Research Of Granular Computing, Rough Sets, Pansystems And Quotient Space Theory

Granular computing is a kind of new concept of information processing and computational normal form, Overlay all relevant researches of the granular's theories, methods, techniques and tools.It is superset of the word computational theory,rough sets theory,quotient space theory and interval computing .It is also a branch of soft compputing science . The thesis focuses on granular computing, what are investigated concern with quotient space theory, operators of pansystems, rough sets theory and granular computing.The main research results are clarified as below.Based on the quotient theory, the granular computing expresses the concept as a subset. A division is composed of a set of concepts, it is a quotient theory.Granular computing is a study which research the subset's relation and conversion, get and synthesize the domain, structure and attribute of granularity in different layers. There are two important theorems: fidelity theorem in fine granulation to coarse granulation and protect false theorem in coarse granulation to fine granulation. Use these two theorem, we can infer and synthesize the different layer's result, get the last result, thus decrease the complexity of problem solving.On this foundation, this text apply the fuzzy quotient space's theory and method in fuzzy granular computing, discuss the granula conversion problem in fuzzy quotient space.Using the thoughts of system and conversion in pansystem theory, this text introduce and use equivalence operator to convert the orginal binary relations into equivalent relations, get different knowledge bases through different equivalence operators. The text present the new concepts of the generalized rough sets, generalized rough equivalence and generalized rough inclusion, deduce the inherent relations between generalized rough equivalence and ordinary equivalence, the generalized rough inclusion and ordinary inclusion in rough sets theory.It deduce and figure out the rules of transformation of the granule's size, the maximize granule, the minimize granule, the precision through the different operator of pansystem.From the rough sets theory, this text discusses the relations between the granularity, resolution and entropy. In information system, the text give in the concept of importance degree, deduce the inherent relation and rules between the importance degree and granularity. In decision-making system, based on the relation between importance degree and granularity, advance the minimal reduction algorithms, deduce the relation between importance degree and coordination degree.The text poses the model for lattice granular computing, discusses the scroll and going down operation in data warehouse.Data discretization is a task in machine learning and data mining,the text discover the relation of vary data discretization's alternatives, organize all kind of data discretization's alternative into lattice space, is entitled discrete lattice. It proves the discrete lattice is a Boolean algera, give the theorems in discrete lattice, structure the mapping from discrete lattice to division lattice, researches the rules of the information granule's transformation, positive region with condition attributes to dicision attributes and entropy.