Research And Application On Some Issues Of Rough Set Theory

Rough set theory is a new mathematical tool to deal with imperfectness, uncertainty and vagueness. Firstly, the basic concepts and present develoments of rough set theory are introduced. In the following, five regions including two operators, uncertain measure method, attribute reduction, attribute subdivision and parameter reduction of soft set based on rough set theory are mainly discussed. The contributions of this thesis are as follows:(1)Two new operators are redefined to express the essential characters of certain increment operator and uncertain decrement operator. It is proved theoretically that the two new operators are equivalent to the original two operators. Then the multiple certain increment operator and multiple uncertain decrement operator are introduced based on two new operators, and these properties are discussed.(2)The information entropy and conditional entropy based on general relation are introduced. And it is proved that the information entropy based on general relation is the extension of information entropy based on equivalent relation and compatible relation. Furthermore, the conditional entropy based on general relation is equal to the weighted sums for components of conditional entropy based on equivalent relation. At last, the conditional entropy and mutual information entropy based on generalized covering are introduced and these properties are discussed.(3)Two important parameters are improved by the difference between maximum and minimum of objective values, and a new adaptive harmony search algorithm is proposed. The new algorithm is compared with three algorithms and tested by five test functions. The simulation results show that AHS has the strong robustness and can escape the local minimum. Then attribute reduction method based on AHS is constructed by introduce the attribute significance. And the test results show the validity and feasibility of this method.(4)The normal parameter reduction is introduced by the indiscemibility relation of rough set theory. And a necessary condition of normal parameter reduction is given by the parameter importance degree of soft set. Then the parameter reduction algorithm is proposed. Finally, a fuzzy soft set approach to decision making problem is discussed. A counter example is introduced and the correction is made for deficiency of the existing approach.(5)The effectively equivalent class subdivision and effective set subdivision are introduced. Then the relationships between the degrees of attribute subdivision and the upper approximation, lower approximation, accuracy of approximate classification, quality of approximate classification, decision-making rule, relative reduction and necessity of attributes are discussed.