Imprecise specification of ill-known functions using gradual rules (2002)
Résumé
Numerical functions modelling systems may be known only at a finite number of points, and then have to be completed by means of interpolation techniques obeying some smoothness conditions. In the following, we rather propose to specify constraints, by means of a special type of implication-based fuzzy if ... then rules, called gradual rules, for delimiting areas where the function may range between the known points.The more general case where the known points of the function are imprecisely located is also dealt with. Moreover, the representation can be augmented by using conjunction-based fuzzy rules in order to refine the areas delimited by the gradual rules, when additional data or information are available. An accurate modelling of ill-known functions is thus provided, which acknowledges the existence of known points and can take into account more uncertain data as well.