多准则敏感性的偏序分析方法

doi:10.15960/j.cnki.issn.1007-6093.2025.01.006

摘要/Abstract

摘要：

多准则决策主要通过权重摄动构造敏感性分析方法, 当赋权困难或者发生争议时, 评价结果往往不够稳健。偏序敏感性分析以决策函数为目标函数、权重空间为约束条件建立规划问题, 借助极值点集构建方案间的偏序关系。最终应用Hasse图表达可能的变动结果, 得到方案和指标的敏感性程度。通过权重空间的变化, 偏序方法可以构造出适用于全局、局部和有限等多种敏感性分析方法。实例应用表明, 三类敏感性分析的偏序结果与仿真结果均完全一致, 体现了偏序方法的有效性和独特性。

关键词: 敏感性分析, 多准则决策, 权重空间, 全局敏感性

Abstract:

The sensitivity analysis method of multiple criteria decision making is mainly constructed by weight perturbation. When weight assignment is difficult or disputes occur, the evaluation results are often not robust enough. Partial order sensitivity analysis takes decision function as objective function and weight space as constraint condition to establish programming problem, and constructs the partial order relationship between schemes with the help of extreme point set. Ultimately, Hasse diagram is used to express the possible change results and the sensitivity of schemes and indicators is obtained. By changing the weight space, the partial order method can construct a variety of sensitivity analysis methods suitable for global, local and finite. The example application shows that the partial order results of the three kinds of sensitivity analysis are completely consistent with the simulation results, which reflects the effectiveness and uniqueness of the partial order method.

Key words: sensitivity analysis, multiple criteria decision making, weight space, global sensitivity

中图分类号:

O225

岳立柱, 姚利微, 崔亚华, 许可. 多准则敏感性的偏序分析方法[J]. 运筹学学报（中英文）, 2025, 29(1): 63-76.

Lizhu YUE, Liwei YAO, Yahua CUI, Ke XU. Partial order analysis method for multiple criteria sensitivity[J]. Operations Research Transactions, 2025, 29(1): 63-76.

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人员编号	工作效率	工作改善	人际关系	培训成绩	团队精神	创新能力	奖惩记录	出勤情况	初始排名
$ A1 $	74	66	72	77	85	64	94	87	9
$ A2 $	85	80	67	83	78	62	88	86	4
$ A3 $	83	81	71	85	84	70	89	84	2
$ A4 $	76	79	80	80	79	76	88	74	7
$ A5 $	87	67	71	77	76	72	93	92	5
$ A6 $	73	74	76	86	81	63	83	89	8
$ A7 $	88	81	71	84	81	70	92	79	1
$ A8 $	81	81	74	85	80	71	90	80	3
$ A9 $	74	69	72	74	78	56	84	75	10
$ A10 $	87	69	72	84	78	55	93	85	6

准则内容	工作效率($ \omega_1 $)	工作改善($ \omega_2 $)	人际关系($ \omega_3 $)	培训成绩($ \omega_4 $)	团队精神($ \omega_5 $)	创新能力($ \omega_6 $)	奖惩记录($ \omega_7 $)	出勤情况($ \omega_8 $)
文献[30] 权重	0.38	0.20	0.14	0.08	0.07	0.06	0.06	0.03
权重排序	1	2	3	4	5	6	6	8

人员编号	工作效率	工作改善	人际关系	培训成绩	团队精神	创新能力	奖惩记录	出勤情况
$ A1 $	3	4	9	6	8	6	7	7
$ A2 $	6	5	6	7	8	3	9	8
$ A3 $	5	4	8	5	4	4	7	5
$ A4 $	7	7	6	8	8	6	8	4
$ A5 $	6	5	9	7	8	6	7	6
$ A6 $	4	7	8	8	8	6	5	6
$ A7 $	3	5	9	8	8	6	8	7
$ A8 $	6	5	6	7	7	5	8	5
$ A9 $	2	3	6	0	3	1	2	1
$ A10 $	6	5	9	8	8	3	7	7

类型	工作效率	工作改善	人际关系	培训成绩	团队精神	创新能力	奖惩记录	出勤情况
全局	0.915**	0.873**	0.604*	0.921**	0.959**	0.900**	0.709*	0.831**
局部	0.814**	0.894**	0.833**	0.741*	0.830**	0.790**	0.743*	0.792**

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