A fuzzy ontology approach for representing Fuzzy Petri Nets

Petri Net (PN) has proven to be quite effective tool for graphical modeling, mathematical modeling, simulation, and real time control by the use of places and transitions. However, information imprecision and uncertainty exist in many real-world applications, and PNs found themselves inadequate to address the problems of imprecision and uncertainty in data. Therefore, the Fuzzy Petri Net (FPN) was developed and had been employed in many different fields like communication, manufacturing, electronics, and etc. In particular, with the wide utilization of FPNs, many researchers suggest that FPNs should be reused and shared. Emerging the Semantic Web technologies, such as fuzzy ontology, can play an important role in this scenario. On this basis, in this paper, we propose a fuzzy ontology approach for representing FPNs. First, we propose a formal definition of FPNs. Then, we give a complete definition of fuzzy OWL ontologies, where fuzzy ontologies formulated in fuzzy OWL language are called fuzzy OWL ontologies. Based on the formalization of FPNs and fuzzy OWL ontologies, we further propose a fuzzy ontology approach for representing FPNs, where we translate the key features of FPNs into the elements of fuzzy OWL ontologies such as fuzzy classes, fuzzy properties, fuzzy individuals, and fuzzy axioms. Finally, based on the translated fuzzy ontologies, we briefly discuss how to reason on FPNs through the reasoning mechanism of fuzzy ontologies.