A Mass Assignment Approach to Granular Association Rules for Multiple Taxonomies

The use of hierarchical taxonomies to organise information (or sets of objects) is a common approach for the semantic web and elsewhere, and is based on progressively finer granulations of objects. In many cases, seemingly crisp granulation disguises the fact that categories are based on loosely defined concepts which are better modelled by allowing graded membership. A related problem arises when different taxonomies are used, with different structures, as the integration process may also lead to fuzzy categories. Care is needed when information systems use fuzzy sets to model graded membership in categories the fuzzy sets are not disjunctive possibility distributions, but must be interpreted conjunctively. We clarify this distinction and show how an extended mass assignment framework can be used to extract relations between fuzzy categories. These relations are association rules and are useful when integrating multiple information sources categorised according to different hierarchies. Our association rules do not suffer from problems associated with use of fuzzy cardinalities. An example of discovering associated film genres is given.