The Research On Reduction Theory Of Dynamic Information Systems Under Big Data And Its Applications

Information system in big data is drawing more attention in the field of information science in recent years, due to the allowance of huge data features and real-time response to the user’s computational requirements, where the classical methods can not handle these issues. Among them, knowledge discovery and rule extraction is one of most important steps in artificial intelligence, data mining, and decision predictable. Rough sets and fuzzy sets theories, as two major theories for the uncertain problems, have showed some signs of progress. However, the theories for solving these issues need to be further expanded to meet the requirements of the diversity of data types, complexity of relationships among data structures, and the rapidity and frequency of information updates in real life. Covering rough sets, as one extend of Pawlak rough set model, can maintain the integrity of knowledge in the information system with missing values, and thereby is widely used in real-world applications. But it faces the thorny issue of computing approximations and reductions rapidly under the situation of big data. On the other hand, the homomorphism between information systems can maintain the equivalent characteristics and at the same time obtain an image system that is relatively smaller than the original system, which provides a new technique to solve computational problems of information systems in big data.In the dissertation, based on the theories of covering rough sets and homomor-phism, we focus on the characteristics of dynamic information system to solves the issues of knowledge discovery and reduction by using incremental approaches in big data environment, which includes the following parts:(1) We systematically analyze the upper and lower approximation operators for cov-ering rough sets, summarize the relationships among operators on set theory, then give the definitions and computational rules of two operators for characteristic ma-trice. Moreover, based on set theory, the non-incremental algorithm for calculating the type-2 and type-6 approximation are designed, respectively. The characteristics of dynamic information system and several typical dynamic covering approxima-tion spaces are introduced.(2) The characteristics of dynamic approximation space are studied for the case of attribute value changing, and the corresponding changes in characteristic matrice are also discussed. We then design the incremental algorithms for computing ap-proximations, and generate a random big data set for validation. Some numerical results are presented to demonstrate that the incremental algorithms are more ef-fective than the non-incremental algorithms. A new example is given to explain the convenience of computing reduction by using incremental approaches.(3) We discuss the variety of covering approximation space when an object is added or removed, and also present the corresponding approaches to compute approxima-tions. In order to compare different operators, the incremental algorthms based on set theory and characteristic matrice are designed to compute type-2 and type-6 approximations, respectively. By employing UCI and random data sets, the numer-ical results show that non-incremental algorithms based on characteristic matrice are better than those based on set theory. More importantly, we show that the newly developed algorithm is an optimal method for characteristic matrice when compared with other classical methods.(4) By using the homomorphism between information systems, we investigate the char-acteristics of consistent function in fuzzy relation information system. The rela-tionships between maximum consistent function and other consistent functions are given. We also develop a non-incremental algorithm for constructing homomor-phism, and consider the characteristics of homomorphism when adding or deleting a fuzzy relation in dynamic situation. Moreover, in order to obtain new image system quickly and achieve dynamic compression, we design the corresponding incremental algorithms. Numerical experiments validate that the approaches are effective and robust for big random data sets.In summary, based on rough sets and fuzzy sets theories, this dissertation follows incremental approach and studies the problems of knowledge acquisition and uncertain computation in big data situation. Related numerical experiments are also provided to support the corresponding theory. We believe that the general methodology is applicable to the practical application challenges of covering approximation space and homomorphisms between information systems.