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Fuzzy Petri Nets and Interval Analysis Working Together

  • Zbigniew SurajEmail author
  • Aboul Ella Hassanien
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 377)

Abstract

Fuzzy Petri nets are a potential modeling technique for knowledge representation and reasoning in knowledge-based systems. Over the last few decades, many studies have focused on improving the fuzzy Petri net model. Various new models have been proposed in the literature on the subject, which increase both modeling strength and usability of fuzzy Petri nets. Recently, generalised fuzzy Petri nets have been proposed. They are a natural extension of the classic fuzzy Petri nets. The t-norms and s-norms are entered into the model as substitutes for operators min, max and \(\cdot \) (the algebraic product). This paper, however, describes how the extended class of generalised fuzzy Petri nets, called type-2 generalised fuzzy Petri nets, can be used to represent knowledge and model reasoning in knowledge-based systems. The type-2 generalised fuzzy Petri nets expand existing generalised fuzzy Petri nets by introducing the triple of operators \((In,Out_1,Out_2)\) in the net model in the form of interval triangular norms that are supposed to act as a substitute for triangular norms in generalised fuzzy Petri nets. Thanks to this relatively simple modification, a more realistic model than the previous one was obtained. The new model allows to use approximate information in relation to the representation of knowledge, as well as modeling reasoning in knowledge-based systems.

Keywords

Fuzzy Petri net Decision making Classification Approximate reasoning Knowledge-based system 

Notes

Acknowledgements

The author is grateful to anonymous reviewers for helpful comments.

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Authors and Affiliations

  1. 1.Faculty of Mathematics and Natural SciencesUniversity of RzeszówRzeszówPoland
  2. 2.Faculty of Computers and InformationCairo UniversityGizaEgypt

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