Fuzzy rough sets with hierarchical quantitative attributes

Machine learning can extract desired knowledge and ease the development bottleneck in building expert systems. Among the proposed approaches, deriving classification rules from training examples is the most common. Given a set of examples, a learning program tries to induce rules that describe each class. The rough-set theory has served as a good mathematical tool for dealing with data classification problems. It adopts the concept of equivalence classes to partition training instances according to some criteria. In the past, we thus proposed a fuzzy-rough approach to produce a set of certain and possible rules from quantitative data. Attributes are, however, usually organized into hierarchy in real applications. This paper thus extends our previous approach to deal with the problem of producing a set of cross-level maximally general fuzzy certain and possible rules from examples with hierarchical and quantitative attributes. The proposed approach combines the rough-set theory and the fuzzy-set theory to learn. It is more complex than learning from single-level values, but may derive more general knowledge from data. Fuzzy boundary approximations, instead of upper approximations, are used to find possible rules, thus reducing some subsumption checking. Some pruning heuristics are adopted in the proposed algorithm to avoid unnecessary search. A simple example is also given to illustrate the proposed approach.