Study On Approaches For Knowledge Uncertainty Measure And Rules Extraction Based On Rough Sets Theory

Ever since Professor Pawlak's proposal of rough sets theory in early 1980s, it has been developed rapidly. As an important mathematic method to deal with knowledge fuzziness and knowledge uncertainty, rough sets theory has been paid more and more attention and widely used in various fields such as data mining, machine learning and pattern recognition with attributes reduction and attributes value reduction being one of the most essential application. Though rough sets theory has obtained many essential achievements, there are still some important issues need to be further resolved, especially the problems reflected in the low-efficiency of knowledge deduction algorithm, which limits the application of rough sets theory. Nowadays, it becomes a common interest for us to find knowledge reduction algorithm with high efficiency.Firstly, the knowledge and measurement of rough set uncertainty have great importance to the application of attributes reduction. However, the existing measurements have some shortcomings, thus to find more reasonable method is a fundamental issue. Secondly, Variable precision parameter is introduced by uncertainty hypothesis, so its estimating method is a major issue worth studying. Meanwhile, it still has a great space in seeking more effective knowledge acquisition method, especially inclusive learning in dynamic data environment, two classes of decision-making system and knowledge acquisition on massive data set. On the basis of these studies, the dissertation here performs a systematical exploration of the problems of measurement of knowledge uncertainty and rules extraction in information system and has got some results. The conclusions made here will have certain effect and have some influence upon the development of rough sets theory and its application in knowledge discovery and relevant fields.The main contributions and innovations in this dissertation are as follows:(1) The uncertainty of knowledge and rough set is discussed and a fuzzy entropy measure method based on boundary region is put forward. It redefines knowledge rough entropy and rectifies the definition of rough entropy of rough set. The definition of boundary condition entropy is proposed and its relevant properties such as monotony are proved. Based on boundary condition entropy, it provides heuristic algorithm of attribute reduction and applies it to qualitative simulation and reasoning. It also discusses the effect of unsuitable knowledge expressive granularity upon uncertainty measure. By introducing maximal tolerance block, it re-measures the problem of knowledge and rough set measure.(2) The influences of variable-precision value on knowledge reduction are discussed. Based on relative discernibility of decision table, an approach for the self-determiningβ-Value and settingβ-Value in variable precision rough sets model is proposed.(3) It carefully studies the method of inductive learning in multi-decision information system and presents a new definition of joint decision discerniable matrix and an algorithm based on this matrix for inductive learning and incremental learning in the environment of incremental data set. It not only could solve the problem of learning on the incremental data sets, but also could considerably reduce the size of traditional decision matrix and avoid the repeated computation in traditional decision matrix algorithm.(4) Rules extraction in two classes of decision information system frequently is studied. Based on equivalence matrix, the definition of joined decision equivalence matrix is given and combines conditional attributes equivalence matrix and decision attribute matrix into one matrix, which considerably enhances the algorithm efficiency of rules extraction. Based on tolerance matrix and aided by general decision function, it gives rules extraction algorithm of joined decision tolerance matrix based on general decision table.(5) Based on the theory of block matrix, it investigates rules extraction in massive data set. It puts forward matrix-blocking method based on arbitrary divisional strategy and the calculating process of rules extraction, thus transforms massive data set into rules extraction among multi-subsystems. The existing problems with algorithm based on arbitrary divisional strategy are analyzed and rules extraction in massive data set based on decision classes division is further studied.