The concept of reducts in pawlak three-step rough set analysis

Rough set approaches to data analysis involve removing redundant attributes, redundant attribute-value pairs, and redundant rules in order to obtain a minimal set of simple and general rules. Pawlak arranges these tasks into a three-step sequential process based on a central notion of reducts. However, reducts used in different steps are defined and formulated differently. Such an inconsistency in formulation may unnecessarily affect the elegancy of the approach. Therefore, this paper introduces a generic definition of reducts of a set, uniformly defines various reducts used in rough set analysis, and examines several mathematically equivalent, but differently formulated, definitions of reducts. Each definition captures a different aspect of a reduct and their integration provides new insights.