Multiobjective interval linear programming in admissible-order vector space.

Multiobjective interval linear programming (MOILP) is one of the most important approaches to real-world optimization problems involving multiple conflicting objectives under imprecision or uncertainty. From the viewpoint of order vector space, this paper aims to solve MOILP problems with an admissible order. We first extend the concept of admissible order on the set of intervals and study some properties of admissible order vector space. We then employ an admissible order and interval ordered weighted aggregation (OWA) operator to transform a MOILP problem into an interval weighted sum scalarization multiobjective optimization problem whose solution can be derived by solving several related real-valued programming problems, and the Pareto optimal solution of this MOILP problem can likewise be obtained. Then, we introduce the W-efficient solutions and axial solutions of the MOILP problem to account for decision makers’ preferences as partial information. Two simple examples and two real-life problems are employed to illustrate and substantiate our conceptual arguments.