Solution types of two-sided interval linear system and their application on interval linear programming problems

Two-sided interval linear systems contain variables on both sides of equations or inequalities. We propose six types of solutions (weak, strong, tolerance, control, left-localized and right-localized solutions) to the system of equations together with four types of solutions (weak, strong, tolerance and control solutions) to the system of inequalities. We prove the necessary and sufficient conditions for checking their solvabilities in the form of systems of linear inequalities depending on the sign of variables. As a result, an interval linear programming problem with nonnegative variables and two-sided interval linear constraints can be solved by a standard linear programming approach. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study introduces six types of solutions for equations and four types of solutions for inequalities, with necessary and sufficient conditions for their solvabilities depending on the sign of variables. A standard linear programming approach can be used to solve an interval linear programming problem with nonnegative variables and two-sided interval linear constraints.