| Article ID: | iaor20116951 |
| Volume: | 150 |
| Issue: | 2 |
| Start Page Number: | 298 |
| End Page Number: | 316 |
| Publication Date: | Aug 2011 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Wu Hsien-Chung |
| Keywords: | programming: linear |
The weak and strong duality theorems in interval‐valued linear programming problems are derived in this paper. The primal and dual interval‐valued linear programming problems are formulated by proposing the concept of a scalar (inner) product of closed intervals. We introduce a solution concept that is essentially similar to the notion of nondominated solution in multiobjective programming problems by imposing a partial ordering on the set of all closed intervals. Under these settings, the weak and strong duality theorems for interval‐valued linear programming problems are derived naturally.