Sur l’apprentissage de capacités pour les intégrales de Sugeno avec des systèmes d’équations relationnelles floues

In this article, we introduce a method for learning a capacity underlying a Sugeno integral according to training data based on systems of fuzzy relational equations. To the training data, we associate two systems of equations : a max?min system and a min?max system. By solving these two systems (in the case that they are consistent) using Sanchez’s results, we show that we can directly obtain the extremal capacities  representing the training data. By reducing the max?min (resp. min?max) system of equations to subsets of criteria of cardinality less than or equal to q (resp. of cardinality greater than or equal to n ? q), where n is the number of criteria, we give a sufficient condition for deducing, from its potential greatest solution (resp. its potential lowest solution), a q-maxitive (resp. q-minitive) capacity. Finally, if these two reduced systems of equations are inconsistent, we show how to obtain the greatest approximate q-maxitive capacity and the lowest approximate qminitive capacity, using recent results to handle the inconsistency of systems of fuzzy relational equations