A CURVE SMOOTHING METHOD BY USING FUZZY-SETS

For a set of points {(t(n),x(n)) \ n = 1,2,3,...} in the plane, a fuzz y set which is the Cartesian product of a B-spline B-n(t) and a triang ular function T-j(x) is assigned to each of the points. Another fuzzy set B-n(t) x I(x), where I(x) is the constant function with value 1 is used to form the intersection with each of B-j x T-k corresponding to (t(j),x(j)). Then we take the union of the resulting fuzzy sets and a pply 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. (C) 1998 Elsevier Science B.V . All rights reserved.