Representing Numeric Values in Concept Lattices.
John L. Pfaltz · 2007
Abstract. Formal Concept Analysis is based on the occurrence of symbolic attributes in individual objects, or observations. But, when the attribute is numeric, treatment has been awkward. In this paper, we show how one can derive logical implications in which the atoms can be not only boolean symbolic attributes, but also ordinal inequalities, such as x ≤ 9. This extension to ordinal values is new. It employs the fact that orderings are antimatroid closure spaces. 1 Extending Formal Concept Analysis Formal Concept Analysis (FCA), which was initially developed by Rudolf Wille and Bernhard Ganter [3], provides a superb way of describing “concepts”, that is closed sets of attributes, or properties, within a context of occurrences, or objects. One can regard the concept as a closed set of objects with common attributes. Frequently clusters of these concepts, together with their structure, stand out with vivid clarity. However, two unresolved problems are often encountered. First, when concept lattices become large, it is hard to discern or describe significant clusters of related concepts. Gregor Snelting used formal concept analysis to analyze legacy code [6, 14]. 1 Snelting’s goal was to reconstruct the overall system structure by determining which variables (attributes or columns)