Theory and applications of granular labelled partitions in multi-scale decision tables

Abstract Granular computing and acquisition of if-then rules are two basic issues in knowledge representation and data mining. A formal approach to granular computing with multi-scale data measured at different levels of granulations is proposed in this paper. The concept of labelled blocks determined by a surjective function is first introduced. Lower and upper label-block approximations of sets are then defined. Multi-scale granular labelled partitions and multi-scale decision granular labelled partitions as well as their derived rough set approximations are further formulated to analyze hierarchically structured data. Finally, the concept of multi-scale information tables in the context of rough set is proposed and the unravelling of decision rules at different scales in multi-scale decision tables is discussed.

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