Shape preserving splines in constructing WOWA operators: Comment on paper by V. Torra in Fuzzy Sets and Systems 113 (2000) 389-396

V. Torra in [8] presents an algorithm for constructing Weighted OWA operators [7] using interpolation (De9nition 1 in [8]). His method relies on the construction of a monotone increasing functionW (x) that interpolates the points (i=n; ∑ j6i wj) together with the origin, where the weights wj denote relative importance or reliability of information sources. In addition to being monotone, the functionW (x) is required to be a straight line if the data permits. As the interpolant, V. Torra uses the monotonicity preserving quadratic spline of McAllister and Roulier [5], which has also been used for representation of membership functions in [3]. I would like to draw attention to another, simpler algorithm for constructing monotone quadratic interpolating spline due to Schumaker [6]. Schumaker’s algorithm requires speci9cation of slopes at data points, however these slopes can be selected automatically using the method by Butland [2]. The modi9ed algorithm is described in detail in [4], and the pseudocode is presented in [1]. In [4] it was proven that with Butland slopes both algorithms produce identical results. However, Schumaker’s algorithm is far less complicated, more e?cient and requires fewer additional