A Novel Quotient Space Computing Model Based on Extension Theory

One of the basic characteristics in human problem solving is the ability to conceptualize the world at different granularities and translate from one abstraction level to the others easily, i.e., the ability of multi-granular computing. The proposed quotient space theory is intended to provide a multi-granular computing model. The traditional single-granular computing methodology usually confronts with high computational complexity when dealing with complex problems. The main aim of multi-granular computing is intended to reduce the computational complexity. By using the quotient space model, we show in what conditions the multi-granular computing could reduce the computational complexity. Based on the quotient space model, the characteristics of the top-down hierarchical problem solving are discussed. The process actually implies the idea of extenics. Extension method is mainly used to solve contradictory problems by transformations of matter-elements. So we integrate extension method with theory of quotient space to solve some complicated problems in artificial intelligence system, and set up an extension-based quotient space computing model. The result shows this method is quite valuable.