Smooth functions and local extreme values
Computational Statistics & Data Analysis
Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra
Journal of Global Optimization
Fuzzy transform in the analysis of data
International Journal of Approximate Reasoning
A neural network approach to the fuzzy transform
Fuzzy Sets and Systems
Introduction to Nonparametric Estimation
Introduction to Nonparametric Estimation
Fuzzy transforms method and attribute dependency in data analysis
Information Sciences: an International Journal
Fuzzy transforms: Theory and applications
Fuzzy Sets and Systems
Fuzzy transforms of monotone functions with application to image compression
Information Sciences: an International Journal
Fuzzy transforms for compression and decompression of color videos
Information Sciences: an International Journal
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The fuzzy transform (F-transform) has some interesting properties that allow its use in curve fitting and smoothing. We suggest the following: (a) a generalization of fuzzy partitions for the F-transform to control and improve the smoothing effect and (b) a parametrization of the fuzzy numbers constituting the basic functions related to the fuzzy partitions. An optimization criterion is then suggested to obtain the F-transform with best approximation properties, by estimating the basic functions from a family of parametric fuzzy numbers. The generalized fuzzy partitions are characterized by the number of subintervals (the bandwidth of the partition) forming the core of each basic function and we suggest two procedures for bandwidth selection: one based on taut-string variation and a second based on generalized cross validation. Some illustrative examples are included.