Computing version spaces in the qualitative approach to multicriteria decision aid

Miguel Couceiro 1 Miklos Maróti 2 Tamas Waldhauser 2 Lazlo Zadori 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : We consider a lattice-based model in multiattribute decision making , where preferences are represented by global utility functions that evaluate alternatives in a lattice structure (which can account for situations of indifference as well as of incomparability). Essentially, this evaluation is obtained by first encoding each of the attributes (nominal, qualitative, numeric, etc.) of each alternative into a distributive lattice, and then aggregating such values by lattice functions. We formulate version spaces within this model (global preferences consistent with empirical data) as solutions of an interpolation problem and present their complete descriptions accordingly. Moreover, we consider the computational complexity of this interpolation problem, and show that up to 3 attributes it is solvable in polynomial time, whereas it is NP complete over more than 3 attributes. Our results are then illustrated with a concrete example , namely, a recommender system for employees based on their psychological records throughout a year.
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Miguel Couceiro, Miklos Maróti, Tamas Waldhauser, Lazlo Zadori. Computing version spaces in the qualitative approach to multicriteria decision aid. International Journal of Foundations of Computer Science, World Scientific Publishing, 2019, 30 (2), pp.333-353. ⟨hal-01404590⟩

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