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On Fixed Points of Linguistic Dynamic Systems 被引量：5

On Fixed Points of Linguistic Dynamic Systems
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摘要 Linguistic dynamic systems (LDS) are dynamic systems whose state variables are generalized from numbers to words. Generally speaking, LDS can model all evolving processes in word domains by using linguistic evolving laws which are naturally the linguistic extension of evolving laws in numbers. There are two kinds of LDS; namely, type-I and type-II LDS. If the word domain is modeled by fuzzy sets, then the evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart. On the other hand, the evolving laws of a type-II LDS are modeled by fuzzy if/then rules. Note that the state spaces of both type-I and type-II LDSs are word continuum. However, in practice, the representation of the state space of a type-II LDS consists of finite number while its computation actually involves a word continuum. In this paper, the existence of fixed points of type-II LDS is studied based on point-to-fuzzy-set mappings. The properties of the fixed point of type-II LDS are also studied. In addition, linguistic controllers are designed to control type-II LDS to goal states specified in words. Linguistic dynamic systems (LDS) are dynamic systems whose state variables are generalized from numbers to words. Generally speaking, LDS can model all evolving processes in word domains by using linguistic evolving laws which are naturally the linguistic extension of evolving laws in numbers. There are two kinds of LDS; namely, type-I and type-II LDS. If the word domain is modeled by fuzzy sets, then the evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart. On the other hand, the evolving laws of a type-II LDS are modeled by fuzzy if/then rules. Note that the state spaces of both type-I and type-II LDSs are word continuum. However, in practice, the representation of the state space of a type-II LDS consists of finite number while its computation actually involves a word continuum. In this paper, the existence of fixed points of type-II LDS is studied based on point-to-fuzzy-set mappings. The properties of the fixed point of type-II LDS are also studied. In addition, linguistic controllers are designed to control type-II LDS to goal states specified in words.
作者 王飞跃
机构地区 美国亚历桑那大学
出处 《系统仿真学报》 CAS CSCD 2002年第11期1479-1485,共7页 Journal of System Simulation
基金 This work has been supported in part by Outstanding Overseas Scholar Award and Outstanding Young Scientist Research Fund.
关键词 计算机语言 语言动力系统 LDS word LDS fixed points linguistic controller
分类号 TP312 [自动化与计算机技术—计算机软件与理论]
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同被引文献46

  • 1莫红,王飞跃.基于词计算的语言动力系统及其稳定性[J].中国科学（F辑:信息科学）,2009,39(2):254-268. 被引量：3
  • 2莫红,石松泉.虫口模型的模糊化及其相关性分析[J].华南理工大学学报（自然科学版）,2005,33(5):92-96. 被引量：1
  • 3王飞跃.词计算和语言动力学系统的基本问题和研究[J].自动化学报,2005,31(6):844-852. 被引量：34
  • 4L．A．扎德.模糊集合，语言变量及模糊逻辑[M].北京:科学出版社,1982..
  • 5Zeng Fanping, Mo Hong, Guo Wenjing. ω-Limit Set of a Tree Map. Northeast Mathematical Journal, 2001, 17(3) : 333 - 339.
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  • 8Kosko B. Neural Network and Fuzzy Systems: A Dynamical System Approach to Machine Intelligence. Englewood Cliffs, NJ: Prentice Hall, 1992.
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系统仿真学报
2002年 第11期

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