Spline interpolation between hyperspaces of convex or fuzzy sets

We consider the interpolation problem for functions whose range and whose domain both consist of convex or fuzzy subsets of a real Euclidean space. This problem arises in fuzzy controlling, namely when the functional dependence between two fuzzy vectors is known only for finitely many cases. To have a criterion for an appropriate choice of an interpolation function, we generalise the well-known idea from spline interpolation: the function should be "as smooth as possible".

• Type: Journal
• Year: 2006
• Where: FSS
• Authors: Thomas Vetterlein
• Keywords: FSS 2006, Interpolation, Interpolation Problem, Real Euclidean Space