Finite convergence of a fuzzy δ rule for a fuzzy perceptron

A learning algorithm based on a fuzzy δ rule is proposed for a fuzzy perceptron with the same topological structure as conventional linear perceptrons. The inner operations involved in the working process of this fuzzy perceptron are based on the max-min logical operations rather than conventional multiplication and summation etc. The initial values of the network weights are fixed as 1. Each value of the network weights is non-increasing in the training process, and it will keep unchange when the value is less than 0.5. The learning algorithm has an advantage, as is proved in this paper, that it converges in finite steps if the training patterns are fuzzily separable. This result generalizes a corresponding classical result for conventional linear perceptrons. Some numerical experiments for the learning algorithm are provided to support our theoretical findings.