Research On Uncertainty Of Rough Sets Of Approximation Sets And Its Application In Image Segmentation

With the development of network technology and information technology, modern society has entered the era of big data. A lot of knowledge that have hidden behind the data urgent need to be explored and acquired. Meanwhile, the uncertainty of the world has created a lot of various and complex data. Facing with the growing data, human eager to discover more essential content and also need to find more effective information processing tools and methods for deal with uncertain information.As a classical mathematical tool for data mining and knowledge discover, rough set theory has become an important theory to deal with uncertain or imprecise data in recent years. Rough set theory can construct upper/lower approximation set by equivalence relation, and it is also regarded to describe the uncertain information of the target concept by a precise method approximately. Rough set provides the theoretical basis for solving the problem of uncertainty and it has been applied to many fields widely and has achieved remarkable results. But there are still some problems worthy of further research, such as, it is lack of precise descriptions for the boundary region, the optimal approximation set is ambiguous and there are many constraints about the image segmentation method based on the traditional rough set theory. According to the above problems, the following contents are researched in this paper.Firstly, the approximation set model is introduced to solve the problem the boundary region of classical rough set model, and the method of knowledge reduction of approximation set is analyzed and discussed from the view of algebra and information. From the view of algebra, the concept of distribution reduction of approximation set model and its identification matrix reduction method are proposed, and the completeness of the reduction method is proved theoretically. Based on the information theory, the concept of information entropy of approximation set and the algorithm of attribute reduction based on conditional information entropy of approximation set are proposed.Secondly, the concept of fuzzy entropy of approximation set is proposed, and the uncertainty measurement method is proposed by analyzing the change rules of fuzzy entropy with changing knowledge granules. Theoretically, uncertainty measurement model of approximate set is consistent with human basic cognitive model. The experiment results show that the knowledge acquisition method based approximation set is feasible and effective, and these researches promote the development of rough set theory.Finally, in order to slove the limitation problem of the image segmentation method based on the classical rough set theory, the approximation set model is introduced. It uses adaptive particle method to obtain the optimal granularity of the image, and the upper approximation set and lower approximate set of target and background are constructed. Then the boundary region is described accurately by approximation theory. And the particle swarm algorithm is used to calculate maximum rough entropy of approximation set. Then the optimal threshold of image segmentation is obtained finally. The experimental results show that the proposed method is feasible and effective, and it can promote the development and application of approximate set theory.