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

机译：模糊理论在曲面插补和曲面变形分析中的应用

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摘要

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.
机译：从数学的角度来看，可以将测量值视为模糊值。他们的不确定性是由于对“绝对真理”的不完全了解所致。在这种情况下，只能提出值范围。从这个意义上说，测量结果为进一步研究提供了一些“原始材料”。可以将它们插值到网格上并通过分析表面进行近似。另外，可能有必要基于网格获得一些更高阶的表面特性。显然，从不确定的测量得出的每个特性也是不确定的。在本文中，我们讨论了一种将测量的不确定性传播（所谓的模糊传播）建模为导出的微分几何特征的方法及其应用。

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