Uncertain Decision-making Problems Based On Rough Set Theory And Applications

Decision depends on knowledge. Rough set is a tool for processing indefinite, imprecise data, which deals with knowledge in terms of classification. Especially, it is very easy to integrate the theory with almost all other soft-computing methods such as neural networks. Integrated systems have the advantage over using a soft computing simply. Under this background, intelligent decision based on rough analysis forms the forefront part of decision science. At the same time, rough set is at us initial stage and many problems that concern are still open. Only the problems are solved, can rough set apply to different domains successfully in the thesis, we study a few important problems in depth. The thesis mainly consists of the following:(1) The discretization of continuous attributes is an important method for compressing data and simplifying analysis. The optimal discretization has been proved to be NP-hard. Some heuristic diseretization algorithms have been used but there exist disadvantages in them. For example, the choice of initial set of cuts is hard to be determined. Based on the rough set theory, we transform the discretization of continuous attributes into 0-1 integer programming, which can be solved successfully by existent software. Furthermore, a genetic algorithm using first and second class of discretization matrix is proposed to compute the optimal discretization.(2) The optimal feature subset selection is also a NP-hard one and there are many limits in previous algorithms. A new heuristic algorithm is presented to solve the difficulty. To decision tables whose number of features is reduced greatly after reduction, the algorithm is illustrated to be effective. Especially, it can give almost all the optimal solutions. Furthermore, the feature selection is changed into an optimization problem and the corresponding models are proposed based on extension theory, which used to be utilized for heuristic algorithms. The models are both solved by existing software or genetic algorithms(GAs) and more understandable.(3) Rough analysis is accomplished in analyzing the pattern existing in decision tables by reduction. Two rule producers æ¡°TIL(information theory based induction learning) and heuristic knowledge elicitation, are designed. As far as complex decision tables are concerned, a decomposition- ii -algorithm is given to lower the analysis difficulty too.