| Petri net is a combination model with graphical representation, which is intuitive, easy tounderstand and easy to use. It has unique strength for description and analysis of concurrentphenomenon. At the same time, Petri nets is strictly defined mathematical object, by means of netsystem structure, analysis method and technology of Petri nets can be used not only to the staticstructure analysis, but also to the dynamic behavior analysis. After 40 years of development, Petrinets have become formal system modeling, model analysis and testing methods and technicalsystem. It has been successfully applied in computer science and technology (such as networkprotocols, software design, artificial intelligence, etc), automatic science and technology (such asdiscrete event dynamic system, hybrid system, etc.), mechanical design and manufacturing (such asflexible manufacturing systems) and many other fields of science and technology. The variousexpanded forms of Petri nets, can not only help to understand qualitatively the dynamic behavior ofmodeling system, but also to calculate quantitatively various performance indicators for the systemstructure design and parameter selection. Combined the classical Petri nets and fuzzy set theory, thispaper focuses on the dynamic behavior of fuzzy Petri nets, in order to better model and analyze theactual system. Fuzzy Petri nets have various features of Petri nets and can broaden the applicationfields of Petri nets.This paper firstly introduces the background of this topic and the state of art at home andabroad, and then illustrates the purpose and significance of the research project combining currentstudy status and the actual applications of this topic. Later on, it describes the basic theory andrelated properties operations of Petri nets. The fuzzy Petri net is given many different definitions indifferent literature. This paper introduces the basic definition and computation rules of fuzzy Petrinets, and describes the general formal algorithm based on the incidence matrix. Then introduces thebasic concept of continuous Petri nets briefly, by studying operation rules of the fuzzy Petri nets andcontinuous Petri nets, we discussed the relationship between them. It is concluded that the fuzzyPetri nets can be converted into a special continuous Petri nets in certain conditions, which canmake fuzzy Petri nets transform into continuous Petri nets. The fuzzy Petri systems can takeadvantage of the relationship between them which gives some properties of fuzzy Petri nets. Sincethe current model of the fuzzy Petri most is based on fuzzy reasoning, and Petri nets is a directedgraph, this paper has also introduced the basic feedback theory of fuzzy Petri nets. In this papersynthetic operation of fuzzy Petri nets is proposed on the basis of synthetic operations of Petri nets,and defined sharing synthesis, synchronous synthesis and link synthesis for the fuzzy Petri nets, andthen from the perspective of the incidence matrix, we discussed the relationship between the subnet and synthesis network, sharing synthesis and synchronous composition, which can be clearly andeasily defined by use of incidence matrix of subnets.This paper transform fuzzy Petri nets into a continuous Petri nets in certain conditions, so wecan use the rich theory of continuous Petri nets to research the nature of fuzzy Petri nets. In addition,synthetic operation of fuzzy Petri nets is proposed on the basis of synthetic operations of Petri nets.It not only provides a good approach for analysis of complex fuzzy Petri nets but also enriches thetheory of fuzzy Petri nets. Finally, a comprehensive summary to this topic is presented; thedrawbacks and future research directions are pointed out. |
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