**Author details**

174 Petri Nets – Manufacturing and Computer Science

**Figure 16.** Comparison of two discovery methods

**6. Conclusion** 

requested service and invoked service is defined as a root of sum of three CO's squares. When a user invoking comes, it is compared with all services in services repository. Then, one service in *Dinv*, which has the biggest proximity value with *Duser*, was selected. We compared the discovery precision probability of this method (conventional method) with the proposed LFPNSD. The simulation results are shown in Figure 16. The LFPNSD method yielded higher precision probabilities than the conventional method proposed in [21]. Especially when the service number of Web services' repository becomes more than 88, the difference is much more significant. Here, a correct service is selected in 14 services, 24 services, 37 services, 54 services, 88 services, 151 services just as they were used in [21].

In this chapter, Learning Petri net (LPN) was constructed based on High-level Time Petri net and reinforcement learning (RL). The RL was used for adjusting the parameter of Petri net. Two kinds of learning algorithm were proposed for Petri net's discrete and continuous parameter learning. And verification for LPN was shown. LPN model was applied to dynamical system control. We had used the LPN in three robot systems control - the AIBO, Guide Dog. The LPN models were found and controlled for these robot systems. These robot systems could adjust their parameters while system was running. And the correctness and effectiveness of our proposed model were confirmed in these experiments. LPN model was improved to the hierarchical LPN model and this improved hierarchical LPN model was applied to QoS optimization of Web service composition. The hierarchical LPN model was constructed based on stochastic Petri net and RL. When the model was used, the Web service composition was modeled with stochastic Petri net. A Web service dynamical composing framework is proposed for optimizing QoS of web service composition. The neural network learning method was used to Fuzzy Petri net. Learning fuzzy Petri net (LFPN) was proposed. Contrasting with the existing FPN, there are three extensions in the new model: the place can possess different tokens which represent different propositions; Liangbing Feng, Masanao Obayashi, Takashi Kuremoto and Kunikazu Kobayashi *Division of Computer Science & Design Engineering, Yamaguchi University, Ube, Japan*

Liangbing Feng *Shenzhen Institutes of Advanced Technology, Shenzhen, China* 
