Coloured fuzzy Petri nets for modelling and analysing membrane systems

Hybrid modelling of biological systems: current progress and future prospects

“…Besides these two aforementioned types of HLQMs, Liu et al [ 7 ] proposed SPNs and CPNs with fuzzy kinetic parameters, where each kinetic parameter is either a crisp value or a fuzzy number if this parameter cannot be precisely estimated. To tackle even more complicated biological scenarios, Assaf et al [ 84 , 85 ] further proposed fuzzy hybrid PNs, and the coloured counterparts for these three fuzzy quantitative PN classes.…”

Modeling analysis of flight support vehicle scheduling based on fuzzy colored petri nets

“…In accordance with the modelling method of Petri net theory, the Petri net model of the flight support vehicle scheduling system [3] is established as shown in denotes the waiting region aircraft state numbered from 1 to i; the proposition set is D; the variation set is T [4] [5] .…”

A refinement and abstraction method of the SPZN formal model for intelligent networked vehicles systems

“…Weight vectors for the 𝑢𝑢 experts are obtained following evaluation, considering their professionalism and reliability, as shown in (12), 𝐹𝐹 = (𝑓𝑓 1 , 𝑓𝑓 2 , ⋯ , 𝑓𝑓 𝑢𝑢 ) (12) Equation 13 of the weighted average algorithm allows us to readily derive (14), where 𝑇𝑇𝑇𝑇 𝑡𝑡𝑡𝑡𝑎𝑎𝑛𝑛𝑡𝑡𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡𝑛𝑛 represents the vector of weighted average time delays across all transitions.…”

“…According to (10), a matrix depicting the average trigger delay for six experts across six transitions can be obtained, as demonstrated in (20), Considering the varying professional levels of these six experts, a weight vector 𝐹𝐹 = (0.23, 0.08, 0.13, 0.2, 0.18, 0.18) is derived after evaluation. Subsequently, utilizing (14), the weighted average time delay vector for the six transitions can be determined, as presented in (21), The implementation rate of each transition can be easily obtained by considering the reciprocal relationship between the transition implementation rate and the transition trigger delay, as illustrated in Table 7. The steady-state probability for various markings can be calculated using (9), Table 8 presents the steady-state probabilities for each flag displayed in Fig.…”

“…Formal method is a verification method based on mathematics and logic, which is used to formally describe the behavior and properties of the system, and reason and analyze it [10][11][12]. Formal methods are often widely used in biology [13,14], hardware [15], software [16], industry [17][18][19] and other fields. In intelligent networked vehicle systems, formal methods can be used to establish precise mathematical models to describe the states, events, and transition rules of the system.…”