Several Types Of Covering Rough Set Models Over Two Universes

Rough set theory is a new tool of mathematical analysis for analyzing and deal-ing with imprecise, inconsistent and incomplete information which is also totally called "three no" information. And it is successfully used in many fields. Covering rough set is a common promotion model of the classical rough set. It has a great application prospect in the field of knowledge discovery; The granular computing theory is used to deal with inconsistent and un-reliable knowledge, but both of them have limitations in solving the practical problems. Based on the rough set, this paper establishes several multi-granularity covering rough set models on two universes from the respects of universe and granular computing. And the specific work is as follows:Firstly, based on the covering rough set model over two universes, the classification rate of covering error of two universes is defined, and the variable precision covering rough set model over two universes is proposed by means of the error parameter β. Meanwhile, some properties and theorems are discussed. It is proved that the model can narrow the boundary region of the approximate space and the approximate results become more accurate by using examples. Then based on the practical need of medical treatment, this paper combines the multi-granularity rough set and covering rough set model over two universes, and proposes two classes multi-granularity covering rough set model over two universes. Then it discusses relat- ed properties and theorems separately, and use medical instance to illustrate the practicability of the model. Lastly, between the upper and lower approximations of multi-granularity cov-ering rough set model over two universes, it proposes two types of multi-granularity covering rough set model including variable precision of optimism and pessimism over two universes by means of classification of error, and gives a comparative analysis to them and multi-granularity covering rough set model over two universes to demonstrate its superiority and promote the predecessors’work.