A FUZZY EXTENDED K-NEAREST NEIGHBORS RULE

The purpose of this paper is to describe an automatic fuzzy classification algorithm working in a partially supervised environment. This algorithm is based on the fuzzy labeling of samples by means of a membership function. As long as the membership function carries more information than the classical characteristic function, the concepts of clustering and discrimination are extended to the fuzzy field. First the learning set is fuzzily clustered. The membership function is based on a weighted k-nearest neighbors rule and does not require the optimization of any criterion. Second the test set is analyzed and a new membership function is proposed. As the learning set is generally incomplete, the creation of new fuzzy classes is studied. The measure of fuzziness involves some analogies with Statistical Thermodynamics, and the link between the membership function and the Fermi-Dirac statistical function is discussed. Finally results on simulated data are reported.