Generating non-redundant bases of data tables with fuzzy attributes by reduction of complete sets of fuzzy attribute implications

Presented is indirect method for generating non-redundant bases of data tables with fuzzy attributes. Fuzzy attribute implications (FAIs) are formulas describing particular dependencies of attributes in data. Non-redundant bases are minimal sets of FAIs describing all FAIs which are true (valid) in given data. Our method is based on reducing sets of FAIs describing all dependencies which can contain redundant FAIs. By removing the redundant FAIs we obtain this way non-redundant bases. We show that the procedure can generate smaller bases than previous methods. We present new theoretical results, the algorithm, its complexity analysis, and statistics demonstrating efficiency of the method.