The Representation of Different Granular Worlds: A Quotient Space
Zhang Yan · Chinese Journal of Computers · 2004
Facing complicated objects, how to describe or represent objects is the base to solve questions frequently. This paper introduces a representation of quotient space theory. In the theory, a problem (or problem space) is described by a triplet ( X,f,T ), in which X is its domain, f is its attributes, T is its structure. Assume R is an equivalence relation on X , [ X ] is a quotient set under R . Regarding [ X ] as a new domain, we have a new problem space ([X],[f],[T] ).The worlds with different grain size are represented by a set of quotient spaces. The representation is intended to describe the worlds with different grain size easily and can be used for analyzing the hierarchical problem solving behavior expediently. Compared to rough set and decision making tree, the quotient space has the stronger representation. Not only it can represent vectors of the problem domain, different structures between vectors, but also it can define different attribute functions and operations etc. In this paper, authors’ discuss the method how to represent and to partition an object in granular worlds, and educe the relationship of different granular worlds and confirm the degree of granule. Authors also supply two examples of representing granular worlds: A routing for internet and another game of weighing heavy balls. The examples indicate that to describe or represent a complicated object is equal to construct its quotient space.