. We also give some more general results.

AB - Based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of g-coherence is equivalent to the 'avoiding uniform loss' property for lower and upper probabilities (a la Walley). Moreover, given a g-coherent imprecise assessment by our algorithms we can correct it obtaining the associated coherent assessment (in the sense of Walley and Williams). As is well known, the problems of checking g-coherence and propagating tight g-coherent intervals are NP and FP^NP complete, respectively, and thus NP-hard. Two notions which may be helpful to reduce computational effort are those of non relevant gain and basic set. Exploiting them, our algorithms can use linear systems with reduced sets of variables and/or linear constraints. In this paper we give some insights on the notions of non relevant gain and basic set. We consider several families with three conditional events, obtaining some results characterizing g-coherence in such cases. We also give some more general results.

KW - Uncertain knowledge

KW - basic sets

KW - coherence

KW - conditional
probability bounds

KW - g-coherence

KW - imprecise probabilities

KW - lower and upper probabilities

KW - non relevant gains

KW - Uncertain knowledge

KW - basic sets

KW - coherence

KW - conditional
probability bounds

KW - g-coherence

KW - imprecise probabilities

KW - lower and upper probabilities

KW - non relevant gains

UR - http://hdl.handle.net/10447/51888

UR - http://www.carleton-scientific.com/isipta/PDF/006.pdf

M3 - Other

SP - 62

EP - 76

ER -