In this paper, we first study the stability and convergence property of fuzzy logic networks (FLN). A random approach is adopted to simulate the convergence speed and steady-state properties based on four fuzzy logical functions. The simulation results show that MV logical function causes the system to be on the edge of chaos when the number of nodes increases. Thus this logical function is more useful to infer real complex networks, such as gene regulatory networks. Then, a novel gene regulatory network inference algorithm based on the FLN theory is proposed and tested. The algorithm uses fuzzy logical functions to model gene regulatory relationships, and the degrees of regulations are represented as the length of accumulated distances during a period of time intervals. Based on the assumption that the distribution of connectivity in yeast protein-protein networks follows the Zipf's law, the criteria for algorithm parameter quantifications are deduced. One unique feature of this algorithm is that it makes limited a priori assumptions concerning the modeling; hence the algorithm is categorized as a data-driven algorithm. The algorithm was applied to the S. pombe time-series dataset and 407 cell cycle regulated genes were used. The algorithm inferred 59 functionally verified regulations, 47 regulations involving genes with unknown functions, and 19 dubious regulations. The 125 regulatory pairs involve 108 genes, and the average connectivity of the inferred network, 1.157, confirms the Zipf's law.
