Interpolation of fuzzy data: Analytical approach and overview

Irina Perfilieva (1) , Didier Dubois (2, 3) , Henri Prade (2) , Francesc Esteva (4) , Lluis Godo (4) , Petra Hodáková (1)

1 Ostravská univerzita / University of Ostrava
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 QUB - Queen's University [Belfast]
4 IIIA / CSIC - Artificial Intelligence Research Institute / Spanish Scientific Research Council

We propose a general framework for the interpolation problem. Our framework stems from the classical elaboration of the problem. We introduce the notion of an interpolating fuzzy function and show how this function can be characterized. We examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically. We also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches.

Mots clés: Fuzzy function; Fuzzy space; Similarity Interpolation of fuzzy data; Interpolating fuzzy function

Domaines: Intelligence artificielle [cs.AI]

Irina Perfilieva, Didier Dubois, Henri Prade, Francesc Esteva, Lluis Godo, et al.. Interpolation of fuzzy data: Analytical approach and overview. Fuzzy Sets and Systems, 2012, Part of special issue: Fuzzy Set Theory - Where Do We Stand and Where Do We Go?, 192, pp.134-158. ⟨10.1016/j.fss.2010.08.005⟩. ⟨hal-03344966⟩