Minimality and comparison of sets of multi-attribute vectors

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Toffano, Federico
Wilson, Nic
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In a decision-making problem, there can be 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. Secondly, we consider how to compare A to another set of alternatives B, where A and B correspond to different initial decision choices. We derive mathematical results that allow different computational techniques for these two problems, using linear programming, and especially, using the extreme points of the epigraph of the utility function.
Toffano, F. and Wilson, N. (2020) 'Minimality and Comparison of Sets of Multi-Attribute Vectors', European Conference on Artificial Intelligence, 29 Aug-02 Sept, in Frontiers in Artificial Intelligence and Applications, Volume 325: ECAI 2020, pp. 913 - 920. doi: 10.3233/FAIA200183