Measuring change in fuzzy concept lattices

The quantity of unstructured and semi-structured data available is growing rapidly. Adding structure to such data (by means of ontologies and tag-based taxonomic classifications) is potentially a very productive approach, which can lead to additional knowledge (e.g. by monitoring association and other relations between classes) as well as enabling more effective use and re-use of online knowledge. Formal concept analysis (and fuzzy formal concept analysis) enables us to identify hierarchical structure arising from similarities in attribute values, giving a starting point for an ontology. However, it is often difficult to determine the “best” attributes to use. Furthermore, in an environment where source data is updated, this data-driven approach may lead to concept lattices which vary in structure. In this paper, we describe a novel way of measuring the distance between concept lattices. The method can be applied to comparison of lattices derived from the same set of objects using different attributes or to different sets of objects categorised by the same attributes. Simple examples are used to illustrate the idea.