Proposal for a New Reduct Method for Decision Tables and an Improved STRIM

Rough Sets theory is widely used as a method for estimating and/or inducing the knowledge structure of if-then rules from a decision table after a reduct of the table. The concept of a reduct is that of constructing a decision table by necessary and sufficient condition attributes to induce the rules. This paper retests the reduct by the conventional methods by the use of simulation datasets after summarizing the reduct briefly and points out several problems of their methods. Then, a new reduct method based on a statistical viewpoint is proposed and confirmed to be valid by applying it to the simulation datasets. The new reduct method is incorporated into STRIM (Statistical Test Rule Induction Method), and plays an effective role for the rule induction. The STRIM including the reduct method is also applied for a UCI dataset and shows to be very useful and effective for estimating if-then rules hidden behind the decision table of interest.