β-Dependent degree for extension of approximate reduction

Knowledge reduction based on rough set theory is an important and core study.At present,there are many types of knowledge reduction in the area of rough sets such as distribution reduction and assignment reduction.When the cardinal number of the universe is large,those methods are limited to computer the reductions of information system.Based on variable precision rough set and the whole certainty measure of decision system,a new method is presented to construct the β-plus positive region and defined β-plus dependent degree.The whole maximal certainty measure of decision system which has the error of classification is obtained by β-plus positive region.A new approximate reduction method is developed based on β-plus dependent degree which extends the approximate reduction of variable precision rough set.The examples and simulation results illustrate the efficiency of this method.