The relationship of controllability between classical and fuzzy discrete-event systems

We have known that the controllability of classical discrete-event systems has already been extended into fuzzy discrete-event systems. In this paper, firstly, we recall some related definitions and results of the controllability for classical and fuzzy discrete-event systems, respectively. Secondly, we are concerned with the relationship of the controllability between classical and fuzzy discrete-event systems. In particular, we show that there is an equivalence of the controllability between the two systems to some extent, some special proofs are also presented. Finally, we use this equivalence to extend some general controllability properties of classical discrete-event systems into fuzzy ones.

[1]  Hongyan Xing,et al.  Diagnosability of Fuzzy Discrete Event Systems , 2006, ArXiv.

[2]  Yongzhi Cao,et al.  Supervisory control of fuzzy discrete event systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Robert Ivor John,et al.  Computer aided fuzzy medical diagnosis , 2004, Inf. Sci..

[4]  Gerasimos G. Rigatos,et al.  Fuzzy stochastic automata for intelligent vehicle control , 2003, IEEE Trans. Ind. Electron..

[5]  Helmut Becker.  Computing with words and machine learning in medical diagnostics , 2001, Inf. Sci..

[6]  Feng Lin,et al.  Fuzzy discrete event systems and their observability , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[7]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[8]  Yongzhi Cao,et al.  Observability and decentralized control of fuzzy discrete-event systems , 2004, IEEE Transactions on Fuzzy Systems.

[9]  Antonio F. Gómez-Skarmeta,et al.  A framework for defining and learning fuzzy behaviors for autonomous mobile robots , 2002, Int. J. Intell. Syst..

[10]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[11]  Feng Lin,et al.  Decision making in fuzzy discrete event systems , 2007, Inf. Sci..

[12]  Feng Lin,et al.  A fuzzy discrete event system for HIV/AIDS treatment planning , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[13]  Ping Li,et al.  Algebraic properties of LA-languages , 2006, Inf. Sci..

[14]  Feng Lin,et al.  Modeling and control of fuzzy discrete event systems , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[15]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[16]  Teresa Escobet,et al.  Wastewater treatment process supervision by means of a fuzzy automaton model , 2000, Proceedings of the 2000 IEEE International Symposium on Intelligent Control. Held jointly with the 8th IEEE Mediterranean Conference on Control and Automation (Cat. No.00CH37147).

[17]  Witold Pedrycz,et al.  Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids , 2005, Fuzzy Sets Syst..

[18]  Vijay K. Garg,et al.  Modeling and Control of Logical Discrete Event Systems , 1994 .

[19]  Daowen Qiu,et al.  Supervisory control of fuzzy discrete event systems: a formal approach , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Walter Murray Wonham,et al.  On observability of discrete-event systems , 1988, Inf. Sci..

[21]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

[22]  Feng Lin,et al.  Theorem of abstraction for equivalent controllers in hybrid systems , 2005, Inf. Sci..

[23]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[24]  Zhihui Li,et al.  The relationships among several types of fuzzy automata , 2006, Inf. Sci..

[25]  A ZadehLotfi,et al.  Toward a generalized theory of uncertainty (GTU) , 2005 .

[26]  Abraham Kandel,et al.  Fuzzy Semantic Analysis and Formal Specification of Conceptual Knowledge , 1995, Inf. Sci..

[27]  Ewa Straszecka,et al.  Combining uncertainty and imprecision in models of medical diagnosis , 2006, Inf. Sci..

[28]  Feng Lin,et al.  A Fuzzy Discrete Event System for HIV/AIDS Treatment , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[29]  Feng Lin,et al.  A fuzzy discrete event system with self-learning capability for HIV/AIDS treatment regimen selection , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[30]  Michele Dassisti,et al.  Pseudo-fuzzy discrete-event simulation for on-line production control , 2005, Comput. Ind. Eng..

[31]  J. F. Baldwin,et al.  Fuzzy Switching and Automata Theory and Applications , 1980 .

[32]  Eugene S. Santos,et al.  Maximin Automata , 1968, Inf. Control..

[33]  Lin Shaoyuan.  Analysis of Fuzzy Sliding Mode Control Systems , 2000 .

[34]  Hao Ying,et al.  Fuzzy Control and Modeling: Analytical Foundations and Applications , 2000 .

[35]  L.R. Crane,et al.  Control of fuzzy discrete event systems and its applications to clinical treatment planning , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[36]  Kevin D. Reilly,et al.  Simulating continuous fuzzy systems , 2005, Inf. Sci..