Minimality and comparison of sets of multi-attribute vectors
| dc.contributor.author | Toffano, Federico | |
| dc.contributor.author | Wilson, Nic | |
| dc.contributor.funder | Science Foundation Ireland | en |
| dc.contributor.funder | European Regional Development Fund | en |
| dc.date.accessioned | 2022-08-31T11:08:50Z | |
| dc.date.available | 2022-08-31T11:08:50Z | |
| dc.date.issued | 2022-08-12 | |
| dc.date.updated | 2022-08-31T11:02:16Z | |
| dc.description.abstract | In a decision-making problem, there is often some uncertainty regarding the user preferences. We assume a parameterised utility model, where in each scenario we have a utility function over alternatives, and where each scenario represents a possible user preference model consistent with the input preference information. With a set A 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 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 to another set of alternatives B , where A and B 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. | en |
| dc.description.sponsorship | Science Foundation Ireland (Grant No. 12/RC/2289 and Grant No. 12/RC/2289-P2 which are co-funded under the European Regional Development Fund.) | en |
| dc.description.status | Peer reviewed | en |
| dc.description.version | Published Version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Toffano, F. and Wilson, N. (2022) 'Minimality and comparison of sets of multi-attribute vectors'. Autonomous Agents and Multi-Agent Systems, 36 (66 pp). doi: 10.1007/s10458-022-09572-8 | en |
| dc.identifier.doi | 10.1007/s10458-022-09572-8 | en |
| dc.identifier.endpage | 66 | en |
| dc.identifier.issn | 1387-2532 | |
| dc.identifier.journaltitle | Autonomous Agents and Multi-Agent Systems | en |
| dc.identifier.startpage | 1 | en |
| dc.identifier.uri | https://hdl.handle.net/10468/13522 | |
| dc.identifier.volume | 36 | en |
| dc.language.iso | en | en |
| dc.publisher | Springer | en |
| dc.relation.project | info:eu-repo/grantAgreement/SFI/SFI Research Centres/12/RC/2289/IE/INSIGHT - Irelands Big Data and Analytics Research Centre/ | en |
| dc.relation.uri | https://doi.org/10.1007/s10458-022-09572-8 | |
| dc.rights | © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made... | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | Possibly strictly optimal alternatives | en |
| dc.subject | Multi-criteria decision making | en |
| dc.subject | Multicriteria utility theory | en |
| dc.subject | Multi-objective decision support systems | en |
| dc.subject | Preference elicitation | en |
| dc.title | Minimality and comparison of sets of multi-attribute vectors | en |
| dc.type | Article (peer-reviewed) | en |
