Research Of Reduction Techniques And Closed Loop Model Of Fuzzy Petri Nets

Petri nets are a graphical and mathematical modeling tool applicable to many systems. They are a promising tool for describing and studying information processing systems and their main characteristics include the following: parallelism, uncertainty, asynchronous, distributed and analyzing ability. Petri nets, as a graphical mathematical tool, provide a uniform environment for modeling, formal analysis and design of discrete event systems. The important information of the simulated systems and its behavior can be revealed through the network model of the actual systems. After several decades of development, Petri nets have not only formed a systemic and independent subject, and have been widely applied in many scientific and technology systems such as mechanical design and manufacturing system, discrete event systems, computer science and technology, automation science and technology. Because of the uncertainty and ambiguity of the real world, Petri nets have their drawbacks in modeling the actual systems. Therefore this thesis combines classic Petri nets with fuzzy sets, emphasizing the system behavior of fuzzy Petri nets, to better model and analyze in the real systems. Fuzzy Petri nets have various features of Petri nets, and extend the behavior of the Petri nets.This thesis firstly introduces the state of art of Petri nets, describes this topic in detail from two aspects of theory and application, and then illustrates the research purpose combining current research state and the actual application of this topic. Later on, it gives the basic theory and the related properties of Petri nets, and similarly describes the fundamental theory of fuzzy Petri nets, then addresses the formal algorithm based on relation matrix. Secondly, a novel type of fuzzy Petri nets named fuzzy closed loop Petri nets (FCLPN) is proposed in this paper. It forms a closed-loop dynamic system, thus the applications of the present fuzzy Petri nets are expanded. It can be better applied to the system which is interrelated and mutually influenced each other such as the economic systems. A sensitivity vector is introduced to characterize the degree of response of every place to the external stimulation. And then the algebraic matrix computation method is presented to formally describe the dynamic operating process of the fuzzy Petri nets. And meanwhile the whole process of state vectors can be obtained. Furthermore, the reduction techniques of fuzzy Petri nets are proposed based on Petri nets. The reduction rules in several cases are proposed to simplify fuzzy Petri nets without changing their dynamic behavior, in some cases such as places and transitions in series connection, places and transitions in parallel connection respectively.This thesis originally put forward a fuzzy Petri nets model composed of closed loop system, which can effectively model and analyze the interconnected, mutual influence system such as economic system, ecological systems and so on. The proposed reduction techniques of Fuzzy Petri nets not only simplify the models, but also can keep the various properties and operating states of original systems. Finally, a comprehensive summary to this topic is given; the drawbacks and future research directions are pointed out.