基于CWPHM算子和C-DEMATEL的语言型多属性决策方法

doi:10.16381/j.cnki.issn1003-207x.2023.0903

摘要/Abstract

摘要：

针对现有的语言型多属性决策方法未能够同时考虑指标间关联性、指标间均衡性和指标间相互影响关系的情况，定义云加权幂Heronian平均（cloud weighted power Heronian mean， CWPHM）算子和改进的云DEMATEL模型，并提出一种基于CWPHM算子和C-DEMATEL的语言型多属性决策方法，并用于解决企业人才选拔问题。首先，给出CWPHM算子的定义，并讨论该算子的一些基本性质；然后，对传统的DEMATEL模型进行改进，并设计一种基于C-DEMATEL的指标权重确定方法；最后，将CWPHM算子和基于C-DEMATEL的指标权重确定方法进行融合，在此基础上计算各方案的综合评价值。选取某企业人才选拔问题进行算例分析，研究结果表明，该方法不仅能够考虑语言信息的模糊性和随机性，还能够考虑指标间关联性、指标间均衡性和指标间相互影响关系。

关键词: 多属性决策, 云模型, 幂算子, Heronian算子, DEMATEL

Abstract:

Multiple attribute decision-making is a very important area of research in normative decision theory. This topic has been widely developed and discussed. Considering that an expert may has vague knowledge about the preference degree of objective things， linguistic terms are often used for a decision maker as the evaluation information in some real-world multiple attribute decision-making problems. In the face of linguistic multiple attribute decision-making problems， there may exist the correlation relationships among attributes， the causal relationships among attributes， and the overall imbalances among attributes. In such situations， a new complex linguistic multiple attribute decision-making problem occurs. The new complex linguistic multiple attribute decision-making problem can be seen everywhere in real life， and it has attracted much attention from domestic and overseas experts over the last years. However， so far the methods that can solve the new complex linguistic multiple attribute decision-making problem are rare.In order to overcome this kind of deficiency， a new cloud weighted power Heronian mean （CWPHM） operator is defined and an improved cloud decision making trial and evaluation laboratory （C-DEMATEL） model is designed， and then it puts forward a novel linguistic multiple attribute decision-making method based on CWPHM operator and C-DEMATEL. First， the basic notion of CWPHM operator is defined， and some properties of CWPHM operator that include the commutativity， idempotency， boundary， and monotonicity are discussed. Then， the traditional DEMATEL method is improved， and the attribute weight determination method based on C-DEMATEL is investigated. Finally， the CWPHM operator and the attribute weight determination method based on C-DEMATEL are fused， which can obtain the comprehensive evaluation values of alternatives. A numerical example in regard to the enterprise talent selection is provided to verify the rationality and validity of the proposed method. It is shown that not only can this method consider the fuzziness and randomness of linguistic information， but this method can also consider the correlation relationships among attributes， the causal relationships among attributes， and the overall balance among attributes.The main contributions of this paper are reflected in the following three aspects　（1） The existing power Heronian mean operators are extended into cloud model decision-making environments， and then a new CWPHM operator is defined， which further expands the general applicability of the power Heronian mean operators. （2） The traditional DEMATEL method is improved to investigate a new attribute weight determination method based on C-DEMATEL， which is able to make the decision results more accurate. （3） The CWPHM operator and the C-DEMATEL model are fused to put forward a novel linguistic multiple attribute decision-making method， which can give some references for solving real-world complex linguistic multiple attribute decision-making problems.

Key words: multiple attribute decision making, cloud model, power operator, Heronian operator, DEMATEL

中图分类号:

C931

王伟明,徐海燕,朱建军, 等. 基于CWPHM算子和C-DEMATEL的语言型多属性决策方法[J]. 中国管理科学, 2026, 34(1): 94-103.

Weiming Wang,Haiyan Xu,Jianjun Zhu, et al. A Novel Linguistic Multiple Attribute Decision Making Method Based on CWPHM Operator and C-DEMATEL[J]. Chinese Journal of Management Science, 2026, 34(1): 94-103.

图/表 5

表1

决策专家给出的语言多属性决策矩阵"

备选干部	$C 1$	$C 2$	$C 3$	$C 4$	$C 5$	$C 6$	$C 7$
$O 1$	极好	极差	很差	很好	很差	极好	一般
$O 2$	极好	极差	一般	极好	很好	很差	很差
$O 3$	极好	极好	极差	很差	很差	好	一般
$O 4$	极好	很差	极好	极好	很好	好	很好
$O 5$	很好	很好	很好	很好	很好	极好	一般

表1

表2

决策专家给出的指标间直接影响矩阵"

