Parameterised Fuzzy Petri Nets for Knowledge Representation and Reasoning

Zbigniew Suraj

2013

Abstract

The paper presents a new methodology for knowledge representation and reasoning based on parameterised fuzzy Petri nets. Recently, this net model has been proposed as a natural extension of generalised fuzzy Petri nets. The new class extends the generalised fuzzy Petri nets by introducing two parameterised families of sums and products, which are supposed to provide the suitable t-norms and s-norms. The nature of the fuzzy reasoning realised by a given net model changes variously depending on t- and/or s-norms to be used. However, it is very difficult to select a suitable t- and/or s-norm function for actual applications. Therefore, we proposed to use in the net model parameterised families of sums and products, which nature change variously depending on the values of the parameters. Taking into account this aspect, we can say that the parameterised fuzzy Petri nets are more flexible than the classical fuzzy Petri nets, because they allow to define the parameterised input/output operators. Moreover, the choice of suitable operators for a given reasoning process and the speed of reasoning process are very important, especially in real-time decision support systems. Some advantages of the proposed methodology are shown in its application in train traffic control decision support.

References

  1. Avram, G. (2005). Empirical study on knowledge based systems. The Electronic Journal of Information Systems Evaluation, 8(1):11-20.
  2. Cardoso, J. and Camargo, H., editors (1999). Fuzziness in Petri Nets, volume 22 of Studies in Fuzziness and Soft Computing. Physica-Verlag, Berlin.
  3. Chen, S., Ke, J., and Chang, J. (1990). Knowledge representation using fuzzy petri nets. IEEE Trans. on Knowledge and Data Engineering, 2(3):311-319.
  4. Delimata, P., Moshkov, M., Skowron, A., and Suraj, Z. (2009). Inhibitory Rules in Data Analysis. A Rough Set Approach. Springer, Berlin.
  5. Dubois, D. and Prade, H. (1996). What are fuzzy rules and how to use them. Fuzzy Sets and Systems, 84:169- 185.
  6. Fedrizzi, M. and Kacprzyk, J. (1999). A brief introduction to fuzzy sets and fuzzy systems. In Cardoso, J. and Camargo, H., editors, Fuzziness in Petri Nets, volume 22 of Studies in Fuzziness and Soft Computing, pages 25- 51. Physica-Verlag, Berlin.
  7. Fryc, B., Pancerz, K., Peters, J., and Suraj, Z. (2004a). On fuzzy reasoning using matrix representation of extended fuzzy petri nets. Fundamenta Informaticae, 60(1-4):143-157.
  8. Fryc, B., Pancerz, K., and Suraj, Z. (2004b). Approximate petri nets for rule-based decision making. In RSCTC'2004, 4th Int. Conf. on Rough Sets and Current Trends in Computing, Uppsala, Sweden, June 1- 4, 2004, volume 3066 of Lecture Notes in Artificial Intelligence, pages 733-742. Springer.
  9. Jackson, P. (1999). Introduction to Expert Systems. Addison-Wesley, New York.
  10. Klement, E., Mesiar, R., and Pap, E. (2000). Triangular Norms. Kluwer Academic Publisher, Dordrecht.
  11. Looney, C. (1988). Fuzzy petri nets for rule-based decisionmaking. IEEE Trans. Syst., Man, Cybern., 18(1):178- 183.
  12. Pedrycz, W. and Gomide, F. (1994). A generalized fuzzy petri net model. IEEE Trans. on Fuzzy Systems, 2(4):295-301.
  13. Pedrycz, W. and Peters, J. (1998). Learning in fuzzy petri nets. In Cardoso, J. and Sandri, S., editors, Fuzzy Petri Nets, Studies in Fuzziness and Soft Computing, pages 858-886. Physica-Verlag, Berlin.
  14. Peters, J., Skowron, A., Suraj, Z., Ramanna, S., and Paryzek, A. (1998). Modelling real-time decisionmaking systems with roughly fuzzy petri nets. In EUFIT'98, 6th European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, September 7-10, 1998, pages 985-989. RWTH Aachen University.
  15. Peterson, J. (1981). Petri net theory and the modeling of systems. Prentice-Hall, Inc., Englewood Cliffs, N.J.
  16. Suraj, Z. (2012a). Generalised fuzzy petri nets for approximate reasoning in decision support systems. In CS&P2012, Int. Workshop on Concurrency, Specification and Programming, Berlin, Germany, September 26-28, 2012, volume 2, pages 370-381. Humboldt University.
  17. Suraj, Z. (2012b). Knowledge representation and reasoning based on generalised fuzzy petri nets. In ISDA'2012, Int. Conf. on Intelligent Systems Design and Applications, Kochi, India, November 27-29, 2012, pages 101-106. IEEE Press.
  18. Suraj, Z. (2012c). Parameterised fuzzy petri nets for approximate reasoning in decision support systems. In AMLTA'2012, 1st Int. Conf. on Advanced Machine Learning Technologies and Applications, Cairo, Egypt, December 8-10, 2012, volume 322 of Communications in Computer and Information Sciences, pages 33-42. Springer.
  19. Zadeh, L. (1965). Fuzzy sets. Information and Control, 8:338-353.
  20. Zimmermann, H. (1993). Fuzzy Set Theory and Its Applications. Kluwer Academic Publisher, Dordrecht.
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Paper Citation


in Harvard Style

Suraj Z. (2013). Parameterised Fuzzy Petri Nets for Knowledge Representation and Reasoning . In Proceedings of the 2nd International Conference on Data Technologies and Applications - Volume 1: DATA, ISBN 978-989-8565-67-9, pages 5-13. DOI: 10.5220/0004403000050013


in Bibtex Style

@conference{data13,
author={Zbigniew Suraj},
title={Parameterised Fuzzy Petri Nets for Knowledge Representation and Reasoning},
booktitle={Proceedings of the 2nd International Conference on Data Technologies and Applications - Volume 1: DATA,},
year={2013},
pages={5-13},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004403000050013},
isbn={978-989-8565-67-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Data Technologies and Applications - Volume 1: DATA,
TI - Parameterised Fuzzy Petri Nets for Knowledge Representation and Reasoning
SN - 978-989-8565-67-9
AU - Suraj Z.
PY - 2013
SP - 5
EP - 13
DO - 10.5220/0004403000050013