Finding Soft Relations in Granular Information Hierarchies

Abstract

When faced with large volumes of information, it is natural to adopt a granular approach by grouping together related items. Frequently, this is extended to a granular hierarchy, with progressively finer division as one moves down the hierarchy. The widespread use of hierarchical organisation shows that this is a natural approach for humans, as is the use of fuzzy granules rather than inflexible category specifications. Care is needed when information systems use fuzzy sets in this way - they 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 granules. 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.