This paper deals with an extension of proper efficiency that considers bounded and unbounded trade-offs between objective functions. While trade-offs between objective functions are unbounded, the rate of growth for these trade-offs is computed by applying a metric. A new concept, namely quasi-proper efficiency is introduced that shows that rate of growth of trade-off between objective functions. Two appropriate characterizations for this concept are developed: the first one is based on a scalar function utilizing the Chebyshev norm and the second one is in terms of the concept of stability.
POURKARIMI, LATIF and KARIMI, MASOUD
"Quasi-proper efficiency: a quantitative enhanced efficiency,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 32.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/32