A fuzzy Lagrange interpolation theorem. (English) Zbl 0685.41005

Summary: The following problem was posed by L. A. Zadeh: “Suppose we are given \(n+1\) points \(x_ 0,...,x_ n\) in \({\mathbb{R}}\), and for each of these points a ‘fuzzy value’ in \({\mathbb{R}}\), rather than a crisp one. Is it then possible to construct some function on \({\mathbb{R}}\) with range also a collection of ‘fuzzy values’; which coincides, on the given \(n+1\) points, with the given ‘fuzzy values’; and which fulfills some natural ‘smoothness’ conditions?” In this paper we present a solution to this problem, based on the fundamental and well-known polynomial interpolation theorem of Lagrange.


41A05 Interpolation in approximation theory
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