An application of the fuzzy theory in surface interpolation and surface deformation analysis

Authors:
Olga Waelder
Affiliations:
Institute of Cartography, Technical University of Dresden, Mommsenstrasse 13, 01062 Dresden, Germany
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

Measurements can be considered to be fuzzy values from mathematical point of view. Their uncertainty is caused by an incomplete knowledge of ''absolute truth''. Only value ranges can be proposed in this case. In this sense measurements provide some ''raw material'' for further researches. They can be interpolated over a grid and approximated by an analytical surface. Additionally, it can be necessary to obtain some surface characteristics of higher order based on the grid. It is clear that each characteristic which is derived from uncertain measurements is also uncertain. In this paper we discuss a method of modelling the propagation of the uncertainty (the so-called fuzzy propagation) of measurements to derived differential-geometric characteristics and its application.