Research On The Matrix-Based Methodes For Updating Knowledge Dynamically In Information Systems

Rough set theory is one of the three basic models of granular computing. It is a powerful tool for investigating and handling the uncertainty problems. The core idea of rough set theory is to represent a vague concept approximately by two concepts which can be defined precisely. Then the knowledge or rules for decision making can be derived from these two defined concepts. The rough set based dynamic knowledge updating is to study the approaches for dynamically updating upper and lower approximations and then derive the updated rules or knowledge from the approximations under the variation of information systems.The motivation of this dissertation is based on the requirements that how to dynamically maintain the approximations of a concept rapidly and effectively under the dynamic environment. The research work is carried on within the framework of investigating several key issues on the rough set based dynamic knowledge discovery. Focusing on the three kinds of variations of granularity in information systems, the approaches for incremental updating upper and lower approximations (dynamic knowledge update) are studied systematically under the variable precision rough set model by using matrix as an expression tool as well as an operational tool. Its aim is to study the effective methods of dynamic knowledge update of information systems from the view of matrix. Furthermore, it is to search for the new theory foundation and practical methods for constructing a granular computing model for dynamic data processing in the view of matrix.In this dissertation, the properties of the equivalent relation matrix are investigated from the partitions of equivalent classes in the classic rough set model. Combined with the equivalent relation matrix and the Boolean column vector of the concept (subset) in the universe, the principles and algorithms on the matrix-based calculation method of approximations of a concept under classic rough set model and its exended models are researched. Then, the theorems, approaches and algorithms for updating approximations of variable precision rough set in the dynamic information system are discussed by using the matrix-based calculation method. Moreover, the incremental matrix-based algorithms are tested on the UCI data sets, and the experimental results are compared with that of the non-incremental matrix-based algorithms. The comparison results demonstrate the feasibility and validity of the matrix-based incremental method. The main achievements of research in each chapter of this dissertation can be described as follows.(1) The properties of the equivalent relation matrix are studied, including the necessary and sufficient conditions if it becomes the singular equivalent relation matrix, the semantics of the singular equivalent relation matrix on the approximations of a concept, the relationship between the rank of the equivalent relation matrix and the partition of equivalent classes on the universe. The relation between the equivalent relation matrix and the uncertainty of rough set is outlined. A novel matrix based approach for computing the knowledge granular, roughness and attributes’importance is proposed and the attributes’ importance can be updated rapidly by utilizing the incremental updating of the equivalent relation matrix under the removal or insertion of a single attribute.(Chapter2)(2) On the basis of the equivalent relation matrix and Boolean column matrix representation of a subset in the universe, a unified matrix-based method for computing upper and lower approximations of a concept under classic rough set model and the variable precision rough set model is proposed. It means the upper and lower approximations of a concept can derive from the operation among the Boolean column matrix of the concept, the equivalent relation matrix of the universe and the induced matrix. Then the formulae for calculating the column matrix of approximations and the corresponding formulae for calculating elements of the column matrix are given. Furthermore, the matrix-based approach for calculation of approximations is generalized to other rough set models (including probabilistic rough sets model, variable precision rough set model, asymmetric similarity relation based rough sets model, tolerant relation based rough sets model and characteristic relation based rough sets model). Their computing formulae and the corresponding algorithms are derived. These works can contribute to the subsequent researches on the rough set based dynamic knowledge discovery.(Chapter2)(3) The principles of matrix-based incremental update of approximations under variable precision rough set model while the object set varies with time are proposed, and then the corresponding algorithms for updating approximations are constructed. In case of object’s removal from the universe, the matrix-based approach is to update the approximations of a concept by updating the product matrix and the inverse of the induced matrix; In the case of object’s addition to universe, the matrix-based approach is to update the approximations of a concept by a block operation of matrix.(Chapter3)(4) The matrix-based approaches for incremental update of approximations under variable rough set model when the attribute set is dynamically changing are proposed and the corresponding algorithms for update of approximations are constructed.(Chapter4)(5) The matrix-based approaches for incremental update of approximations under variable rough set model when attributes’values are coarsened or refined are proposed, and then the corresponding algorithms for approximations’update are constructed.(Chapter5)All these researches are concerned with the issues on dynamic knowledge updating from three aspects of granularity variations in information systems from the view of matrix. The research results will enrich and improve the rough set based dynamic learning theory and can provide new ideas and solutions for dynamic knowledge update.