The Study Of Roughness Of Non-classical Logic Algebras

Rough set theory is a new theory of data analysis, it was first put forward by Poland scientist Z.Pawlak. At present it has been developed to be a new mathematical tool to deal with vagueness and uncertainty. It has been applied to many areas successfully including machine learning, pattern recognition, decision support, data mining and process control.The successful application of rough set theory to knowledge discovery in database promotes the study of rough set theory. Algebraic analysis of rough set is one of the most active branches in the research of rough set theory. If the relation between rough algebra and logic algebra was given, we could research the rough logic using the conclusion of logic system and study the structure of rough set.This paper studies the relationship between rough set algebra and non-classical logic algebra, and applys rough set theory to MV-algebra and R₀-algebra. The roughness of filter is studied. The main conclusions are as following:1. Based on the description of the pairs () of rough set, we define some basic operators on the approximation pairs and construct some rough algebras. Some general algebras structure were selected to describle the pairs of rough set, for exarnple, residuated lattice, BL-algebra,MV-algebra and R₀-algebra.2. In non-classical logic algebras filter is a basic structure and it plays an important role in the research of relative logic system. In this paper, the notions of upper and lower rough filters were introduced, with their basic properties being discussed.3. For homomorphism of R₀-algebra, we introduce the notion of dual kernel and have proved that each dual kernel is a filter.