With the rapid development of the information science,the vast amounts of static and dynamic data can be collected every day.The existing analytical tools and algorithms have been facing with serious challenges increasingly when they analysed and processed for such a large datum.The Pawlak rough sets theory is a mathematical theory for dealing with uncertain and fuzzy knowledge,which provides an effective method for data analysis.However,the classical Pawlak rough sets is based on equivalence relations,which can't deal with data other than incomplete discrete data effectively,and the dynamic data processing also suffers from significant shortcomings.Therefore,generalizing Pawlak rough sets is one of the main issues.And the covering rough sets model is one of the most important generalizations.In this paper,under the maximum description,the coverage probability rough sets,covering rough sets theory and its reduction are presented.In addition,the computing of rough sets upon matrix method and the incremental updating method are discussed in the dynamic covering information systems and the dynamic incomplete information systems respectively.The main contribution of this paper is present as follows:(1)By using the minimal neighbourhood of the maximal description sets,a type of covering probability rough sets is proposed,and some important properties of it are investigated.Furthermore,based on the uncertainty of covering probability rough sets,the fuzziness of the covering probability rough sets is given by applying the classical fuzzy entropy,which enrich the covering rough sets theory.(2)A type of covering rough sets based on the maximal description is discussed in this paper firstly,and some basic properties are given.Then,a necessary and sufficient condition for different coverings generating the same covering approximation operators and the reduction of a covering are provided.Finally,we construct a discernibility matrix to give judgment theorems for the reduction and coreof the covering information systems,thus providing a method for the reduction of covering information systems.(3)To calculate the upper and low approximations effectively and quickly under the number of coverings variations in the covering information systems,a relation matrix is defined by the characteristic function.Then the calculation for the approximations,positive,boundary and negative regions intuitively by the relation matrix are put forward.Furthermore,the approaches for incremental updating approximations of sets are discussed by the relation matrix.Then,the properties of the relation matrix are investigated,and the relationship between the relation matrix and the uncertainty of rough sets is discussed.The results enrich and improve the covering rough set based dynamic learning theory and provide a method for dynamic knowledge update based in covering information systems.(4)In complete information systems,the computing of rough sets upon matrix method is proposed under the dominance relation,which can be applied to the following two cases respectively: the same number of attributes but changes in the number of objects,and changes in the number of attributes but the same number of objects. |