@ARTICLE{Mrówczyńska_Maria_Approximation_2010,
 author={Mrówczyńska, Maria},
 volume={vol. 59},
 number={No 1},
 journal={Geodesy and Cartography},
 howpublished={online},
 year={2010},
 publisher={Commitee on Geodesy PAS},
 abstract={The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules “if-then”, generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of “classic” neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.},
 type={Artykuły / Articles},
 title={Approximation abilities of neuro-fuzzy networks},
 URL={http://journals.pan.pl/Content/105910/PDF/art2.pdf},
 doi={10.2478/v10277-012-0006-9},
 keywords={neural network, neuro fuzzy system, clustering},
}