Extraction of Fuzzy Rules Using Sensibility Analysis in a Neural Network

This paper proposes a new method for the extraction of knowledge from a trained type feed-forward neural network. The new knowledge extracted is expressed by fuzzy rules directly from a sensibility analysis between the inputs and outputs of the relationship that model the neural network. This easy method of extraction is based on the similarity of a fuzzy set with the derivative of the tangent hyperbolic function used as an activation function in the hidden layer of the neural network. The analysis performed is very useful, not only for the extraction of knowledge, but also to know the importance of every rule extracted in the whole knowledge and, furthermore, the importance of every input stimulating the neural network. Introduction This paper proposes a new method for the extraction of knowledge from an artificial neural network (NN) that is represented by fuzzy rules. The quality of the rules extracted and the easy method used to obtain them improve the current procedures used in this field until now [4]. The rules derived from the NN can be used for several purposes: Knowledge representation in fuzzy terms of the relationships modelled by the NN Suggestion of modifications for the architecture of the NN studied by adding new knowledge required or eliminating some knowledge not needed. Retraining of particular zones of the NN with less knowledge. Possible complement of the knowledge of an expert system by the addition of the knowledge extracted from the NN This method is based on a set of procedures that analyse how and when the neurons are activated by a particular input, the importance of the inputs for the NN prediction and the monitoring of its performance. An important parameter obtained from the new method is the reliability of the knowledge included in the rules extracted. This is key information to be taken into account in many applications such as failure detection, or adaptive control. Type of NN analysed The methodology proposed for knowledge extraction has been analysed and tested using feed forward NN [1]. In particular, this paper pays attention to the feed forward NN consisting of three layers: input, hidden and output. The neurons located in the hidden layer have a hyperbolic tangent activation function and the neurons in the output layer have a linear activation function. The notation that will be used for the analysis of this NN is represented as follows. Let e be a vector with n components corresponding to the inputs exciting the NN. Let m be the number of neurons at the NN hidden layer. The activation weights between the input and hidden layers are represented by the mxn matrix W1. The activation weights between the hidden and the output layers are represented by the pxm matrix W2, where p is the number of outputs in the NN. The vectors 1 b and 2 b will represent the bias of the hidden and output layers, with dimensions m and p respectively. Method for fuzzy explanation of a NN According to the notation described, the mathematical equation 1 represents the ith output of the NN.