A truncated normalized max product set of equations and its solution for a recurrent fuzzy neural network

Defines the truncated normalized max product operation and provides an iterative method for solving a set of equations based on this operation. The operation may serve as the transformation for the set of fully connected units in a fully recurrent network that generally consists of linear threshold units as in a discrete generalized Hopfield network. Component values are not restricted to binary values as would be the case if the network consisted of linear threshold units but can now take on the values in the sets {0,0.1...0.9,1}, {0,0.01,...0.99,1} or similar sets of higher cardinality depending upon the degree of truncation specified. Each unit, although still having discrete output, can provide finer granularity. Due to truncation and normalization the network acting under this transformation has a finite number of states and components of the state vector are bounded. The operation defined can form the basis of transformations in a recurrent network with a finite number of states. This means that fixed points or cycles are possible and the network based on this operation for transformations can be used as an associative memory or pattern classifier with fixed points taking on the role of prototypes