Improvement of First-order Takagi-Sugeno Models Using Local Uniform B-splines

First-order Takagi-Sugeno models are mainly based on the interpolation between several local affine functions usually defined on trapezoidal fuzzy partitions. The standard computational model presents some shapefailures: 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 improved model that primarily transforms the original first-order trapezoidal TS system into an equivalent zeroorder triangular TS one. Furthermore, for each univariate transition region: two equidistant triangular labels are added, one at each end of the corresponding interval, to capture the information of derivatives of the affine functions. Finally in each transition region, a local even box filter is applied to the corresponding four triangular labels in order to obtain a local uniform quadratic B-spline partition. This transform preserves the original affine functions in the reduced cores of the original fuzzy partition and converts the intermediate C piecewise linear-multilinear output function into a C piecewise linearmultiquadratic one.