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One of the central problems of the rapidly developing interval mathematics is the classical problem of describing, researching and applying sets of solutions to an interval system of linear algebraic equations (ISLAE). The set of solutions of ISLAU can be determined in different ways, depending on which quantifiers the coefficients of the left and right parts of this system are related to. Since every desired set of solutions of ISLAE is given by the domain of compatibility of a system of linear inequalities and, in a number of cases, one nonlinear condition, it is difficult to work with practical problems with it. Therefore, the paper proposes a method of point characterization of the sets of solutions of ISLAE, consisting in using the well-known in the theory of multicriteria choice of the maximization of the resolution of the indicated inequalities. In the case of the emptiness of the required set, it is proposed, by analogy with the theory of ill-posed problems, to seek a quasisolution of ISLAE. In both cases, it is necessary to solve problem of linear or partial boolean linear programming.

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