Abstract: A method is disclosed for for computing clusters, relationships amongst clusters, and association rules from data at various levels of significance. First the clusters are found via a dual-approximation method followed by Boolean minimization. Then a customized multiplicative neural network which uses a special kind of fuzzy logic is constructed from the association rules. This particular fuzzy-logic shows how make arithmetic equal to fuzzy-logic. Other types of fuzzy logics appropriate for this datamining tool are described. This particular method of clustering is multiplicative, resembling “dimensional analysis” of physics and engineering in contrast to the linear methods such as principal component analysis (PCA). The complete set of association rules is constructed from the data automatically. Then 2-dimensional and 3-dimensional visualization and visual-datamining tools are constructed.