关键词: 模糊Petri网, 层次化, 逆向搜索, 虚库所-虚变迁对, 关联矩阵

Abstract:

Fuzzy Petri Net （FPN） is one of the main tools to represent， model， and analyze the Knowledge-Based System （KBS）. For clear hierarchical structures and uncertain affiliations between places/transactions in some FPNs， a Hierarchical algorithm of FPN by Reverse Search （HFPN-RS） was proposed to realize the automatic conversion from a non-hierarchical FPN to a Hierarchical FPN （HFPN）. Firstly， a reverse search of the entire FPN was launched starting from the output place（s） at first. The front set of input place（s） and the back set of output place（s） were divided into the same layer. Then， the hierarchical structure of the entire FPN was clarified by adding virtual place-virtual transition pairs. Meanwhile， two theorems were proven to define the infimum of the number of hierarchical layers of FPN and the minimum number of virtual place-virtual transition pair（s） that need to be added in the hierarchical operation， respectively. Moreover， the dimension calculation formula of the incidence matrix of the complete hierarchical structure was also introduced. In the experimental part， hierarchical operation was performed on several types of FPN models with different characteristics and the proposed theorems were used to verify the HFPN-RS algorithm. The experimental results show that the new FPN has a clear hierarchical structure by adding the virtual place-virtual transition pair（s）. It provides a theoretical base to further study the FPN generalization ability.

Key words: Fuzzy Petri Net (FPN), hierarchy, reverse search, virtual place-virtual transition pair, incidence matrix