Linguistic dynamic systems and computing with words for complex systems

This paper outlines a computational theory of linguistic dynamic systems for computing with words by fusing procedures and concepts from several different areas: Kosko's (1992) geometric interpretation of fuzzy sets, Hsu's (1987) cell-to-cell mappings in nonlinear analysis, equi-distribution lattices in number theory, and dynamic programming in optimal control theory. The proposed framework enables us to conduct a global dynamic analysis, system design and synthesis for linguistic dynamic systems that use words or linguistic terms in computation, based on concepts and methods well developed for conventional dynamic systems. This theory has significant potential for modeling and analysis of systems where model, goal, control and feedback are primarily specified in words or linguistic terms.

[1]  J. Halton.  On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[2]  C. S. Hsu,et al.  Cell-to-Cell Mapping , 1987 .

[3]  H. Keng,et al.  Applications of number theory to numerical analysis , 1981 .

[4]  Ebrahim H. Mamdani,et al.  A linguistic self-organizing process controller , 1979, Autom..

[5]  C. Hsu,et al.  A Generalized Theory of Cell-to-Cell Mapping for Nonlinear Dynamical Systems , 1981 .

[6]  Paul P. Wang,et al.  Fuzzy dynamic system and fuzzy linguistic controller classification , 1994, Autom..

[7]  Fei-Yue Wang,et al.  A cell-to-cell mapping based analysis and design of fuzzy dynamic systems and its applications , 1995 .

[8]  E. H. Mamdani,et al.  Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis , 1976, IEEE Transactions on Computers.

[9]  M. Braae,et al.  Theoretical and linguistic aspects of the fuzzy logic controller , 1979, Autom..

[10]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[11]  Lucien Duckstein,et al.  Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological and Engineering Systems , 1995 .

[12]  C. Hsu,et al.  An Unravelling Algorithm for Global Analysis of Dynamical Systems: An Application of Cell-to-Cell Mappings , 1980 .

[13]  F. Y. Wang,et al.  Cell-to-cell mapping method for time-optimal trajectory planning of multiple robot arm systems , 1995 .

[14]  A. Meystel,et al.  Dynamic predictive planning+fuzzy logic control=intelligent control , 1990, Proceedings. 5th IEEE International Symposium on Intelligent Control 1990.