Application of fuzzy neural networks for defining crystal lattice types in nanoscale images

The article proposes the application of neural fuzzy networks for defining the overlapping classes of crystal lattices. We discuss the following neural fuzzy networks: Takagi-Sugeno-Kung network and a modification of Wang-Mendel neural fuzzy network proposed by the authors. A three-step scheme of neural network training is proposed. The results prove the efficiency of the proposed approach for the determination of crystal lattice types.