The Research Of Rough Set Theory And Granular Computing Crossing Problems

Rough set theory is mathematical theory to analytically solving incomplete, imprecise and inconsistent information and data. The solving process is without additional information. Granular computing is an methodology about the way of problem solving and thinking mode. Rough set theory is regarded as one of important models about granular computing. There are many commonalities and differences between the theories. That the two theories are studied is to expand rough set theory with the idea of granular computing, and also research granular deeper and comprehensively.Firstly, through analyzing the simulation and differences between granular computing and rough set, the binary granule-based granular matrix and its AND operation are studied, and tolerance granular matrix and covering granular matrix are proposed, its properties are also presented. And then, covering granular matrix based rough set' property and ideology are explored and deepened. Secondly, the algorithms of attribute reduction and rules mining are analyzed to concentrated for raising efficiency. In the research of attribute reduction, the ideology of dynamical granular matrix quotient is presented and used to realized attribute reduction. According to the specialty of practical life, the algorithm of attribute reduction based on tolerance attribute reduction is put forward. Through the research of attribute reduction, data preprocessing would be better. At last, linear granular structure based on Flag-bit granular matrix is proposed to solve rules mining. All innovative points in this paper are as follows:(1)In the field of granule model in granular computing, both tolerance granular matrix and covering granular matrix based on granular matrix are proposed. And both approximation representation are defined. An novel covering rough set--the rough set based on covering granular matrix is put forward. The properties and cover reduction of novel covering rough set are studied deeply and proved.(2)Algorithm of attribute reduction. Algorithm of attribute reduction about decision table and incomplete information systems are studied. In the research of attribute reduction about decision table, pawlak granular matrix-based granular matrix quotient and ideology of dynamical granular matrix quotient are proposed. Algorithm of attribute reduction based on dynamical granular matrix quotient is presented. In the incomplete information systems, tolerance granular matrix and its AND operation based on tolerance relation are defined. And algorithm of attribute reduction about incomplete information systems based on tolerance granular matrix is proposed. All novel algorithms of attribute reduction based on granular computing are efficiency.(3)Algorithm of rules mining. At first, the linear granular structure based on flag-bit granular matrix is constructed. Then, algorithm of rules mining based on linear granular structure is presented and proved.