Characterizations of set relations via oriented distance function

What is it about?

In this paper, we characterize several known set relations with respect to variable domination structures by defining scalarization functions in terms of the oriented distance function. The characterization of minimal elements of a family of sets and the properties of sets of minimal elements are discussed by means of scalarization functionals. An application of variable domination structures to uncertain vector optimization is also given.

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Why is it important?

We characterize several known set relations with respect to variable domination structures by using the oriented distance function.