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

In this paper, a new approach is presented forthe evaluation of membership functions in fuzzy clusteringalgorithms. Starting from the geometrical representation of clustersby polygons, the fuzzy membership is evaluated througha suited point-to-polygon distance estimation. Three differentmethods are proposed, either by using the geometrical propertiesof clusters in the data space or by using Gaussian or coneshapedkernel functions. They differ from the basic trade-offbetween computational complexity and approximation accuracy.By the proposed approach, fuzzy clusters of any geometricalcomplexity can be used, since there is no longer required toimpose constraints on the shape of clusters resulting from thechoice of computationally affordable membership functions. Themethods illustrated in the paper are validated in terms of speedand accuracy by using several numerical simulations.