Applications of fuzzy theory to spatially resolved analysis of solids

Abstract Fuzzy theory is applied to compare response profiles and surfaces in spatially resolved materials analysis. Different options are proposed for the type of membership function, the definition of spreads, and specially defined similarity values. These similarity values are expressed analytically, thus permitting the development of a fast computer program. A special normalization in the calculation of the similarity values allows a set of distributions to be arranged hierarchically by clustering; the distributions are displayed as a dendrogram. The fuzzy techniques are also used to judge the homogeneity of a solid with respect to the distribution of chemical elements on its surface. Depth profiles from Rutherford back-scattering spectrometry and results of surface analysis by spark-source mass spectrometry are investigated as practical examples.