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To ease the computation, we propose to transform the initial model into another one that (1) belongs to some subclass with better mathematical properties, such as supermodularity or complete monotonicity; (2) is at least as informative as the original model, while being as close as possible to it. We show that the problem can be approached in terms of linear or quadratic programming and that it can be connected with the one of determining the incenter of a credal set. Finally, we compare the solutions of a decision making problem with the initial and the transformed models and illustrate how our approach can be applied in a decision making problem under severe uncertainty.<\/jats:p>","DOI":"10.1007\/s10479-023-05577-y","type":"journal-article","created":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T09:50:52Z","timestamp":1694685052000},"page":"2777-2815","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Inner approximations of coherent lower probabilities and their application to decision making problems"],"prefix":"10.1007","volume":"355","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7763-3779","authenticated-orcid":false,"given":"Enrique","family":"Miranda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6686-6534","authenticated-orcid":false,"given":"Ignacio","family":"Montes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andr\u00e9s","family":"Presa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,9,14]]},"reference":[{"key":"5577_CR1","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1214\/aoms\/1177704255","volume":"34","author":"FJ Anscombe","year":"1963","unstructured":"Anscombe, F. 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