Interval-Valued Multiobjective Programming Problems Based on Convex Cones

The new solution concepts of interval-valued multiobjective optimization problems using ordering cone are proposed in this paper. An equivalence relation is introduced to divide the collection of all bounded closed intervals into the equivalence classes. The family of all equivalence classes is also called a quotient set. In this case, this quotient set can turn into a vector space under some suitable settings for vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. It means that an ordering in the quotient set can be defined to study the Pareto optimal solution in multiobjective optimization problems. In this paper, we consider the multiobjective optimization problem such that its coefficients are taken to be the bounded closed intervals. With the help of the convex cone, we can study the Pareto optimal solutions of the multiobjective optimization problem with interval-valued coefficients.