乐胖代购免代理版

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$$A$$<\/jats:tex-math>\n A<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of alternatives available to the decision-maker, we can consider the associated utility function, expressing, for each scenario, the maximum utility among the alternatives. We consider two main problems: firstly, finding a minimal subset of

$$A$$<\/jats:tex-math>\n A<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that is equivalent to it, i.e., that has the same utility function. We show that for important classes of preference models, the set of possibly strictly optimal alternatives is the unique minimal equivalent subset. Secondly, we consider how to compare

$$A$$<\/jats:tex-math>\n A<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to another set of alternatives

$$B$$<\/jats:tex-math>\n B<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where

$$A$$<\/jats:tex-math>\n A<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and

$$B$$<\/jats:tex-math>\n B<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> correspond to different initial decision choices. This is closely related to the problem of computing setwise max regret. We derive mathematical results that allow different computational techniques for these problems, using linear programming, and especially, with a novel approach using the extreme points of the epigraph of the utility function.<\/jats:p>","DOI":"10.1007\/s10458-022-09572-8","type":"journal-article","created":{"date-parts":[[2022,8,13]],"date-time":"2022-08-13T20:16:56Z","timestamp":1660421816000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Minimality and comparison of sets of multi-attribute vectors"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-9582-8278","authenticated-orcid":false,"given":"Federico","family":"Toffano","sequence":"first","affiliation":[]},{"given":"Nic","family":"Wilson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,13]]},"reference":[{"key":"9572_CR1","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1109\/TAC.1981.1102777","volume":"26","author":"M Aizerman","year":"1981","unstructured":"Aizerman, M., & Malishevski, A. 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