Geometry and Logic in Pattern Classifiers

In this study, we discuss an important synergy emerging between the geometric representation of data and fuzzy logic in pattern classification. Next we show how this synergy is made operational and translates into a coherent architecture of a classifier. The crux of the proposed topology lies in a collection of simple linear classifiers (perceptrons) being combined into a logically coherent topology. In a nutshell: perceptrons come with simple geometrical interpretation while processing based on fuzzy operators (AND and OR logic units-fuzzy neurons) results in highly transparent and interpretable results. When combined together (forming a fuzzy adaptive logic network), they give rise to the computing construct that retains the advantages (processing and interpretability) of these two paradigms of information processing. We discuss a comprehensive development environment of adaptive logic networks and show their application to several classification problems.