Dynamic Quotient Space Model and Its Basic Properties
ZHANG Ling1, ZHANG Bo2,3,4
1.College of Computer Science and Technology,Anhui University,Hefei 230039 2.Department of Computer Science and Technology,College of Information Science and Technology,Tsinghua University,Beijing 100084 3.Tsinghua National Laboratory for Information Science and Technology,Beijing 100084 4.State Key Laboratory of Intelligent Technology and Systems,Beijing,100084
Abstract To solve problems under dynamic conditions, a time variable is introduced based on the original quotient space model (X,f,T), and the original model is extended to a dynamic quotient space (X(t),f(t),T(t)). There are two cases as follows: 1) If structure T is fixed, i.e.,(X(t), f(t),T), the dynamic quotient space model is transformed into a high dimensional static model by introducing a time variable into domain X. Then, the properties of the static model can be used. 2) When both domain X and attribute f are fixed, i.e., (X, f,T(t)), the necessary and sufficient condition for forming a chain of quotient space are discussed. And the corresponding principle of quotient approximation is established and its basic properties are discussed. Finally, the application of the dynamic quotient space model to problem solving is given.
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2012, Vol. 25 
