Research On Theory And Method Of Granular Computing Based On Rough Set Theory

The basic ideas and principles of granular computing(GrC) have been studied explicitly or implicitly in many fields in isolation such as evidence theory, clustering analysis, database system, machine learning and data mining and so on. More and more people have been interested in information granulating since the problem was firstly proposed and discussed in the world by L.A. Zadeh. With the rapid development of the theory in recently two decades, granular computing will play a more important role in soft computing, knowledge discovery and data mining.Tracking the international research status, based on rough set theory, using for reference some known theory fruits of soft computing, the paper lucubrated some basic theories and methods of granular computing. Achieved results not only enrich and improve granular computing theory and information entropy theory, but also are expected enormous applied value due to the widespread applied background of these theories.Some theoretical problems were mainly researched in the paper as follows1. As for syncretization between rough set theory and granular computing, dynamic granulation is proposed. Owing to non-dynamic of concept description in classical rough set, rough set approximation under granulation is discussed in the paper, positive approximation and reverse approximation under dynamic granulation are defined, their some important properties are given. These ideas will provide new research method for granular computing and rough set theory. In addition, measure of harmony between approximation classification and original universe classified is analyzed, a approximation classification algorithm based-on positive approximation is presented, its validity is proved using a concrete instance.2. As for depicting the essence of the granulation in information system, the axiom definition of the knowledge granulation is proposed. Knowledge in a complete information system and in an incomplete information system isuniformly expressed in order to describe and measure the extent of closeness and difference among knowledge, the concept of knowledge closeness and the concept of knowledge distance are introduced, the relationship between two concepts with one equivalence relation or tolerance relation is restrict complementary relationship by proving. Allowing for some potentially principle followed about the depiction and the definition of knowledge granulation, the axiom definition of knowledge granulation is presented, several known knowledge granulation are all special forms under the definition. Whereafter, the relationships between knowledge granulation and information entropy are established, there is a complementary relationship between them by proving theoretically. And we propose a suppose so-called information conservation suppose, the sum of knowledge content appeared and knowledge content hided is unchangeable in a knowledge space.3. As for research on information entropy theory, combination entropy and combination granulation are presented. A new information entropy (combination entropy) in information system is proposed firstly, its gain function considered here possesses intuitionistic knowledge content characteristic, some important properties are derived. Accordingly, a new knowledge granulation (combination granulation) is defined; its some correlative properties are given. Degeneration and extension relationship of combination entropy and combination granulation between complete information system and incomplete information system are proved. Furthermore, we build the relationship between combination entropy and combination granulation, and prove that the relationship is a restrictive complementary relationship. These results will greatly enrich and develop entropy theory and granular computing.4. As for research on intelligent decision theory, two more profound evaluation parameters are given. Based on rough set theory, deduction of decision rule in decision table under dynamic granulation is discussed using ideas of granulation. Because whole decision performance of decision table can't be reflected via known decision parameters, two more profound...