A New Order Relation for Set Optimization Problems on Complete Lattice Structure

In this paper, we propose a new class of set order relations based on the concepts of infimum and supremum for set optimization problems defined on a complete lattice structure. We systematically investigate the fundamental properties of the proposed order relations and their relationship with the order relations introduced by Kuroiwa. On this basis, we further examine the connection between solution concepts defined by the vector approach and those defined by the set approach, and establish the corresponding optimality conditions using the Tchebycheff scalarization method. Finally, the effectiveness of the proposed order relations is demonstrated through application examples in power system stability analysis and waste treatment technologies.