Constructing consistent fuzzy surfaces from fuzzy data

Authors:
Weldon A. Lodwick;Jorge Santos
Affiliations:
Department of Mathematics, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO;Department of Mathematics, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO
Venue:
Fuzzy Sets and Systems - Theme: Modeling and learning
Year:
2003

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Abstract

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 α-cut values of the fuzzy data are contained within the surfaces generated by lower α-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.