Fuzzy Membership Functions Based on Point-to-Polygon Distance Evaluation

In this paper, a new approach is presented for the evaluation of membership functions in fuzzy clustering algorithms. Starting from the geometrical representation of clusters by polygons, the fuzzy membership is evaluated through a suited point-to-polygon distance estimation. Three different methods are proposed, either by using the geometrical properties of clusters in the data space or by using Gaussian or cone-shaped kernel functions. They differ from the basic trade-off between computational complexity and approximation accuracy. By the proposed approach, fuzzy clusters of any geometrical complexity can be used, since there is no longer required to impose constraints on the shape of clusters resulting from the choice of computationally affordable membership functions. The methods illustrated in the paper are validated in terms of speed and accuracy by using several numerical simulations.