Narrow Results

Comparing frequency distributions of experimental data is a routine engineering task in the semiconductor industry. The existing statistical approaches to the problem suffer from several limitations, which can be partially overcome via the time-consuming visual examination of frequency histograms by an experienced process engineer. This paper presents a novel, fuzzy-based method for automating the cognitive process of comparing frequency histograms. We use the evolving approach of type-2 fuzzy logic to utilize the domain knowledge of human experts. The proposed method is evaluated on the actual results of an engineering experiment, where it is shown to represent the experts' perception of the visualized data more accurately than a wide range of statistical tests. We also outline the potential directions for integrating the perception-based approach with other methods of data visualization and data mining.

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.