随机不等式的若干确定型等价类之比较  

COMPARISON AMONG SOME DETERMINISTIC EQUIVALENT FORMULATIONS OF STOCHASTIC INEQUALITIES

作　　者：万中[1] 阳彩霞[1] 江卫[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083

出　　处：《数学杂志》2010年第6期1073-1076,共4页Journal of Mathematics

基　　金：教育部新世纪优秀人才支持计划(NCET-07-0864);国家自然科学基金(60804037)

摘　　要：本文研究了处理随机不等式的若干确定型转化形式.在讨论已有方法(如均值法和机会约束法)的基础上,我们提出了一种反映决策者满意度的随机变量的序数关系,并据此得到一种新的随机不等式转化为确定型不等式的满意度方法.同以往方法比较,满意度方法对处理随机不等式同时具备简洁性和科学性.将该方法应用于求解随机约束优化问题说明了它的优势.This article studies the deterministic methods dealing with the stochastic inequalities. Based on the discussion of the existing methods, such as the mean-value approach and the chance constraint approach, a new order relation between stochastic variables is proposed, which measures the satisfaction degree of decision-maker. From this definition, we obtain a deterministic equivalent formulation of stochastic inequality, which is called the satisfaction degree approach. Compared with the existing approaches, the proposed one is more practical and valid. The application of this approach to stochastic constrained optimization problem shows its advantages.

关 键 词：随机不等式 均值法 机会约束法 满意度 确定型等价类 

分 类 号：O211.5[理学—概率论与数理统计]