Applications of fuzzy sets in curve fitting

This paper presents several methods for functional approximation with variable-knot variable-degree splines, with variable-knot first order splines, which are relatively easy to find, as the intermediate input. By means of a fuzzy characteristic function determining how “sharp” the angle at each knot is (the higher the polynomial degree, the “sharper” its first order spline approximation bends), we can decide whether we can group certain adjacent segments together to be approximated by a single higher order polynomial segment. Some simulation experiments have also been done.