Given a large set of Pareto optima, it can be challenging to identify good solutions within this set. A discrete optimization problem is formulated to obtain such a set of good solutions. This problem’s complexity is discussed, as well as particular examples that illustrate the challenge when solving this problem.

In this paper an extrusion process example is studied to illustrate a new methodology in the field if decision engineering, which is based on the Rough Set approach. Rough sets are used to aid to the Decision Maker in choosing the best point in the Pareto's region. The rough Set approach allows us to make a rough approximation of a preference relation on a simple of experomental points choosen from the Pareto set. These approximations are done to induce the decision rules, which can be afterwards applied on whole sets of potential points. To give the final recommendation the concept of technical robustness is suggested

The concept of lower semicontinuity introduced for scalar functions by R. Baire has been recognized as a fundamental tool in different areas of mathematical analysis. It has been used in different contexts. The rapid development of optimization theory, in particular Pareto optimization, has made evident the necessity of extending this concept to vector-valued mappings. The main scope of this paper is then to define an appropriate lower semicontinuous regularization for vector-valued.