Relational Calculus in Designing Fuzzy Petri Nets
This paper discusses the design of Fuzzy Petri Net in the context of fuzzy relational equations. The High Level Fuzzy Petri Nets proposed earlier to represent fuzzy production rules, is described as a modeling tool in the more general setting of relational equations. The connection of the high level net to its correspondent detailed models is approached. The relational equations problems and their solutions are reviewed, as a background to the work developed here. The representation of direct and dual relational equations is described. A suggestion to use the method to solve relational equations in the development of a backward reasoning algorithm for fuzzy production rules is presented.
Unable to display preview. Download preview PDF.
- T. Cao, A. Sanderson, “Variable Reasoning and Analysis about Uncertainty with Fuzzy Petri Nets”, in Application and Theory of Petri Nets 1993, Marco A. Marsan (ed.), LNCS, Springer-Verlag, pp. 126–145, 1993.Google Scholar
- J. Cardoso, R. Valette, D. Dubois, “Petri Nets with Uncertain Markings”, in Advances in Petri Nets 1990, G. Rosenberg (ed.), LNCS 483, Springer-Verlag, pp. 64–78, 1990.Google Scholar
- M. Chun, Z. Bien, “Fuzzy Petri Net Representation and Reasoning Methods for Rule-Based Decision Making Systems”, IEICE Trans. Fundamentals, vol. E76-A, no. 6, July 1993.Google Scholar
- H. Scarpelli, F. Gomide, W. Pedrycz, “Modeling Fuzzy Reasoning using High Level Fuzzy Petri Nets”, Technical Report RT-DCA 023/92, DCA/FEE/UNICAMP, 1992. (submitted)Google Scholar
- H. Scarpelli, F. Gomide, R. Yager, “A Reasoning Algorithm for High Level Fuzzy Petri Nets”, Technical Report RT-DCA 004/93, DCA/FEE/UNICAMP, 1993. (submitted)Google Scholar
- H. Scarpelli, F. Gomide, “Fuzzy Reasoning and Fuzzy Petri Nets”, Proc. Fifth IFSA World Congress, Seoul, Korea, July 5–9, pp. 1326–1329, 1993.Google Scholar
- H. Scarpelli, F. Gomide, “Fuzzy Reasoning and Fuzzy Petri Nets in Manufacturing Systems Modeling”, Journal of Intelligent and Fuzzy Systems, vol.1, no. 3, pp. 225–241, July, 1993.Google Scholar
- H. Scarpelli, F. Gomide, “Fuzzy Reasoning and High Level Fuzzy Petri Nets”, Proc. First European Congress on Fuzzy and Intelligent Technologies, Aachen, Germany, September, 7–10, pp. 600–605, 1993.Google Scholar
- H. Scarpelli, “Fuzzy Petri Nets and Alternative Reasoning Methods”, Proc. 6th IFSA World Congress, São Paulo, Brazil, pp. 345–348, July 1995.Google Scholar
- P. Srinivan, D. Gracarin, “Approximate Reasoning with Fuzzy Petri Nets”, Proc, IEEE Int. Conf. on Fuzzy Sustems, San Francisco, California, USA, pp. 396–401, 1993.Google Scholar
- R. Yager, D. Filev, Essentials of Fuzzy Modeling and Control, John Wiley, 1994Google Scholar
- L. A. Zadeh, “A Theory of Approximate Reasoning”, Machine Inteligence 9, Hayes, Michie & Kulich, (eds.), 9, pp.149–194, 1979.Google Scholar