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.
Priority wise channelization of resources is the key to successful environmental management, especially when funds are limited. The study in hand has successfully developed an algorithmic criterion to compare hazardous effects of Municipal Solid Waste (MSW) dumping sites quantitatively. It is a Multi Criteria Analysis (MCA) that has made use of the scaling function to normalize the data values, Analytical Hierarchy Process (AHP) for assigning weights to input parameters showing their relevant importance, and Weighted Linear Combination (WLC) for aggregating the normalized scores. Input parameters have been divided into three classes namely Resident’s Concerns, Groundwater Vulnerability and Surface Facilities. Remote Sensing data and GIS analysis were used to prepare most of the input data. To elaborate the idea, four dumpsites have been chosen as case study, namely Old-FSD, New-FSD, Saggian and Mahmood Booti. The comparison has been made first at class levels and then class scores have been aggregated into environmental normalized index for environmental impact ranking. The hierarchy of goodness found for the selected sites is New-FSD > Old-FSD > Mahmood Booti > Saggian with comparative scores of goodness to environment as 36.67, 28.43, 21.26 and 13.63 respectively. Flexibility of proposed model to adjust any number of classes and parameters in one class will be very helpful for developing world where availability of data is the biggest hurdle in research based environmental sustainability planning. The model can be run even without purchasing satellite data and GIS software, with little inaccuracy, using imagery and measurement tools provided by Google Earth.