is a topologic or a semi-order space, we discuss how to construct the quotient topology and quotient (pseudo) semi-order on its corresponding quotient space [X] and after the construction what kind of quotient structures that we can have.1.7. Conclusions
In this chapter, we present a quotient space representation method for problem solving. Based on the method, a problem is represented by a triplet 
. Compared to general graph and AND/OR graph representations, it enables us to describe different structures, attribute functions and operations on a domain. Especially, it offers a tool for depicting different grain-size worlds. In the following chapters, we will show the application of the representation.
. Compared to general graph and AND/OR graph representations, it enables us to describe different structures, attribute functions and operations on a domain. Especially, it offers a tool for depicting different grain-size worlds. In the following chapters, we will show the application of the representation.When is a topologic or a semi-order space, we discuss how to construct the quotient topology and quotient (pseudo) semi-order on its corresponding quotient space [X] and after the construction what kind of quotient structures that we can have.
is a topologic or a semi-order space, we discuss how to construct the quotient topology and quotient (pseudo) semi-order on its corresponding quotient space [X] and after the construction what kind of quotient structures that we can have.We show the three different kinds of complete semi-order lattices we can have and how they correspond to different construction methods. We also investigate the relation among three lattices. These results offer the mathematical tools and methods for granular analysis and computing later on.
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