Nonadditive grey single-layer perceptron with Choquet integral for pattern classification problems using genetic algorithms

Since the output of a single-layer perceptron can be interpreted as the synthetic evaluation of the relationship between the input pattern and one class for two-class pattern classification problems, this paper proposes a novel perceptron with nonadditive property, named the grey single-layer perceptron, by measuring the grades of relationship between an input pattern and this class for individual attributes with the grey relational analysis. A nonlinear integral, namely the Choquet integral, with respect to the fuzzy measure serves as an activation function of a neuron to synthesize the performance values owing to the interaction among attributes. Moreover, the connection weights are interpreted as the degrees of importance of the respective input signals and can be determined by the genetic algorithm-based learning algorithm. The experimental results further demonstrate that the generalization ability of the proposed grey single-layer perceptron is better than or comparable to that of other fuzzy or non-fuzzy classification methods.