Symbolic and Quantitative Approaches to Reasoning with by Sébastien Destercke, Thierry Denoeux

By Sébastien Destercke, Thierry Denoeux

This e-book constitutes the refereed lawsuits of the thirteenth eu convention on Symbolic and Quantitative techniques to Reasoning with Uncertainty, ECSQARU 2015, held in Compiègne, France, in July 2015. The forty nine revised complete papers offered have been conscientiously reviewed and chosen from sixty nine submissions and canopy issues on choice thought and personal tastes; argumentation; conditionals; online game idea; trust replace; type; inconsistency; graphical versions; Bayesian networks; trust services; good judgment; and probabilistic graphical versions for scalable facts analytics. Papers come from researchers attracted to advancing the know-how and from practitioners utilizing uncertainty ideas in real-world functions. The scope of the ECSQARU meetings encompasses primary matters, illustration, inference, studying, and selection making in qualitative and numeric uncertainty paradigms.

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Extra resources for Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings

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1 > x1,2 − x1 x1,2 − x1 . or γ1 = x2 − x1 x2 − x1 (8) The identification of γ1 is independent of unknown u2 . The second use of Dichotomy method CEE is on interval [x2 , x3 ]. If 1, [x2 , x3 ] is less preferred (resp. preferred or indifferent) to x2,3 ∈ [x2 , x3 ], then x2,3 − x2 x2,3 − x2 x2,3 − x2 resp. γ2 > . (9) or γ2 = γ2 < x3 − x2 x3 − x2 x3 − x2 The identification of γ2 is independent of unknown u2 . Finally, the last use of Dichotomy method CEE is on the interval [x1 , x3 ]. The decision maker is asked to compare 1, [x1 , x3 ] with the sure outcome x1,3 ∈ [x1 , x3 ].

This comes from utility EUuPA γ the fact that the points x1 , . . , xm are fixed. Hence we need to find another representation. 2 Piecewise Affine Function Around a Diagonal Instead of fixing the value of x and letting the associated utility be a variable, the idea is to allow both the value of x and its utility to be variable (but not independently). 30 C. Labreuche et al. Fig. 1. Piecewise affine utility function around the diagonal (a, d) − (b, c). We start by defining a utility function, depending on only one parameter γ, in an interval [a, b] and with fixed values of the utility at the boundary: uγ (a) = c and uγ (b) = d.

4 an analytical formula, as it is done in decision under uncertainty. Section 5 presents the related works. Finally some conclusions are drawn. 2 General Approach for the Elicitation of a Utility Function Let X be an interval of R. Without loss of generality, we will consider in the whole paper only strictly increasing utility functions over X. In an elicitation phase, one cannot expect to uniquely identify the utility function. Hence we assume a family U of compatible utility functions, where U is to be determined.

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Symbolic and Quantitative Approaches to Reasoning with by Sébastien Destercke, Thierry Denoeux
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