A curve smoothing method by using fuzzy sets

Abstract For a set of points { (t n, X n )ƒ n = 1, 2, 3, …} in the plane, a fuzzy set which is the Cartesian product of a B-splineBn(t) and a triangular function Tj(x) is assigned to each of the points. Another fuzzy set Bn(t) × I(xz), where I(x) is the constant function with value 1 is used to form the intersection with each of Bj × Tk corresponding to (tj, xj). Then we take the union of the resulting fuzzy sets and apply the center of gravity method to obtain a smoothing algorithm. The results of applying this algorithm to a set of A/D converted data and a comparison with the ones by an optimal solution are presented. The natural generalization of this algorithm to arbitrary plane curves or higher-dimensional curves are discussed.