A note on the interdependence of the objectives and their entropy regularization solution

Considering that the concept of interdependence concept proposed by Carlsson and Full'er [1,2,3], found that it can only be applied to one dimension decision space, In this paper, we generalize the concept of objectives interdependence under the multidimensional conditions based on the gradients of the objectives. The new interdependence concept can reflect both the relationship and the degrees of the objectives' support or conflict. Then the application functions are constructed based on the interdependence grades of the objectives, and they are aggregated by entropy regularization procedure to solve the multiobjective programming problems. A numerical example shows the effect of the approach.