指标	$C 1$	$C 2$	$C 3$	$C 4$	$C 5$	$C 6$	$C 7$
$C 1$	极弱	极强	极强	很强	很强	极强	极弱
$C 2$	极强	极弱	极强	极强	很强	强	一般
$C 3$	极强	极强	极弱	很弱	很弱	强	一般
$C 4$	很强	极强	很弱	极弱	极弱	强	弱
$C 5$	一般	弱	弱	弱	极弱	强	很强
$C 6$	极弱	很弱	很弱	很弱	很弱	极弱	强
$C 7$	极弱	很弱	极弱	很弱	极弱	一般	极弱

表2

表3

语言型多属性决策矩阵转化后的云矩阵"

备选干部	$C 1$	$C 2$	$C 3$	$C 4$	$C 5$	$C 6$	$C 7$
$O 1$	$(50,19.28,4.68)$	$(100,29.65,1.23)$	$(22.10,26.63,2.23)$	$(77.90,26.63,2.24)$	$(22.10,26.63,2.23)$	$(100,29.65,1.23)$	$(50,19.28,4.68)$
$O 2$	$(100,29.65,1.23)$	$(0,29.65,1.23)$	$(50,19.28,4.68)$	$(100,29.65,1.23)$	$(77.90,26.63,2.24)$	$(22.10,26.63,2.23)$	$(22.10,26.63,2.23)$
$O 3$	$(100,29.65,1.23)$	$(100,29.65,1.23)$	$(0,29.65,1.23)$	$(22.10,26.63,2.23)$	$(22.10,26.63,2.23)$	$(61.77,21.08,4.09)$	$(50,19.28,4.68)$
$O 4$	$(100,29.65,1.23)$	$(22.10,26.63,2.23)$	$(100,29.65,1.23)$	$(100,29.65,1.23)$	$(77.90,26.63,2.24)$	$(61.77,21.08,4.09)$	$(77.90,26.63,2.24)$
$O 5$	$(77.90,26.63,2.24)$	$(77.90,26.63,2.24)$	$(77.90,26.63,2.24)$	$(77.90,26.63,2.24)$	$(77.90,26.63,2.24)$	$(100,29.65,1.23)$	$(50,19.28,4.68)$

表3

表4

指标间直接影响矩阵转化后的云矩阵"

备选干部	$C 1$	$C 2$	$C 3$	$C 4$	$C 5$	$C 6$	$C 7$
$C 1$	$(100,29.65,1.23)$	$(0,29.65,1.23)$	$(100,29.65,1.23)$	$(77.90,26.63,2.24)$	$(77.90,26.63,2.24)$	$(100,29.65,1.23)$	$(0,29.65,1.23)$
$C 2$	$(100,29.65,1.23)$	$(0,29.65,1.23)$	$(100,29.65,1.23)$	$(100,29.65,1.23)$	$(77.90,26.63,2.24)$	$(61.77,21.08,4.09)$	$(50,19.28,4.68)$
$C 3$	$(100,29.65,1.23)$	$(100,29.65,1.23)$	$(0,29.65,1.23)$	$(22.10,26.63,2.23)$	$(22.10,26.63,2.23)$	$(61.77,21.08,4.09)$	$(50,19.28,4.68)$
$C 4$	$(77.90,26.63,2.24)$	$(100,29.65,1.23)$	$(22.10,26.63,2.23)$	$(0,29.65,1.23)$	$(0,29.65,1.23)$	$(61.77,21.08,4.09)$	$(38.23,21.08,4.09)$
$C 5$	$(50,19.28,4.68)$	$(38.23,21.08,4.09)$	$(38.23,21.08,4.09)$	$(38.23,21.08,4.09)$	$(0,29.65,1.23)$	$(61.77,21.08,4.09)$	$(77.90,26.63,2.24)$
$C 6$	$(0,29.65,1.23)$	$(22.10,26.63,2.23)$	$(22.10,26.63,2.23)$	$(22.10,26.63,2.23)$	$(22.10,26.63,2.23)$	$(0,29.65,1.23)$	$(61.77,21.08,4.09)$
$C 7$	$(0,29.65,1.23)$	$(22.10,26.63,2.23)$	$(0,29.65,1.23)$	$(22.10,26.63,2.23)$	$(0,29.65,1.23)$	$(50,19.28,4.68)$	$(0,29.65,1.23)$

表4

表5

五种方法的备选干部综合评价值及其排序对比"

备选干部	本文方法		LWAA算子		CWAA算子		CWPA算子		CWHM算子
备选干部	评价值	排序	评价值	排序	评价值	排序	评价值	排序	评价值	排序
$O 1$	38.520	4	$s 0.078$	5	36.163	4	36.048	5	35.024	4
$O 2$	38.389	5	$s 0.107$	4	36.090	5	39.419	4	35.018	5
$O 3$	43.048	3	$s 0.626$	3	41.706	3	44.239	3	40.906	3
$O 4$	54.226	1	$s 1.3620$	2	51.783	2	55.782	1	52.257	2
$O 5$	53.807	2	$s 1.461$	1	55.776	1	55.591	2	54.157	1

表5

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