向量优化中 f ree_disposal 集的代数性质
On Algebraic Properties of Free_Disposal Sets in Vector Optimization
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摘要: 基于集合代数闭包和代数内部的概念，在free_disposal集条件下证明了代数闭包必是代数闭集，代数内部必是代数开集；研究了凸锥和与其对应的free_disposal集的代数性质，同时获得了两个free_disposal集和的代数性质；建立了两个free_disposal集的等价条件。
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关键词:
- 向量优化 /
- free_disposal集 /
- 代数性质
Abstract: Free_disposal sets is one of the important tools with which to study the characterizations of uni_fied solution in vector optimization .In this paper ,by applying the concepts of algebraic closure and interior of sets ,it has been proved that the algebraic closure is closed and the algebraic interior is open with the condition of the free_disposal set .T he properties of a convex cone and its corresponding free_disposal set are studied .The properties of the sum of two free_disposal sets have been obtained ,and the equivalent conditions between two free_disposal sets have been established .This paper extends some of the relevant results about free_disposal sets in recent literature . -
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