关键词: 多目标最优化, 有效性, 有效解集的结构, 数据包络分析(DEA).

Abstract:

E(M, K) (E_w(M, K)), the set of efficient (weak efficient) points of a set M in Rⁿ, is expressed as a difference of two sets M and (M+K\{0}). With the new representation, some properties of E(M, K) are proved more easily than that before. When M or K is in the form of union, intersection, sum or difference of two sets, some properties of E(M, K) are considered. Most of the properties are proved by the binary operations of sets, which is a new method in the multiobjective optimization. Then these properties are used to solve some types of multiobjective linear programming problems corresponding to DEA models. The structures of the DEA efficient solution sets of four input-orient DEA models are developed. Thereby the  relationship between efficiencies of four input-orient DEA models is deduced.

Key words: Multiobjective optimization, Efficiency, Structure of efficient solution set, Data envelopment analysis