Fuzzy reasoning supported by Petri nets

We develop a representational model for the knowledge base (KB) of fuzzy production systems with rule chaining based on the Petri net formalism. The model presents the execution of a KB following a data driven strategy based on the sup-min compositional rule of inference. In this connection, algorithms characterizing different situations have been described, including the case where the KB is characterized by complete information about all the input variables and the case where it is characterized by ignorance of some of these variables. For this last situation we develop a process of “incremental reasoning”; this process allows the KB to take information about previously unknown values into consideration as soon as such information becomes available. Furthermore, as compared to other solutions, the rule chaining mechanism we introduce is more flexible, and the description of the rules more generic. The computational complexity of these algorithms is O((C/2+M+N)R²) for the “complete information” case and O((M+N)R²) and O(2(M+N)R²) for the other cases, where R is the number of fuzzy conditional statements of the KB, M and N the maximum number of antecedents and consequents in the rules and C the number of chaining transitions in the KB representation