Resumen
The subject of research in the article are the processes of formalization of the pixel-by-pixel classification problem using the modified fuzzy neural production network of Wang-Mendel for segmentation of urban structures in the automated analysis of space and aerial photographs of the city. The purpose of the work is to develop the architecture of the modified fuzzy neural production network of Wang-Mendel as a classifier for image segmentation to increase the values of efficiency and reliability of urban monitoring. The following tasks are solved in the article: analysis of possibilities of Wang-Mendel network modification based on representation of membership functions in terms of interval fuzzy sets of the second type (IFST2) and realization of phasing, aggregation and activation operations using IFST 2 operations, development of the architecture of the modified fuzzy neural production network of Wang-Mendel as a classifier for image segmentation. The following methods and models are used: methods and models of fuzzy set theory (fuzzy Wang-Mendel neural network, interval fuzzy sets of the second type), methods and models of deep learning methodology (convolutional neural network for image segmentation (auto coder) U-net). The following results were obtained: the use of a fuzzy Wang-Mendel neural network as a classifier of a modified U-Net decoder based on the representation of membership functions in IFST2 and the implementation of phasing, aggregation and activation operations using operations on IFST2; introduction of an additional operation of type reduction in the phase of dephasification of the original variable based on the classical method of the center of gravity (centroid); introduction of several outputs of the network to recognize the appropriate number of classes (subclasses) of the subject area. To do this, the third layer is represented as a set of several pairs of adder neurons, and the fourth implements several normalizing neurons, the number of which corresponds to the number of pairs of the third layer. Conclusions: the use in the architecture of a convolutional neural network for segmentation of U-net images as a classifier of the modified fuzzy neural production network of Wang-Mendel will provide an additional increase in the accuracy of pixel-by-pixel classification of certain objects. Instead of fuzzy sets of the first type (FST1) in this network IFST2 are used. The proposed IFST2, on the one hand, provide a formalization of more additional degrees of uncertainty compared to FST1, on the other hand, are "implemented" in the development of fuzzy systems (models) and have less computational complexity, compared to fuzzy sets of the second type (FST2).