Fuzzy Petri Nets

Because normal Petri net cannot deal along with vague or fuzzy information as like: "very high" and "good", the idea of FPN or Fuzzy Petri Nets has been initiated. As a model of knowledge based systems, Fuzzy Petri Nets are employed for fuzzy knowledge reasoning and representations. Furthermore, by implementation of Fuzzy Petri Nets models, major features offered by Petri Net models still hold good and such can be applied. Petri Net has an inherent quality in showing the logic in an intuitive and visual manner therefore can also simulate systems in operations. Moreover, a Fuzzy Petri Nets theory can also offers means to manipulate vague and imprecise information.

In this subdivision we emphasize the power of Petri net in phrases of knowledge representation, inconsistency checking, knowledge learning and uncertainty management. Our major focus will be on knowledge representation via weighted fuzzy production rules and inference along with Fuzzy Petri Nets. Further, a slight enhancement to Fuzzy Petri Nets resulted in Adaptive Fuzzy Petri Nets or AFPN. This Adaptive Fuzzy Petri Nets cannot simply do knowledge inference although, also has a learning ability like Neural Networks or NN. This is supposed that the reader previously has a background of Fuzzy Theory and Neural Networks before going via this section.

Definition: Fuzzy Petri Nets

Usually a Fuzzy Petri Net is defined as an 8-tuple in mathematical notation as given below:

FPN = {P, T, D, I, O, α, β}

Here

P = { p1 , p2 , ... , pn } indicates a set of places,

T = {t1 , t2 , . . . , tn } indicates a set of transitions,

D = {d1 , d2 , ... , dn } indicates a set of propositions,

P ∩ T ∩ D = φ

| P | = | D |. I (O): T → P∞

Above is an input output function a mapping from transition to bags of places.

f: T → [0, 1] is a relationship function that assigns a real time value among zero to one to each place and,

α: P → [0, 1] is a relationship function that assigns a real value in between 0 to 1 TP each place.

β: P → D is a objective mapping between the place label and proposition for each node.

A Fuzzy Petri Nets can deal along with various types of compound fuzzy production rules and can hence decode mystic logic implication relations. Fuzzy Petri Nets has the advantage of supporting the execution and representation of fuzzy rules and by combining along with some other techniques; this can prove to be very helpful in several actual application.