The authors introduce two new concepts for •-efficiency and investigate these and some known concepts under the following aspects: (1) What are the relationships between the efficient and the •-efficient point set? (2) If the sequence (ℝepsiv;) of •-efficient points converges for •⇒0, is the limit efficient, or weakly efficient? (3) Can the distance between the v’•-efficient and the efficient point set be estimated in terms of •?