Preference Optimality (An optimality concept in multicriteria problems)

Summary

Any concept of optimality on a set is based on an ‘ordering’ of the set. In its most general form such an ‘ordering’ will be termed a ‘preference’ on a set and it will simply be a binary relation whose purpose it is to introduce a hierarchy among the elements of the set. In finite-dimensional multicriteria decision problems one basically deals with a mapping g(.):D → a, where D is some decision set and a = {a∈R^N: a=g(d),d∈D } is the set of corresponding criterion values, e.g. D may be a functional constraint set in programming or a set of admissible controls in control theory. The optimality concept introduced here consists of a preference ≲ on a and the definition of preference optimal decisions d*∈D as those for which g(d*)=a* is a least or a minimal element of a with respect to ≲ .