Rough Neurons: Petri Net Models and Applications

Abstract

This chapter presents Petri net models for two forms of rough neural comput-ing: training set production and approximate reasoning schemes (AR schemes) defined in the context of parameterized approximation spaces. The focus of the first form of rough neural computing is inductive learning and the production of training (optimal feature set selection), using knowledge reduction algorithms. This first form of neural computing can be important in designing neural networks defined in the context of parameterized approximation spaces. A high-level Petri net model of a neural network classifier with an optimal feature selection procedure in its front end is given. This model is followed by the development of a number of Petri net models of what are known as elementary approximation neurons (EA neurons). The design of an EA neuron includes an uncertainty function that constructs a granule appro-ximation and a rough inclusion (threshold activation) function that measures the degree to which granule approximation is part of a target granule. The output of an EA neuron is an elementary granule. There are many forms of elementary granules (e.g., conjunction of de-scriptors, rough inclusion function value). Each of the EA neurons considered in this chapter output a rough inclusion function value. An EA neuron can be designed so that it is trainable, that is, a feedback loop can be included in the design of the EA neuron so that one or more approximation space parameters can be tuned to improve the performance of the neuron. The design of three sample EA neurons is given. One of these neurons behaves like a high-pass filter.