A decomposition algorithm of fuzzy Petri net using an index function and incidence matrix

Abstract

As with Petri nets (PNs), the state space explosion has limited further studies of fuzzy Petri net (FPN), and with the rising scale of FPN, the algorithm complexity for related applications using FPN has also rapidly increased. To overcome this challenge, we propose a decomposition algorithm that includes a backwards search stage and forward strategy for further decomposition, one that divides a large-scale FPN model into a set of sub-FPN models using both a presented index function and incidence matrix. In the backward phase, according to different output places, various completed inference paths are recognized automatically. An additional decomposition operation is then executed if the "OR" rule exists for each inference path. After analysing the proposed algorithm to confirm its rigor, a proven theorem is presented that calculates the number of inference paths in any given FPN model. A case study is used to illustrate the feasibility and robust advantages of the proposed decomposition algorithm.