Abstract
The developed approach allows to construct an algorithm which theoretically gives exact solution of pattern recognition problem if some conditions on input data of the problem hold. For the crisp model the conditions are conditions of solvability for the operator equation and they are the conditions of the correctness of an special algebra over pattern recognition (p.r.) tasks. The approach is not connected with a functional minimization and this is new aspect which differs from classical approaches to neural network constructions including fuzzy models also. The last means that the similar conditions can be given for the appropriate fuzzy recognition model.