Fuzzy Petri nets for rule-based decisionmaking

The technique of fuzzy reasoning by transformations of fuzzy truth state vectors by fuzzy matrices is extended to Petri nets. The result is a novel type of neural network in which the transition bars serve as the neutrons, and the nodes are conditions. Conditions may be conjuncted and disjuncted in a natural way to allow the firing of the neurons. The neuron fires to feed the implication truths into one or more consequent conditions when the MIN of the truth values of the antecedent conditions is greater than the neuron threshold. Disjunctions are also modeled in a natural way. Modifications are made to the usual Petri model to allow fuzzy rule-based reasoning by propositional logic. First, fuzzy values are allowed for rules and truths of conditions that appear in rules. Next, multiple copies, rather than the original, of the fuzzy truth tokens are passed along all arrows that depart a node or transition bar where the truth resides. An algorithm is presented for reasoning using these networks, as well as a simple example for exercising the algorithm. Abduction may be done analogously be reversing all arrows and propagating truth tokens backwards