A CENTERED FORMULATION OF TAKAGI-SUGENO RULES FOR IMPROVED LEARNING EFFICIENCY

We derive the Gradient Descent optimization equations for Takagi-Sugen o fuzzy rule bases learning with symmetric triangular membership funct ions, Minimum operator (as AND operator), and affine output functions (standard Sugeno rules). A new type of affine output Takagi-Sugeno rul es called 'centred Takagi-Sugeno rules' is proposed. As proved on a si mple example, it enables to avoid convergence problems which appear in precisely defined cases (especially when there are many rules or when the variation domain of the inputs is not centred around zero). Gradi ent Descent is tested for the approximation of a specially built one-i nput, one-output analytical function including a discontinuity and a h igh curvature point, and for the approximation of two-input functions. Test and theoretical results are consistent, and show that the propos ed method is more efficient when the stated conditions are verified.