Fuzzy integral-based perceptron for two-class pattern classification problems

The single-layer perceptron with single output node is a well-known neural network for two-class classification problems. Furthermore, the sigmoid or logistic function is usually used as the activation function in the output neuron. A critical step is to compute the sum of the products of the connection weights with the corresponding inputs, which indicates the assumption of additivity among individual variables. Unfortunately, because the input variables are not always independent of each other, an assumption of additivity may not be reasonable enough. In this paper, the inner product can be replaced with an aggregation value obtained by a useful fuzzy integral by viewing each of the connection weights as a value of a λ-fuzzy measure for the corresponding variable. A genetic algorithm is then employed to obtain connection weights by maximizing the number of correctly classified training patterns and minimizing the errors between the actual and desired outputs of individual training patterns. The experimental results further demonstrate that the proposed method outperforms the traditional single-layer perceptron and performs well in comparison with other fuzzy or non-fuzzy classification methods.