A Fuzzy Petri Net Approach with Automated ANFIS Rule Learning for Modelling Real-Time Systems

Abstract

In this paper, we propose a modelling approach for real-time intelligent systems using Fuzzy Petri Nets (FPNs), a formalism that generates dynamic fuzzy rules, supports uncertainty, and enables concurrent reasoning. FPNs offer a well-defined tool for dynamically evaluating Fuzzy Production Rules (FPRs), Certainty Factors (CFs), and truth degrees, and for making real-time decisions. To reduce the complexity of manually constructed or probabilistically modelled fuzzy rules, we extend the modelling toolkit with the Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS learns membership functions and Sugeno-type rules from numeric datasets through a feature. This results in a richer and more accurate set of rules. At the novelty level, we propose a rule-integrating scheme that maps Sugeno rules learned by ANFIS into FPN transitions to obtain more clearly explained reasoning and traceable rule execution within a neuro-fuzzy Petri net. Based on these learned rules, FPN executes them within a two-layer real-time (prediction and decision) while maintaining concurrent inference and real-time execution. The hybrid methodology is verified by fitting a real-time expert system for solar collector cleaning. Results from the experiments demonstrate that, in terms of predictive performance, ANFIS-induced rules drastically boost accuracy (from 85% to 93%) and reduce Root Mean Square Error (RMSE) from 4.82 to 2.57 relative to those generated by a single probabilistic FPN model. These results indicate that using neural learning combined with an FPN-based expert system makes real-time decision-making much more accurate and reliable.