N2 - 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.
JO - Geodesy and Cartography
L1 - http://www.czasopisma.pan.pl/Content/105910/PDF/art2.pdf
L2 - http://www.czasopisma.pan.pl/Content/105910
IS - No 1
KW - neural network
KW - neuro fuzzy system
KW - clustering
ER -
A1 - Mrówczyńska, Maria
PB - Commitee on Geodesy PAS
VL - vol. 59
JF - Geodesy and Cartography
T1 - Approximation abilities of neuro-fuzzy networks
UR - http://www.czasopisma.pan.pl/dlibra/docmetadata?id=105910
DOI - 10.2478/v10277-012-0006-9