The importance of weakly Pareto optimal points

In multicriteria optimization problems appart from the notion of Pareto optimality there is also the term weakly Pareto optimality. For that case, the definition is that

A feasible solution $\hat{x} \in \mathcal{X} \quad$ is called weakly efficient if there is no $x \in \mathcal{X} \quad$ such that $f(x) < f(\hat{x})$, i.e. $f_k(x) < f_k(\hat{x}) \quad \forall k = 1, \ldots , p$.

Notice that the Pareto optimal set is a subset of the weakly Pareto optimal set.

I wonder the practical importance of the weakly Pareto optimal set. Do you any situation where they are important?

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