The Attribute Reductions Based on Indiscernibility and Discernibility Relations

Knowledge reduction and knowledge discovery in information systems are important topics of rough set theory. Based on the relative indiscernibility relation and relative discernibility relation of decision systems, the notions of lambda reduction and mu reduction are proposed. The judgement theorems for lambda consistent set and mu consistent set are provided. The discernibility matrices with respect to lambda reduction and mu reduction are obtained and the reduction approaches are presented. Furthermore, the relationships among lambda reduction, mu reduction, positive region reduction and assignment reduction are analyzed.