Interpolation that leads to the narrowest intervals and its application to expert systems and intelligent control (Q1904317)

Interpolation problems \(y_i= f(x_i)\), \(x_i\in \mathbb{R}^n\) for \(i= 1,\dots, N\) are considered, where only bounds of the values \(x_i\) and \(y_i\) are known. Since the solution functions \(f\) are, in general, not defined uniquely. It is suggested to choose such functions, which have an uncertainty width as small as possible. A few simple examples for the cases \(n= 1, 2\) are discussed. Some applications to expert systems in situations where the knowledge of the experts cannot be expressed by precise values, are given.