The fuzzy belief Petri net we propose in this paper propagates fuzzy beliefs from observations at nodes that represent measured parameters to fuzzy beliefs of the truths of parameters at hidden and decision nodes. The fuzzy influences spread from the observation nodes throughout our new enhanced bidirectional fuzzy belief Petri net. Compared with Bayesian belief networks, it is simpler and faster in that it needs neither the conditional probability tables that are difficult or impossible to obtain nor is it overly constrained by the mathematical axiomatic structure that makes Bayesian belief inferencing NP-hard. Compared with our previous fuzzy belief networks, it is more flexible in modeling particular situations. We develop here the concept, data structures and algorithm for this network, while future work will make comparative runs.

We survey research of recent years on the supervised training of feedforward neural networks. The goal is to expose how the networks work, how to engineer them so they can learn data with less extraneous noise, how to train them efficiently, and how to assure that the training is valid. The scope covers gradient descent and polynomial line search, from backpropagation through conjugate gradients and quasi Newton methods. There is a consensus among researchers that adaptive step gains (learning rates) can stabilize and accelerate convergence and that a good starting weight set improves both the training speed and the learning quality. The training problem includes both the design of a network function and the fitting of the function to a set of input and output data points by computing a set of coefficient weights. The form of the function can be adjusted by adjoining new neurons and pruning existing ones and setting other parameters such as biases and exponential rates. Our exposition reveals several useful results that are readily implementable.

A paradigm is developed for a controller to learn to control an environment by use of a benefit measure to judge the control. Rules are acquired that fire in a stimulus-response fashion for control, and rules continue to be acquired to adapt to an evolving environment. The model includes both knowledge acquisition and skill refinement through bottom-up (data driven) learning of the top-down control strategy. It is more flexible than hardware learning systems such as ADELINE or MADELINE. The controller model self-organizes by acquiring rules, and adapts by continuing to update its rules while controlling an external environment. It does this by judging the benefit of feedback due to the selected control rules and keeping counts in cells from which a rule function is generated.>

A class of large-scale decision systems is described, and a multilevel, multi-intelligence information/knowledge/control structure is defined. The description is in a form that features the various levels of signal processing, data fusion, autonomous fuzzy logic and pattern recognition (via neural networks), system knowledge base, and personal expert system, and the way in which these processors are integrated so as to form an operational model for the overall decision system.>

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.>