Incorporating Fuzzy Membership Functions into the Perceptron Algorithm

The perceptron algorithm, one of the class of gradient descent techniques, has been widely used in pattern recognition to determine linear decision boundaries. While this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable, it exhibits erratic behavior if the data are not linearly separable. Fuzzy set theory is introduced into the perceptron algorithm to produce a ``fuzzy algorithm'' which ameliorates the convergence problem in the nonseparable case. It is shown that the fuzzy perceptron, like its crisp counterpart, converges in the separable case. A method of generating membership functions is developed, and experimental results comparing the crisp to the fuzzy perceptron are presented.