belong to the class they indicate the selection of the classification points and the postulated classification rule determine the result of the classification when fractional probabilities for a classified point have been determined a u201c hard u201d classification can be obtained by e g assigning the point to the class with the highest posterior probability the class membership attribute then simplifies to a simple indicator of the class to which an attribute vector is assigned similar to the classification according to the nearest classification point such a hard classification divides the attribute space into zones as illustrated in fig3 b dashed lines indicate zone boundaries so that each attribute vector belongs to only one of the classes if a location in interpretation space has an associated attribute vector that vector belongs to one of the classes attribute vector a lies in the triangle class vector b lies in the circle class and each of both vectors is found at several locations in the interpretation space for the sake of clarity only a few characterizing points are shown in interpretation and attribute space note that the boundaries of classes obtained by such a classification are in general not plane surfaces or straight lines polygons but are typically curved in interpretation space several regions can.