A Shape-preserving Affine Takagi-Sugeno Model Based on a Piecewise Constant Nonuniform Fuzzification Transform

First-order Takagi-Sugeno systems are described by means of a set of affine functions defined on fuzzy regions usually specified by the corresponding trapezoidal tensor product. The standard computational model presents some shape-failures: the approximation does not preserve the positivity, monotony or convexity of the data that belong to the corresponding antecedent term cores. Moreover the standard output does not have a continuous derivative. This paper presents an alternative efficient model based on an initial transformation of the first-order trapezoidal TS model into a zero-order triangular TS model followed by a nonuniform first-order even B-spline filter applied to the corresponding triangular antecedent partition. The obtained output is a smooth piecewise multiquadratic C function.