Localized solutions to interval linear equations

In this paper, we propose a new type of solutions, localized solutions, to interval linear equations Ax=b. The new solutions are based on L-localized solutions and R-localized solutions. The concepts of the three solutions are given and the characteristics of the new solutions to the interval linear equations are described by means of nonlinear inequality, as is similar to the well-known Oettli–Prager inequality which is related to the mid-point and interval radius. Some necessary conditions of the three types of solutions to the equations are given.