Finite approximations of data-based decision problems under imprecise probabilities
In decision theory under imprecise probabilities, discretizations are a crucial topic because many applications involve infinite sets whereas most procedures in the theory of imprecise probabilities can only be calculated for finite sets so far. The present paper develops a method for discretizing s...
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| Veröffentlicht in: | International journal of approximate reasoning 2009-07, Vol.50 (7), p.1115-1128 |
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| container_title | International journal of approximate reasoning |
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| creator | Hable, Robert |
| description | In decision theory under imprecise probabilities, discretizations are a crucial topic because many applications involve infinite sets whereas most procedures in the theory of imprecise probabilities can only be calculated for finite sets so far. The present paper develops a method for discretizing sample spaces in data-based decision theory under imprecise probabilities. The proposed method turns an original decision problem into a discretized decision problem. It is shown that any solution of the discretized decision problem approximately solves the original problem.
In doing so, it is pointed out that the commonly used method of natural extension can be most instable. A way to avoid this instability is presented which is sufficient for the purpose of the paper. |
| doi_str_mv | 10.1016/j.ijar.2009.05.003 |
| format | Article |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Applied sciences Artificial intelligence Coherent lower prevision Computer science control theory systems Data-based decision theory Decision theory. Utility theory Discretization Exact sciences and technology Imprecise probability Learning and adaptive systems Operational research and scientific management Operational research. Management science |
| title | Finite approximations of data-based decision problems under imprecise probabilities |
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