Finite approximations to coherent choice

Troffaes, Matthias

Abstract

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.

Citation

Troffaes, M. (2009). Finite approximations to coherent choice. International Journal of Approximate Reasoning: Uncertainty in Intelligent Systems, 50(4), 655-665. https://doi.org/10.1016/j.ijar.2008.07.001

• Journal Article Type: Article
• Publication Date: Apr 1, 2009
• Deposit Date: Jun 19, 2009
• Publicly Available Date: Oct 17, 2014
• Journal: International Journal of Approximate Reasoning
• Print ISSN: 0888-613X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 50
• Issue: 4
• Pages: 655-665
• DOI: https://doi.org/10.1016/j.ijar.2008.07.001
• Keywords: Decision making, E-admissibility, Maximality, Numerical analysis, Lower prevision, Sensitivity analysis.
• Public URL: https://durham-repository.worktribe.com/output/1527828