A general approach to the measurement of change in fuzzy concept lattices

The quantity of unstructured and semi-structured data available is growing rapidly. Adding structure to such data by grouping similar items into fuzzy categories (or granules) can be a productive approach, and can lead to additional knowledge (e.g. by monitoring association and other relations between classes). Formal concept analysis (and fuzzy formal concept analysis) enables us to identify hierarchical structure arising from similarities in attribute values. However, in an environment where source data is updated, this data-driven approach may lead to concept lattices whose structure varies over time (that is, the number of concepts and their relation to each other may change significantly as updates are processed). 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. We prove that the proposed method is a distance metric and illustrate its use by means of examples.