A FUZZY LAGRANGE INTERPOLATION THEOREM

The following problem was posed by L.A. Zadeh: "Suppose we are given n + 1 points x0, ..., xn in R, and for each of these points a 'fuzzy value' in R, rather than a crisp one. Is it then possible to construct some function on R with range also a collection of 'fuzzy values'; which coincides, on the given n + a points, with the given 'fuzzy values'; and which fulfills some natural 'smoothness' condition?". In this paper we shall present a solution to this problem, based on the fundamental and well-known polynomial interpolation theorm of Lagrange. © 1990.