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.
[1] Greiff S,Funke J.What Makes a Problem Complex? Factors Determining Difficulty in Dynamic Situation and Implications for Diagnosing Complex Problem Solving Competence // Greiff S,Funke J,eds.Beyond Knowledge: The Legacy of Competence.New York,USA: Springer,2008: 199-200 [2] Rasmussen J.The Role of Hierarchical Knowledge Representation in Decision Making and System Management.IEEE Trans on Systems,Man and Cybernetics,1985,15(2): 234-243 [3] Yu Xinyao,Lau E,Vicente K J,et al.Advancing Performance Measurement in Cognitive Engineering: The Abstraction Hierarchy as a Framework for Dynamical System Analysis // Proc of the Human Factors and Ergonomics Society Annual Meeting.Chicago,USA,1998: 359-363 [4] Quesada J,Kintsch W,Gomez E.A Computational Theory of Complex Problem Solving Using Latent Semantic Analysis // Proc of the 24th Annual Conference of Cognitive Science Society.Fairfax,USA,2002: 750-755 [5] Cornforth D J.An Investigation into Dynamic Problem Solving in a Hybrid Evolutionary Market-Based Multi-Agent System // Proc of the IEEE Congress on Evolutionary Computation.Singapore,Singapore,2007: 25-28 [6] Back T.On the Behavior Evolutionary Algorithms in Dynamic Environments // Proc of the IEEE International Conference on Evolutionary Computation.Perth,Australia,1995: 446-451 [7] Michael W.An Introduction to Multiagent Systems.New York,USA: John Wiley Sons,2002 [8] Zhang Ling,Zhang Bo.Theory and Applications of Problem Solving-Theory and Applications of Granular Computing on Quotient Space.Beijing,China: Tsinghua University Press,2007: 238-245 (in Chinese) (张 铃,张 钹.问题求解理论及应用——商空间粒度计算理论及应用.北京:清华大学出版社,2007: 238-245) [9] Zhang Ling,Zhang Bo.The Quotient Space Theory of Problem Solving.Fundamenta Informaticae,2004,59(2/3): 287-298 [10] Zhang Ling,Zhang Bo.The Structural Analysis of Fuzzy Sets.Journal of Approximate Reasoning,2005,40(1/2): 92-108 [11] Zhang Ling,Zhang Bo.Fuzzy Reasoning Model under Quotient Space Structure.Information Sciences,2005,173(4): 353-364 [12] Zhang Ling,Zhang Bo.Fuzzy Quotient Space Theory (Method of Fuzzy Granular Computing).Journal of Software,2003,14(4): 770-776 (in Chinese) (张 铃,张 钹.模糊商空间理论(模糊粒度计算方法).软件学报,2003,14(4): 770-776) [13] Zhang Ling,Zhang Bo.Fuzzy Tolerance Quotient Space and Fuzzy Subsets.Science China: Information Science,2011,41(1): 1-11 (in Chinese) (张 铃,张 钹,模糊相容商空间与模糊子集,中国科学:信息科学,2011,41(1): 1-11) [14] Zhang Ling,He Fugui,Zhang Yanping,et al.A New Algorithm for Optimal Path Finding in Complex Networks Based on the Quotient Space.Fundamenta Informaticae,2009,93(4): 459-469
2012, Vol. 25 
