Variable Precision Of Generalized Rough Set Model

Rough set theory, proposed by Pawlak in the early 1980s, is a mathematical theory for reasoning about data. The main idea of the theory is to approximate inexact, uncertain concepts by using of available knowledge or information. Since 1990s, it has attracted much attention of researchers around the world, and has been well developed and applied. Now, this theory has become a flash point in the research area of computer science and information science.Variable precision rough set is an extension of Pawlak-rough set theory, it relaxes the restricted defining of approximation boundary in standard rough set theory and improves the anti-interference ability and prediction ability to the new data of rough set model by setting up threshold value parameter (0.5<β≤1). Nick Cercone, Wojciech Ziarko have already utilized this model to predict water demand for a medium-sized city in North America successfully.This paper begins with Pawlak-rough set and variable precision rough set theory, then introduces three main parts of the authors work. They are:(1) It analyses the relation between β value and quality of classification in variable precision rough set, and provides two kinds of algorithms to confirm the range of β threshold value by the r threshold value of quality of classification.(2) In the reference [54], several kinds of attribute reduction have been put forward; we know provide two kinds of new discernibility matrix of flower and upper distribution reduction, which are equivalence to discernibility matrix in the reference[54].(3)It discusses serial, generalized approximation operators over different universes and the variable precision rough set model over different universes then gets the variable precision generalized rough set model.