Highly scalable rough set reducts generation

Rough set theory is used to represent, analyze, and manipulate knowledge in information or decision tables. To remove superfluous attributes without changing the original knowledge, reduction is must in rough set. This paper introduces the pseudo decision table to replace the original table and two algorithms, RGonCRS and SRGonCRS, based on the current rules size, CRS, are presented to generate all reducts which ensure the lower approximation for each instance in the table with a minimal number of attributes. RGonCRS finds reducts by merging candidate attributes and SRGonCRS is a scalable version of RGonCRS which generates reducts for very large tables. Propositions and proofs are presented in this paper. Empirical tests are shown for RGonCRS using simulated information tables and UCI benchmark datasets and a preliminary test is generated for SRGonCRS. Results are compared to the well-known rough set software - Rough Set Exploration System (RSES).