**5. Petri networks as a manufacturing knowledge representation method**

Contemporary CAPP systems have the architecture of expert systems [8]. Systems based on rules prevail among knowledge representation methods applied in expert systems. Petri networks do not constitute a turning point here. They are only another variant of the rule method. However, it is a ready carrier of knowledge with a large potential of expanding its capabilities, flexible as frames, able to capture the context to the extent not smaller than semantic networks, allowing for intelligent inference by way of introducing fuzzy rules. An advanced suggestion for using Petri networks for knowledge representation in CAPP systems has been put forward in the work [15], the authors of which present characteristics of the component of a rule approach to knowledge representation and an approach based on Petri network. Multilateral usefulness of Petri networks at various stages of building and using expert systems should be noted. Starting from a knowledge acquisition system [22, 30], to knowledge representation in a knowledge database [31, 32], user interface handling [33], inference mechanism [32, 34] to knowledge validation [33], the Petri network technique is helpful in all of these aspects.

Knowledge engineers most frequently use the structural formalism of knowledge representation based on the Petri network technique. Logical Petri Net (LPN) allows for easy modeling and verification of knowledge. The work [30] puts forward a fuzzy inference algorithm and a backward propagation algorithm for Adaptive Fuzzy Petri Network (AFPN). AFPN might be a finished platform for an expert system allowing for knowledge acquisition based on a teaching set.

The following example uses a maximally simplified version of AFPN, which still is a logical fuzzy Petri network (Eq.(6)) in the form of organized five units:

$$PT\_{\mathfrak{z}} = \langle P, T, E, \mathfrak{a}, \mu \rangle. \tag{6}$$

**Figure 7.** A fragment of knowledge database represented in the form of a petri network.

Petri Networks in the Planning of Discrete Manufacturing Processes

http://dx.doi.org/10.5772/intechopen.75135

49

**Table 2.** List of places.

where *P* is a set of facts: premises and conclusions; *T*: a set of rule cores; *E*: flow relation; *α*: *P*→[0, 1], association function which assigns a real value to each *p*∈*P*; and *μ*: *T*→[0, 1], certainty factor of the rule.

*M0* functions are replaced here with α component. A rule in PT<sup>3</sup> includes *t* transition and a set of premises (input locations) and conclusions (output locations). The fuzzy nature of inference results from using fuzzy aggregation functions used for calculating the certainty factor (CF) of the generated conclusions. If a conclusion is generated by only one rule (**Figure 6a**), we

**Figure 6.** Setting the CF of conclusion.


**Table 2.** List of places.

**Figure 6.** Setting the CF of conclusion.

tainty factor of the rule.

*M0*

**5. Petri networks as a manufacturing knowledge representation** 

Contemporary CAPP systems have the architecture of expert systems [8]. Systems based on rules prevail among knowledge representation methods applied in expert systems. Petri networks do not constitute a turning point here. They are only another variant of the rule method. However, it is a ready carrier of knowledge with a large potential of expanding its capabilities, flexible as frames, able to capture the context to the extent not smaller than semantic networks, allowing for intelligent inference by way of introducing fuzzy rules. An advanced suggestion for using Petri networks for knowledge representation in CAPP systems has been put forward in the work [15], the authors of which present characteristics of the component of a rule approach to knowledge representation and an approach based on Petri network. Multilateral usefulness of Petri networks at various stages of building and using expert systems should be noted. Starting from a knowledge acquisition system [22, 30], to knowledge representation in a knowledge database [31, 32], user interface handling [33], inference mechanism [32, 34] to knowledge validation [33], the Petri network technique is helpful in all of these aspects.

Knowledge engineers most frequently use the structural formalism of knowledge representation based on the Petri network technique. Logical Petri Net (LPN) allows for easy modeling and verification of knowledge. The work [30] puts forward a fuzzy inference algorithm and a backward propagation algorithm for Adaptive Fuzzy Petri Network (AFPN). AFPN might be a finished platform for an expert system allowing for knowledge acquisition based on a teaching set. The following example uses a maximally simplified version of AFPN, which still is a logical

*PT*<sup>3</sup> = (*P*, *T*, *E*, *α*, *μ*), (6)

where *P* is a set of facts: premises and conclusions; *T*: a set of rule cores; *E*: flow relation; *α*: *P*→[0, 1], association function which assigns a real value to each *p*∈*P*; and *μ*: *T*→[0, 1], cer-

of premises (input locations) and conclusions (output locations). The fuzzy nature of inference results from using fuzzy aggregation functions used for calculating the certainty factor (CF) of the generated conclusions. If a conclusion is generated by only one rule (**Figure 6a**), we

includes *t* transition and a set

fuzzy Petri network (Eq.(6)) in the form of organized five units:

functions are replaced here with α component. A rule in PT<sup>3</sup>

**method**

48 Petri Nets in Science and Engineering

**Figure 7.** A fragment of knowledge database represented in the form of a petri network.

use fuzzy conjunction. Its CF is a product of premises of the rule and the CF of the very rule. If a conclusion is supported by two (**Figure 6b**) or more rules, fuzzy disjunction should be used. Its CF is a soft logical sum of indices generated by each of the rules separately. If the CF of transition is negative, what we have is a fuzzy negation (**Figure 6c**). All the three aggregation functions ensure maintaining CF between 0 and 1. Contrary to the previously presented PN1 and PN2 classes, PN3 class cannot include a loop. It is also allowed that a graph is inconsistent. The threshold value of certainty indices is defined as global for the entire network. **Table 2** presents a description and list of CF for the shown example. **Figure 7** puts forward a fragment of the manufacturing knowledge database related to the method of mounting parts on a lathe, developed using the mechanism presented above.

analysis, open and intuitive character. Solutions have been put forward for several years, also in the form of standards, presenting data representation for the Petri network model in a format based on the Petri Net Markup Language (PNML) [38]. PNML has been introduced as a data exchange format for all Petri network classes. All of this is a fundamental premise for formulating a favorable forecast for acceptance and quick popularization of AML language as

Petri Networks in the Planning of Discrete Manufacturing Processes

http://dx.doi.org/10.5772/intechopen.75135

51

**Figure 8** shows a scheme of an integrated production unit design system, taking into account data exchange streams and main functions of individual modules. Attention should be drawn

a data exchange language in industrial automation and its environment.

**Figure 8.** Data exchange streams in integrated manufacturing cell planning system.
