Research On Weighted Fuzzy Petri Net And Its Applications In Imprecise Knowledge Representation And Reasoning

As an efficient tool for modeling and analysis, in recent years, Petri nets have been rapidly developed. However, as a pure theoretical tool, Petri nets do not always meet the requirements of all applications. Therefore, aiming at research objects of different fields, many scholars proposed various extended Petri net theories, such as the stochastic Petri net, colored Petri net which have been universally applied in recent years, and so on. Being an important branch of the Petri net, the fuzzy Petri nets are increasingly attracted interest of the people. Since fuzzy Petri nets accord with the ways of human thinking and understanding, they act with broad meaning in the description and analysis of the parallel and concurrent actions of many physical systems and even social systems. Particularly, they are very appropriate for the applications of the human knowledge representation and artificial intelligence, and many scholars have been investigated in this context.In this paper, we studied the theory and method of the uncertainty knowledge representation and reasoning based on the weighted fuzzy Petri net (WFPN), and developed the WFPN knowledge reasoning experimental system based on the matrices operations. The contents of this paper are summarized as follow:(1) We investigated the uncertainty reasoning models based on the uncertainty factor. The threshold value, weight are incorporated in the uncertainty reasoning model based on the uncertainty factor, a weighted CF model containing threshold is proposed. We studied the basic concepts of the Petri net, formal description and analytical methods. In order to make the WFPN suitable for knowledge reasoning, we extended the transition firing rule of the WFPN and introduced the complementary arc into the WFPN. The weighted CF model containing threshold is incorporated in the extended WFPN for imprecise knowledge representation and reasoning.(2) We investigated the fuzzy reasoning algorithms based on fuzzy Petri nets. By introducing matrices operations into the reasoning algorithm, we proposed the formal algorithms of the WFPN based on the matrices operations used to perform the forward reasoning and backward reasoning respectively.(3) By using weighted fuzzy Petri net, the knowledge reasoning and consistence maintaining have been studied. We discussed and supplied two algorithms to solve the loop and contradict problem existed in the WFPN respectively.(4) We investigated the learning ability of the fuzzy Petri net, incorporated the BP algorithm of the neural network in the WFPN, and presented a learning algorithm based on the WFPN to learn the parameters of the input arcs (the weights of the propositions) of the WFPN. The application of the genetic algorithm for obtaining the parameters of the output arcs (the certainty factors of the rules) is discussed, and a related algorithm is presented.