Study On The Approach Of Incremental Updating Approximations Based On Set-Valued Information Systems

In recent years, the classical rough set theory has successfully been applied in the area of knowledge acquisition. However, the classical rough set theory under the indiscernibility relation is no longer valid for dealing with incomplete information systems. The incomplete information system that the attribute value of an object is the subset of the domain of attributes can be described by a set-valued information system. The set-valued information system is the generalization of the single-valued information system, and it has been studied extensively in recent years from various points of perspectives.Current research on rough sets is mainly based on the static data. However, in real applications, many data sources have dynamic characteristics. Therefore, it is meaningful to study the incremental leaning approaches based on rough set theory.The purpose of this paper is to research on the approach for incremental updating approximations and the extended model based on the set-valued information system. Firstly, the recent work of rough set theory, set-valued information systems and the incremental leaning approaches based on rough set are reviewed. After giving the basic concepts, the tolerance relation and the approximations under the tolerance relation are analyzed, and an approach for incremental updating approximations is presented based on the set-valued information systems under the tolerance relation. An example is employed to illustrate that the proposed approach is valid. Then, the definitions of attribute values'coarsening and refining in set-valued information systems are introduced. An approach for incrementally updating approximations of a concept is presented while attribute values coarsening and refining. Finally, a new relation called a tolerance relation is defined in the set-valued information system by a tolerance degree of the attribute value to overcome the limitation of tolerance relation and predominance relation. Its basic properties as well as the relations among the tolerance relation, predominance relation and a tolerance relation are discussed. An extended rough set model based on a tolerance relation is proposed, and the relations between this model and other extended models are compared.