Fuzzy classification methods a variational approach

The proposed fuzzy classification model covers numerous conventional models as particular cases. A variational approach is described to design of such classifications. The dependence of the form of optimal classification on that of the classification performance functional and on the fuzziness type is studied. An iterative algorithm is proposed for maximizing the chosen functional and its convergence is proved. The general approach is illustrated for a conventional classification, a fuzzy classfication, and a classification with fuzzy boundaries.