Research On Quotient Space Combination

Abstract:The framework of quotient space theory is proposed by the domestic scholars Academician Zhang Bo and Professor Zhang Ling when they research on problem solving, which has become one of the three models of granular computing. The theory unites the different granular spaces and quotient set in mathematics using a triple with universe, attribute function and structure to describe the problem. The purpose is to research on the relationship between different quotient spaces and the rules in decomposition, combination and reasoning. The theory has an impact on solving heuristic search, path planning and so on.This combination studies the relationship between the quotient space and the original space, which is the basis of the quotient space theory. In this thesis, by learning finite topology and many related journal articles, we have expanded the universe combination and structure combination in order to describe the relationship between the original space and quotient space more clearly. In the meanwhile, we have improved the attribute function combination by using some concepts of information system in rough set so that the combination can be easier to understand and operate. The universe combination reflects the transformation of different granular layers. The structure combination studies the relationship between the different granular structures. The attribution function combination represents some features of the granule.In addition, we give a new concept—converse quotient space and describe its basic properties. The converse quotient space and quotient space provide further explanation of the original space and quotient space, and they form a hierarchical space structure. All these researches aim at enriching the theory of quotient space, make it better applied to the granular computing. Lastly, we propose a new model—structured information system combining rough set theory with quotient space theory, and analyze its advantages and disadvantages. This model can be viewed as a new exploration of unified framework of granular computing.