A New Class of Fuzzy Petri Nets for Knowledge Representation and Reasoning

This paper presents a new class of Petri nets called generalised fuzzy Petri nets. The new class extends the existing fuzzy Petri nets by introducing three operators in the form of triangular norms, which are supposed to function as substitute for the min, max and * algebraic product operators. To demonstrate the power and the usefulness of this model, an application of the generalised fuzzy Petri nets in the domain of train traffic control is provided. The new model is more flexible than the classical one as in the former class the user has the chance to define the input/output operators. The proposed approach can be used for knowledge representation and reasoning in decision support systems.

[1]  C. Petri.  Kommunikation mit Automaten , 1962 .

[2]  Zbigniew Suraj,et al.  Timed Approximate Petri Nets , 2006, Fundam. Informaticae.

[3]  Marcin Szpyrka,et al.  Decision Tables in Petri Net Models , 2007, RSEISP.

[4]  Witold Pedrycz.  Generalized fuzzy Petri nets as pattern classifiers , 1999, Pattern Recognit. Lett..

[5]  Jin-Fu Chang,et al.  Knowledge Representation Using Fuzzy Petri Nets , 1990, IEEE Trans. Knowl. Data Eng..

[6]  Krzysztof Pancerz,et al.  On Fuzzy Reasoning Using Matrix Representation of Extended Fuzzy Petri Nets , 2003, Fundam. Informaticae.

[7]  Zbigniew Suraj.  Parameterised Fuzzy Petri Nets for Approximate Reasoning in Decision Support Systems , 2012, AMLTA.

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

[9]  Xiaoou Li,et al.  Adaptive fuzzy petri nets for dynamic knowledge representation and inference , 2000 .

[10]  Janette Cardoso,et al.  Fuzziness in Petri Nets , 1998 .

[11]  Witold Pedrycz,et al.  A generalized fuzzy Petri net model , 1994, IEEE Trans. Fuzzy Syst..

[12]  Marcin Szpyrka.  Design and Analysis of Rule-based Systems with Adder Designer , 2008 .

[13]  S. I. Ahson,et al.  A Fuzzy Petri Net for Knowledge Representation and Reasoning , 1991, Inf. Process. Lett..

[14]  Zbigniew Suraj,et al.  Generalised Fuzzy Petri Nets for Approximate Reasoning in Decision Support Systems , 2012, CS&P.

[15]  Krzysztof Pancerz,et al.  Approximate Petri Nets for Rule-Based Decision Making , 2004, Rough Sets and Current Trends in Computing.

[16]  Zbigniew Suraj.  Knowledge representation and reasoning based on generalised fuzzy Petri nets , 2012, 2012 12th International Conference on Intelligent Systems Design and Applications (ISDA).

[17]  Carl G. Looney,et al.  Fuzzy Petri nets for rule-based decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[18]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .