Defining separability of two fuzzy clusters by a fuzzy decision hyperplane

摘要

The aim of this paper is to propose a definition for separability of two fuzzy clusters of a training set and to give implementation methods to be used in a supervised learning environment. Fuzzy decision hyperplanes are defined as pairs consisting of a classical hyperplane and a non-decreasing function with subunitary values. This function approximates the membership degrees of the training set objects situated at a certain distance from the hyperplane. Our definition allows modelling the fuzzyness of the border between the two fuzzy clusters, an aspect which has not been solved by previous definitions. The decision error of a given fuzzy decision hyperplane is defined and its minimization is investigated. The results obtained are illustrated by a numerical example.