One of the basic characteristics of human intelligence is the ability to conceptualize the world at different granularities and deal with it from different abstraction levels. But so far computers solve problems at one abstraction level generally. The quotient space theory is intended to endow computers with the above human’s ability. A quotient space based multi-granular model is proposed to represent the world in computers at different granularities. In the theory there are two basic issues: hierarchical problem solving and hierarchical learning. We’ll show that the aim of hierarchical problem solving and learning is to reduce the computational complexity and in what conditions the computational complexity can be reduced. We’ll discuss the relationship between fuzzy and granularity and show that a fuzzy information can be represented at a multi-granular world and can be handled in fuzzy quotient space easily. Besides the theory, some applications are mentioned.
Zhang Bo, computer scientist, is a fellow of Chinese Academy of Sciences and a professor of Computer Science and Technology Department of Tsinghua University and State Key Lab of Intelligent Technology and Systems. In 1958 he graduated from Automatic Control Department of Tsinghua University. From 1980/02 to 1982/02 he visited University of Illinois at Urbana-Champaign, USA as a scholar. Now he served as chairman of academic committee of Information Science and Technology College in Tsinghua University, Beijing, China. He is engaged in the research on artificial intelligence, artificial neural networks, genetic algorithms, fractal, wavelet theory and so on. And he also is engaged in the research applying technology that applies the theories mentioned above into pattern recognition, knowledge engineering, robotics and intelligent control.
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