2020/02/12 by Jasper De Bock, De Bock, Jasper
Computer Science · Mathematics · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Mathematical and Theoretical Analysis #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2002.05196
openalex publication_date 2020/02/12 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
If uncertainty is modelled by a probability measure, decisions are typically\nmade by choosing the option with the highest expected utility. If an imprecise\nprobability model is used instead, this decision rule can be generalised in\nseveral ways. We here focus on two such generalisations that apply to sets of\nprobability measures: E-admissibility and maximality. Both of them can be\nregarded as special instances of so-called choice functions, a very general\nmathematical framework for decision making. For each of these two decision\nrules, we provide a set of necessary and sufficient conditions on choice\nfunctions that uniquely characterises this rule, thereby providing an axiomatic\nfoundation for imprecise decision making with sets of probabilities. A\nrepresentation theorem for Archimedean choice functions in terms of coherent\nlower previsions lies at the basis of both results.\n