Granular Space And Granular Computing Of Information Systems Based On Binary Relation

Granular computing, as one world outlook and methodology, exists widely in the real world and its essence is not only to research user oriented concept effectively from the outside world but also to simplify our cognition of the physical and virtual world. The theory of rough set which is based on sort mechanism can be viewed as a powerful granular computing tool to deal with complex problems, mass data mining and fuzzy intellectual information. Since it does not require any prior knowledge except given data to settle the problem, the theory has been used in many fields such as artificial intelligence, pattern recognition, and data mining.From the view point of granular computing, some elementary knowledge in infromation systems based on general binary relations is discussed carefully. The main innovations of this paper list as following.1. We extend the equivalence relation based method of knowledge representation to general binary relation based knowledge representation method and reached the significance conclusion that the new knowledge representation method is equivalent to Pawlak's algebra expression.2. For the problem of uncertainty of knowledge, a new rough set model which is graded rough set model based on rough membership in general information system is constructed. In addition, one can find that this new model can be regarded not only as the extension of original graded rough set model in precision coefficients but also as the generalization of precision rough set model from the view of binary relation.3. The vector representation method of knowledge is proposed and operations among them are discussed in detail. On base of taking the distance between any two knowledge granules into consideration, granular space is defined and some of its peoperties are researched carefully. Moreover, the spatial position of every knowledge granule is constructed by its granularity after researching the relation's distinguishable ability.4. As to the issue of knowledge reduction, we investigate the information systems with the most complicated context with the tool of distinguishable matrix, from which information systems with decision and information systems with interval valued intuitionistic fuzzy decision are discussed in detail, and examples are used to illustrate the necessity and feasibility.