Pareto-optimality and qualitative aggregation structures

Didier Dubois (1)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

Among non-additive, ordinal methods for criteria aggregation and decision under uncertainty, some have their origin in an approach first proposed by Bellman and Zadeh in 1970. Instead of maximising sums of degrees of satisfaction pertaining to various criteria, they proposed to maximise the minimum of such degrees, thus leading to a calculus of fuzzy constraints, for instance [1]. Unfortunately, rankings of solutions using such qualitative techniques are usually rather coarse. This drawback seems to undermine the merits of qualitative techniques, whose appeal is to obviate the need for quantifying utility functions. Worse, some of the generally not unique maximin optimal solutions, may fail to be Pareto Optimal. Besides, other well-behaved aggregation operations on finite ordinal scales seem to be constant on significant subsets of their domains [4], which make these aggregations not so attactive in practice. This work starts an investigation of some limitations of finitely-scaled methods for criteria aggregation, and a search for remedies to these limitations.

Domaines: Intelligence artificielle [cs.AI]

Didier Dubois. Pareto-optimality and qualitative aggregation structures. 22nd Linz seminar on Fuzzy Sets Theory : Valued Relations and Capacities in decision theory (LINZ 2001), Feb 2001, Linz, Austria. ⟨hal-03463131⟩