Imprecise specification of ill-known functions using gradual rules

Functional laws may be known only at a finite number of points, and then the function is completed by interpolation techniques obeying some smoothness conditions. We rather propose here to specify constraints by means of gradual rules for delimiting areas where the function may lie between known points. The more general case where the known points of the function are imprecisely located is also dealt with. The use of gradual rules for expressing constraints on the closeness with respect to reference points leads to interpolation graphs that are imprecise but still crisp. We thus propose a refinement of the rule-based representation that enables the handling of fuzzy interpolation graphs.