A new hybrid-system method of Machine Learning using a new method of fractal geometry and a new method of graph theory

In the paper we present a hybrid system method to predict the volume of the robot-laser-hardened specimens when one of the parameters in the existing model cannot be measured or calculated the intelligentsystem. Also, we have a model of the intelligent system to predict the volume of hardened specimens developed by someone, but we can not calculate one parameter in it. Thus, we develop a new method of the hybrid intelligent system to solve this problem. We develop a hybrid of genetic programming and multiple regression. To predict the volume of hardened specimens, we use teh neural network, genetic algorithm and multiple regression. The genetic programming modelling results show a good agreement with the measured volume of hardened specimens. We analyse the SEM picture of the microstructure of robot-laser-hardened specimens with a mathematical method. In this open problem we use the graph theory and fractal geometry. Fractal dimensions are calculated using image processing of a SEM micrographs in combination with a box-counting algorithm using ImageJ software.