On Fuzzy Reasoning Using Matrix Representation of Extended Fuzzy Petri Nets

• Autorzy: Fryc B. , Pancerz K. , Peters J.F. , Suraj Z.
• Języki publikacji: EN

Abstrakty

EN

In 1990 Shyi-Ming Chen et al. presented a new approach to knowledge representation using fuzzy Petri nets (FPN). A fuzzy Petri net model allows a structural representation of knowledge and has a systematic procedure for supporting fuzzy reasoning. In this paper we propose an algebraic (matrix) representation of FPNs. We use this representation in a fuzzy reasoning algorithm which is simple to implement in modern programming languages such as C++, C# or Java. Furthermore, there exists MATLAB - a computer system which makes it possible to solve many computing problems, especially those with matrix and vector formulations. We present also an approach enabling us to carry out a fuzzy reasoning process using the MATLAB environment.

Słowa kluczowe

EN

algebraic representation; fuzzy Petri nets; fuzzy reasoning; knowledge representation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2004
• Tom: Vol. 60, nr 1-4
• Strony: 143--157
• Opis fizyczny: Bibliogr. 13 poz., tab.

Twórcy

autor

Fryc B.

• Chair of Computer Science Foundations, University of Information Technology and Management, Sucharskiego Str. 2, 35-225 Rzeszów, Poland

autor

Pancerz K.

• Chair of Computer Science Foundations, University of Information Technology and Management, Sucharskiego Str. 2, 35-225 Rzeszów, Poland

autor

Peters J.F.

• Department of Electrical and Computer Engineering, University of Manitoba, R3T 2N2 Winnipeg, Canada

autor

Suraj Z.

• Institute of Mathematics, Rzeszów University, Rejtana Str. 16A, 35-310 Rzeszów, Poland

Bibliografia

• [1] Chen, S.-M., Ke. J.-S., Chang. J.-F.: Knowledge Representation Using Fuzzy Petri Nets. IEEE Transactions on Knowledge and Data Engineering, Vol. 2, No. 3, 1990. pp. 311-319.
• [2] Fedrizzi, M., Kacprzyk. J.: A Brief Introduction to Fuzzy Sets and Fuzzy Systems. In: J. Cardoso, H. Camargo (Eds.), Fuzziness in Petri Nets, Studies in Fuzziness and Soft Computing. Vol. 22. Physica-Verlag, Berlin. 1999, pp. 25-51.
• [3] Frye, B., Makara Z., Pancerz K., Suraj Z.: A Petri Net System. An overview (draft).
• [4|]Li, X., Yu. W., Lara-Rosano, F.: Dynamic Knowledge Inference and Learning under Adaptive Fuzzy Petri Net Framework. IEEE Transactions on Systems, Man, and Cybernetics - Fart C: Applications and Reviews. Vol. 30, No. 4, November 2000. pp. 442-450.
• [5] Looney, C.G., Alfize, A.R.: Logic Controls via Boolean Rule Matrix Transformation. IEEE Transactions on Systems. Man. and Cybernetics, Vol. SMC-17. No. 6, November/December 1987. pp. 1077-1082.
• [6] Looney. C.G.: Fuzzy Petri Nets for Rule-Based Decision-making. IEEE Transactions on Systems. Man. And Cybernetics, 18-1. 1988. pp. 178-183.
• [7] Olejko. В., Suraj, Z.: Modelling of approximate reasoning using fuzzy Petri nets. Zeszyty Naukowe Politechniki Rzeszowskiej. Nr 199, Matematyka, Zeszyt 26, Rzeszów, 2002. pp. 191-204, (in Polish).
• [8] Peters. J.F., Skowron. A., Suraj, Z., Pedrycz. W., Ramanna, S.: Approximate Real-Time Decision Making: Concepts and Rough Fuzzy Petri Net Models. International Journal of Intelligent Systems, 14-4. 1998, pp.4-37.
• [9] Peters, J.F., Skowron, A., Suraj, Z., Ramanna, S., Paryzek, A.: Modelling Real-Time Decision Making Systems with Roughly Fuzzy Petri Nets. In: J. Komorowski. A. Skowron (Eds.), Proceedings of the 6 th European Congress on Intelligent Techniques and Soft Computing (EUFIT'98), Aachen. Germany, September 7-10. 1998, pp. 985-989.
• [10] Peterson. J.L.: Petri Net Theory' and the Modeling of Systems. Englewood Clifts, NJ. Prentice-Hall, 1981.
• [11] Petri. C.A.: Kommunikation mit Automaten, Schriften des UM Nr. 2, Institut für Instrumentelle Mathematik, Bonn, Germany, 1962. See, also. Communication with Automata (in English), Technical Report RADC-Tr-65377, 1, Suppl. 1, Griftiss Air Force Base, New York, 1966.
• [12] Reisig, W.: Petri Nets. An Introduction. EATCS Monographs on Theoretical Computer Sciences, Vol. 4, Springer-Verlag, Berlin, 1985.
• [13] Skowron. A., Suraj, Z.: A Parallel Algorithm for Real-Time Decision Making: A Rough Set Approach. Journal of Intelligent Information Systems, 7, Kluwer Academic Publishers. Dordrecht, 1996. pp. 5-28.