Fuzzy Petri Nets for Knowledge Representation and Reasoning

Fuzzy Petri nets combine the structural clarity of Petri nets with the uncertainty‐handling capabilities of fuzzy logic. At their core, Petri nets model concurrent and distributed systems through places, transitions and tokens, providing a graphical and mathematical representation of system states and events. Fuzzy logic extends classical Boolean reasoning by permitting degrees of truth, thus enabling the expression of vagueness and partial information. In a fuzzy Petri net, transitions fire according to fuzzy inference rules, tokens carry membership degrees, and weighted arcs quantify the strength of relationships. This integration yields a versatile formalism for capturing and reasoning with complex, uncertain knowledge in domains such as expert systems, decision support and automated diagnostics.

Advanced variants enrich the basic model by introducing coloured tokens to represent multi‐attribute information, picture fuzzy sets to encode positive, neutral and negative belief degrees, or adaptive weighting schemes to reflect mutual influences among factors. These enhancements have broadened the applicability of fuzzy Petri nets to gene regulatory network modelling, software verification, fault diagnosis and energy management. Practical implementations demonstrate how extensive rule bases can be visualised, analysed and verified, and how scalable reasoning algorithms can maintain performance in large‐scale settings.

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Contemporary studies have propelled both theoretical refinements and real‐world applications of fuzzy Petri nets. A 2023 work introduced a fuzzy coloured Petri net framework for visualising and verifying high‐level system specifications. By incorporating weights for premise and conclusion propositions, threshold values and certainty factors, the model supports large rule sets and was validated on a secure water treatment scenario, achieving enhanced scalability and interpretability of complex fuzzy rules.

Another 2023 contribution proposed a smart fuzzy Petri net controller for building temperature regulation. This approach merges fuzzy logic with Petri net modelling to create an energy‐efficient air‐conditioning framework. User preferences are modelled via token firing and communicated to a PID controller, resulting in a 94 % reduction in energy consumption compared to a standard Petri net controller and demonstrating the practical benefits of fuzzy extensions.

A foundational 2019 study presented picture fuzzy Petri nets that employ picture fuzzy sets to capture expert knowledge with positive, neutral and negative membership grades. A similarity‐based expert‐weighting method was introduced to resolve conflicting evaluations during rule acquisition. The model’s feasibility was illustrated through a gene regulatory network example, showcasing its ability to manage contradictory information and improve the accuracy of inferred rules.

Fuzzy Petri Nets for Knowledge Representation and Reasoning publication trend

The graph below shows the total number of articles in fuzzy petri nets for knowledge representation and reasoning across all publications each year (not limited to Nature Index journals).

Technical terms

Petri net: A mathematical and graphical formalism for modelling concurrent, distributed systems using places (conditions), transitions (events) and tokens (state markers).

Fuzzy logic: A reasoning framework that allows variables to have degrees of truth between 0 and 1, thereby modelling imprecision and uncertainty.

Fuzzy Petri net: An extension of Petri nets in which fuzzy logic determines transition firing and tokens carry membership degrees, enabling uncertain knowledge representation and inference.

Picture fuzzy set: A generalisation of fuzzy sets characterised by three membership functions—positive, neutral and negative—used to express varying levels of agreement, abstention and disagreement in expert assessments.

References

1. Fuzzy coloured petri nets‐based method to analyse and verify the functionality of software. CAAI Transactions on Intelligence Technology (2023).
2. Smart Fuzzy Petri Net-Based Temperature Control Framework for Reducing Building Energy Consumption. Sensors (2023).
3. Picture Fuzzy Petri Nets for Knowledge Representation and Acquisition in Considering Conflicting Opinions. Applied Sciences (2019).
4. A Fuzzy Petri-Net Approach for Fault Analysis Considering Factor Influences. IEEE Access (2020).
5. A New Approach for Modelling Gene Regulatory Networks Using Fuzzy Petri Nets. Journal of Integrative Bioinformatics (2010).