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|a The state explosion problem has limited further research of Fuzzy Petri Net (FPN). With the rising scale of FPN, the algorithm complexity for related applications using FPN has also rapidly increased. To overcome this challenge, this research proposed three algorithms, which are transformation algorithm, decomposition algorithm and bidirectional reasoning algorithm to solve the state explosion problems of knowledge-based system (KBS) modelling and reasoning using FPN. Based on the goal of this research, the entire research is separated into two tasks, which are KBS modelling and reasoning using FPN. In modelling, a transformation algorithm has been proposed while in reasoning, decomposition and bidirectional reasoning algorithms have been proposed. In transformation, the algorithm is proposed to generate an equivalent large-scale FPN for the corresponding large-size KBS using a novel representation method of Fuzzy Production Rule (FPR). In decomposition, the algorithm is proposed to separate a large-scale FPN into a group of sub-FPNs by using a presented index function and incidence matrix. In bidirectional reasoning, the algorithm for optimal path is proposed to implement inference operations. Experimental results show that all proposed algorithms have successfully accomplished the requirements of each link of KBS modelling and reasoning using large-scale FPN. First, the proposed transformation algorithm owns ability to generate the corresponding FPN for the large-size KBS automatically. Second, the proposed decomposition owns ability to divide a large-scale FPN into a group of sub-FPNs based on the inner-reasoning-path. Lastly, the proposed bidirectional reasoning algorithm owns ability to implement inference for the goal output place in an optimal reasoning path by removal of irrelevant places and transitions. These results indicate that all proposed algorithms have ability to overcome the state explosion problem of FPN.
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