Linear Binary Classification under Interval Uncertainty of Data

The problem of the linear binary classification of interval sets is considered. This problem is formulated as a problem of finding a solution to an interval system of linear inequalities. Necessary and sufficient conditions for the existence of a solution to this problem and its form are established by a theorem that is a well-known result of the theory of interval systems of linear inequalities. The problem of linear binary classification of interval sets is reduced to the problem of finding a solution to a system of linear inequalities of a special form. To construct a solution (or a pseudo-solution in the case of linear inseparability of classes), the corresponding problems of unconditional minimization are proposed. Illustrative numerical examples are given. This article notes the potential possibility of adapting a very wide range of known and newly developed methods of linear binary classifications to the case of interval sets, due to the practically coinciding form of systems of linear inequalities that describe the problem of binary linear classification of both exact and interval sets.