Fuzzy interpolation and level 2 gradual rules

Sylvie Galichet (1, 2) , Didier Dubois (2) , Henri Prade (2)

1 LISTIC - Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

Functional laws may be known only at a finite number of points, and then the function can be 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. Such an approach results in an imprecise interpolation graph whose shape is controlled by tuning the fuzziness attached to the reference points. However, the graph so-built is still crisp, which means that different possible paths between the interpolation points cannot be distinguished according to their plausibility. The paper discusses a method for introducing membership degrees inside the interpolation graph. The developed formalism relies on the use of weighted nested graphs. It amounts to handling level 2 gradual rules for specifying a family of flexible constraints on the reference points. The proposed approach is compared with the one of extending gradual rules for dealing with type2 fuzzy reference points.

Domaines: Intelligence artificielle [cs.AI]

Sylvie Galichet, Didier Dubois, Henri Prade. Fuzzy interpolation and level 2 gradual rules. 3rd European Society for Fuzzy Logic and Technology Conference (EUSFLAT 2003), European Society for Fuzzy Logic and Technology, Sep 2003, Zittau, Germany. pp.506-511. ⟨hal-00482900⟩