Knowledge base generation based on fuzzy clustering

The article states fuzzy Takagi–Sugeno rule base generation problem based on ellipsoidal clustering. After obtaining clusters of ellipsoidal shape the problem of building minimal volume ellipsoids, enclosing all clusters points, appears. The premises of the generated fuzzy rules are formed by constructing projections of ellipsoids on the coordinate axis, and conclusions – either using ellipsoid axes, or based on the projection. In the article, the authors suggest to use Khachiyan’s algorithm for building minimal volume enclosing ellipsoid in order to increase the accuracy of approximation and they compare two approaches of choosing optimal parameters of ellipsoids which enclose all clusters points.