Local attribute reductions for decision tables

- Give an lth decision class lower approximation reduction algorithm.
- Give an lth decision class reduction algorithm for decision tables.
- Give an lth decision class β-reduction algorithm for decision tables.
- Study the relationship between lth 1-reduction and positive region reduction.

Attribute reduction is among the most important areas of research in rough sets. This paper investigates the types of local attribute reduction for decision tables. We propose the concepts of lth decision class lower approximation reduction, lth decision class reduction, and lth decision class β-reduction for decision tables, and provide their corresponding reduction algorithms via discernibility matrices. We also establish the relationship between positive-region reduction and the lth decision class β-reduction, and report a case study using the University of California-Irvine dataset to verify the theoretical results.