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Uncertainty Management with Fuzzy and Rough Sets pp 395–413Cite as

Fuzzy Petri Nets and Interval Analysis Working Together

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Part of the book series: Studies in Fuzziness and Soft Computing ((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.

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Acknowledgements

The author is grateful to anonymous reviewers for helpful comments.

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Authors and Affiliations

  1. Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów, Poland

    Zbigniew Suraj

  2. Faculty of Computers and Information, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

Authors
  1. Zbigniew Suraj
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  2. Aboul Ella Hassanien
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Correspondence to Zbigniew Suraj .

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Editors and Affiliations

  1. Department of Computer Science, Universidad Central "Marta Abreu" de Las Villas, Santa Clara, Villa Clara, Cuba

    Rafael Bello

  2. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Rafael Falcon

  3. Department of Computer Science and Artificial Intelligence, Technical School of Informatics and Telecommunications Engineering, University of Granada, Granada, Spain

    José Luis Verdegay

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Suraj, Z., Hassanien, A.E. (2019). Fuzzy Petri Nets and Interval Analysis Working Together. In: Bello, R., Falcon, R., Verdegay, J. (eds) Uncertainty Management with Fuzzy and Rough Sets. Studies in Fuzziness and Soft Computing, vol 377. Springer, Cham. https://doi.org/10.1007/978-3-030-10463-4_20

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