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山东大学学报(工学版) ›› 2016, Vol. 46 ›› Issue (2): 72-77.doi: 10.6040/j.issn.1672-3961.0.2015.381

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基于决策人满意度的区间UTA方法

熊文涛1,2,冯育强1   

  1. 1. 冶金工业过程系统科学湖北省重点实验室(武汉科技大学), 湖北 武汉 430081;2. 湖北工程学院数学与统计学院, 湖北 孝感 432000
  • 收稿日期:2015-11-19 出版日期:2016-04-20 发布日期:2015-11-19
  • 作者简介:熊文涛(1978— ),男,湖北汉川人,副教授,博士,主要研究方向为决策分析、最优化理论与方法.E-mail:xiong-2009@foxmail.com
  • 基金资助:
    湖北省自然科学基金重点资助项目(2013CFA131);冶金工业过程系统科学湖北省重点实验室基金资助项目(Y201401);湖北省教育厅科学研究计划资助项目(Q20132706)

An interval UTA method based on the satisfaction degree of decision maker

XIONG Wentao1,2, FENG Yuqiang1   

  1. 1.Hubei Province Key Laboratory of System Science in Metallurgical Process(Wuhan University of Science and Technology), Wuhan 430081, Hubei, China;
    2. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China
  • Received:2015-11-19 Online:2016-04-20 Published:2015-11-19

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摘要： 针对区间数多准则决策问题,扩展了传统的效用加性(utility additive, UTA)方法,提出了一种区间UTA方法。该方法首先根据传统的UTA方法,将参考方案的所有指标值转换为效用范围,即效用区间;然后利用区间数运算,得到参考方案的综合效用,进一步根据决策人的满意度和区间数的中点、半宽构建一个线性规划模型,计算出最小误差;在再优化分析中,以各指标下所有节点郊用的方差最小为目标函数,建立二次规划模型,计算出每一指标下各节点的效用值,利用效用值得到待评方案的综合效用区间和排序。算例表明,提出的区间UTA方法能有效地对方案排序,并与决策人以往的偏好信息一致。

关键词: 多准则决策, 满意度, UTA方法, 区间数, 效用值

Abstract: An interval UTA method was proposed for inferring interval utility functions from a partial preorder of alternatives evaluated on multiple criteria, which was an extension of the well-known UTA method capable to handle the interval evaluation data. Firstly, according to the original UTA method, the interval attribute values of all reference options were transformed into the ranges of utility, namely, the utility intervals. Next, the overall utility intervals were calculated using the arithmetic operations of interval number. A linear programming model was constructed based on the satisfaction degree of decision maker utilizing the mid-point and half-width of interval numbers. After the total error value was obtained, a quadratic programming model was established in the post-optimization step, where the objective function was the minimum utility variance of all nodes along all criteria. The obtained utility values of all nodes were used to calculate the overall utility intervals and ranking of alternatives under evaluation. Numerical example showed that the alternatives could effectively ranked using the proposed interval UTA method, which was compatible with the preference information of decision maker.

Key words: UTA method, multiple criteria decision, utility value, interval number, the satisfaction degree

中图分类号: 

  • C934
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