Constructing consistent fuzzy surfaces from fuzzy data

Given fuzzy data describing a three-dimensional entity such as terrain, we develop methods to construct surfaces that are consistent with the uncertainty in the data and surface model itself. In particular, surfaces generated from higher a-cut values of the fuzzy data are contained within the surfaces generated by lower a-cut values of the fuzzy data. Moreover, the smoothness and continuity conditions of the surface generating method is maintained by each level surface. We demonstrate the ideas by developing two- and three-dimensional surfaces from fuzzy data for cubic splines and digital terrain models generated from triangulation. (C) 2002 Elsevier Science B.V. All rights reserved.