Discovering reduct rules from N-indiscernibility objects in rough sets

In rough set theory, the reduct is defined as a minimal set of attributes that partitions the tuple space and is used to perform the classification to achieve the equivalent result as using the whole set of attributes in a decision table. This paper is to present an incremental partitioning algorithm to discover decision rules with minimal set of attributes from rough set data. Besides developing the heuristic algorithm for discovering rules in rough sets, this paper analyzes the time complexity of the algorithm, and presents the lower bound, upper bound, and average cost of the algorithm. This paper also finds the characteristics that the lower bound and upper bound of the algorithm presented in this paper are closely related to cardinalities of attribute values from set of attributes involved in a decision table.