Finite approximations to coherent choice

Details Finite approximations to coherent choice Finite approximations to coherent choice

2012-03-05

arxiv.org/abs/1203.0919v1

International Journal of Approximate Reasoning 50 (2009) 655-665

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15 pages, 1 figure, 2 tables

Scientific paper

10.1016/j.ijar.2008.07.001

This paper studies and bounds the effects of approximating loss functions and credal sets on choice functions, under very weak assumptions. In particular, the credal set is assumed to be neither convex nor closed. The main result is that the effects of approximation can be bounded, although in general, approximation of the credal set may not always be practically possible. In case of pairwise choice, I demonstrate how the situation can be improved by showing that only approximations of the extreme points of the closure of the convex hull of the credal set need to be taken into account, as expected.

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