Guaranteed fuzzy function approximation using interval analysis

Vincent Vigneron (1) , Hichem Maaref (1) , Claude Barret (1) , Riadh Kallel (2, 3)

1 LSC - Laboratoire Systèmes Complexes
2 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques
3 SAMOS - Statistique Appliquée et MOdélisation Stochastique

Usually, fuzzy systems approximate functions by covering their graphs with fuzzy patches in the input-output state space. Each fuzzy rule defines a fuzzy patch. The approximation increases in accuracy as the fuzzy patches increase in number and decrease in size. In this paper, we propose an other approach for fuzzy approximation in which fhe estimation of the fuzzy parameters from experimental data is viewed as one of set invertion, which is solved in an approximate but guaranteed way with the tools on interval analysis. Is is, for instance, possible to characterize the set of all parameters vectors that are consistent with the data in the sense that the errors between the data and corresponding model outputs fall within known prior bounds. Any prior knowldge that can be expressed as a series of inequalities to be satisfied by the parameters can be taken into account. The purpose of this paper is to briefly present some results recently obtained in the field of fuzzy approximation.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Vincent Vigneron, Hichem Maaref, Claude Barret, Riadh Kallel. Guaranteed fuzzy function approximation using interval analysis. IEEE International Conference on Systems, Man and Cybernetics, Oct 2002, Hammamet, Tunisia. pp.00. ⟨hal-00233009⟩