Algebraic methods for solving recognition problems with non-crossing classes

In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced on recognizing operators, and based on the application of these operators, a family of recognizing algorithms is created. An upper estimate is constructed for the model, which guarantees the completeness of the extension.