The Relational Equations approach is one of the most usual ones for describing (Fuzzy) Systems and in most cases, it is the final expression for other descriptions. This is why the identification of Relational Equations from a set of examples has received considerable atention in the specialized literature. This paper is devoted to this topic, more specifically to the topic of max-min neural networks for identification. Three methods of learning Fuzzy Systems are developed by combining the most...
In previous papers, we presented an empirical methodology based on Neural Networks for obtaining fuzzy rules which allow a system to be described, using a set of examples with the corresponding inputs and outputs. Now that the previous results have been completed, we present another procedure for obtaining fuzzy rules, also based on Neural Networks with Backpropagation, with no need to establish beforehand the labels or values of the variables that govern the system.
We have shown a model of fuzzy neural network that is able to infer the relations associated to the transitions of a fuzzy automaton from a fuzzy examples set. Neural network is trained by a backpropagation of error based in a smooth derivative [1]. Once network has been trained the fuzzy relations associated to the transitions of the automaton are found encoded in the weights.
In previous works, we have presented two methodologies to obtain fuzzy rules in order to describe the behaviour of a system. We have used Artificial Neural Netorks (ANN) with the Backpropagation algorithm, and a set of examples of the system. In this work, some modifications which allow to improve the results, by means of an adaptation or refinement of the variable labels in each rule, or the extraction of local rules using distributed ANN, are showed. An interesting application on the assignement...
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