Quotient space based multi-granular computing

Summary form only given. 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. In this paper, we address the following four problems. 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. Second, based on the quotient space model, the characteristics of the top-down hierarchical problem solving are discussed. Third, the well-known multi-resolution signal analysis is managed under the framework of the quotient space model. And we show the close relationship between the quotient space based multi-resolution model and the second-generation wavelet transforms. This relationship may provide a new idea for signal analysis. Finally, a quotient space based hierarchical machine-learning model is discussed. And a new hierarchical constructive learning algorithm is presented.