Algebraic closures of a generalized model of estimation algorithms

A generalized model of estimation algorithms (EA) for solving recognition problems in which objects are specified in an arbitrary way is described. It is shown that the algebraic closures of this model admit the same description as in the case of the classical EA model. In setting the problem, it would be natural to consider a system of partially ordered sets and functions of the form. The positive parameter x11(j) introduces a term which rewards the object Si for its proximity to the jth class. Similarly, the negative parameter x10(j) punishes the object for remoteness from objects of the jth class. In an algebra over the set of all recognizing operators not necessarily belonging to an EA model that is, operators transforming training information into matrices from the space was introduced. The operations including addition of operators, multiplication, and multiplication by a constant induce the corresponding fixed decision rule.