基于2-可加Choquet积分的混合信息灰关联决策方法及其应用

doi:10.16381/j.cnki.issn1003-207x.2022.2502

Abstract

Abstract:

With the rapid development of modern technology and information， there are many complex multi-attribute decision-making problems with overlapping grey areas and ambiguities， and the decision attributes often have mutual interaction effects. To address the mixed multi-attribute decision-making problem with interaction effects between attributes， and a mixture of precise numbers， interval grey numbers， intuitionistic fuzzy numbers， hesitant fuzzy numbers， and linguistic variables， a mixed information grey relational decision-making method based on 2-additive Choquet integral is proposed.The specific research process as follows　（1） First， the mixed information decision matrix $R ˜ = r ˜ i j m × n$ is defined， and the mixed information grey relational coefficient $η i j$ is constructed. （2） Then， the 2-additive Choquet integral operator is introduced to nonlinearly aggregate the grey relational coefficients of different attributes and construct the mixed information grey relational degree based on 2-additive Choquet integral， which can be expressed as $η i = ∑ j = 1 n I j η i j - 12 ∑ c j, c k ⊆ C I j k η i j - η i k$ . $I j k$ indicates the interaction index between attribute $j$ and attribute $k$ . （3） To objectively determine the interaction indices between attributes， a mixed information grey relational multi-objective nonlinear optimization model is established， and the whale intelligence algorithm is used to solve the parameters. （4） Subsequently， a novel grey relational decision-making method with mixed information based on 2-additive Choquet integral is constructed， and specific algorithm steps are given.

Key words: grey relational decision-making, mixed information, interaction, 2-additive Choquet integral, whale optimization algorithm

CLC Number:

C931

Yu Feng, Yaoguo Dang, Junjie Wang, Zhangcheng Yang. Grey Incidence Decision-making Method with Mixed Information Based on 2-additive Choquet Integral and Its Application[J]. Chinese Journal of Management Science, 2025, 33(9): 189-200.

Figures/Tables 6

语言变量	模糊数
极差（ $s 1$ ）	（0, 0, 0, 0.1）
差（ $s 2$ ）	（0, 0.1, 0.2, 0.3）
较差（ $s 3$ ）	（0.2, 0.3, 0.4, 0.5）
一般（ $s 4$ ）	（0.4, 0.5, 0.5, 0.6）
较好（ $s 5$ ）	（0.5, 0.6, 0.7, 0.8）
好（ $s 6$ ）	（0.7, 0.8, 0.9, 1）
极好（ $s 7$ ）	（0.9, 1, 1, 1）

一级指标	二级指标	指标描述	单位	数据类型
质量保证能力	产品合格率( $c 1$ ）	合格产品数与产品总数的比值	%	区间灰数
	产品先进度（ $c 2$ ）	产品技术水平的先进程度	—	直觉模糊数
	产品生产经验（ $c 3$ ）	同类产品的生产经验	—	语言变量
生产供货能力	准时履约率（ $c 4$ ）	准时履约产品数与应履约产品数的比值	%	区间灰数
	产品报价得分（ $c 5$ ）	报价最低值与该供应商报价的比值	%	精确数
	供货时间柔性（ $c 6$ ）	交货可缩短时长与合同规定交货时长比值	%	犹豫模糊数
技术服务能力	技术服务能力（ $c 7$ ）	提供全过程技术服务的能力	—	语言变量
技术服务能力	服务响应度（ $c 8$ ）	解决后期问题的及时程度	—	直觉模糊数
经营发展能力	军工意识（ $c 9$ ）	军工政治意识、质量意识和保密意识水平	—	语言变量
经营发展能力	企业盈利能力（ $c 10$ ）	企业的资本增值能力	—	语言变量

决策属性	$c 1$	$c 2$	$c 3$	$c 4$	$c 5$	$c 6$	$c 7$	$c 8$	$c 9$	$c 10$
$c 1$	—	-0.003	-0.071	0.007	0.011	0.068	0.073	-0.014	0.003	0.003
$c 2$	-0.003	—	-0.011	0.019	-0.067	0.023	-0.133	0.148	-0.006	-0.012
$c 3$	-0.071	-0.011	—	-0.020	-0.008	-0.149	0.012	-0.007	-0.020	-0.059
$c 4$	0.007	0.019	-0.020	—	-0.005	0.006	-0.011	-0.007	-0.021	0.003
$c 5$	0.011	-0.067	-0.008	-0.005	—	-0.098	0.018	-0.003	0.109	-0.090
$c 6$	0.068	0.023	-0.149	0.006	-0.098	—	0.012	0.006	0.009	0.128
$c 7$	0.073	-0.133	0.012	-0.011	0.018	0.012	—	0.065	0.144	0.030
$c 8$	-0.014	0.148	-0.007	-0.007	-0.003	0.006	0.065	—	0.005	-0.020
$c 9$	0.003	-0.006	-0.020	-0.021	0.109	0.009	0.144	0.005	—	-0.020
$c 10$	0.003	-0.012	-0.059	0.003	-0.090	0.128	0.030	-0.020	-0.020	—

决策方法	综合评价值	排序结果
TOPSIS	$P 1 = 0.796$ , $P 2 = 0.324$ , $P 3 = 0.259$ , $P 4 = 0.365$ , $P 5 = 0.515$ .	$X 1 ≻ X 5 ≻ X 4 ≻ X 2 ≻ X 3$
VIKOR	$C 1 = 0$ , $C 2 = 0.624$ , $C 3 = 1$ , $C 4 = 0.375$ , $C 5 = 0.196$ .	$X 1 ≻ X 5 ≻ X 4 ≻ X 2 ≻ X 3$
灰关联决策方法	$D 1 = 0.613$ , $D 2 = 0.492$ , $D 3 = 0.391$ , $D 4 = 0.495$ , $D 5 = 0.551$ .	$X 1 ≻ X 5 ≻ X 4 ≻ X 2 ≻ X 3$
基于模糊Choquet积分的灰色综合评价方法	$r 1 = 0.827$ , $r 2 = 0.699$ , $r 3 = 0.598$ , $r 4 = 0.773$ , $r 5 = 0.745$ .	$X 1 ≻ X 4 ≻ X 5 ≻ X 2 ≻ X 3$
关联变权空间多属性决策方法	$C C 1 = 0.674$ , $η 2 = 0.579$ , $η 3 = 0.376$ , $η 4 = 0.571$ , $η 5 = 0.620$ .	$X 1 ≻ X 5 ≻ X 2 ≻ X 4 ≻ X 3$
基于2-可加Choquet积分的混合信息灰关联决策方法	$η 1 = 0.915$ , $η 2 = 0.669$ , $η 3 = 0.586$ , $η 4 = 0.625$ , $η 5 = 0.807$ .	$X 1 ≻ X 5 ≻ X 2 ≻ X 4 ≻ X 3$

References 20

[1]	Deng J L. Introduction to grey system theory［J］. The Journal of Grey System， 1989， 1（1）： 1-24.
[2]	刘勇，刘思峰， Forrest Jeffrey. 一种新的灰色绝对关联度模型及其应用［J］. 中国管理科学， 2012， 20（5）： 173-177.
	Liu Y， Liu S F， Forrest J. A new grey absolute degree of grey incidence model and application［J］. Chinese Journal of Management Science， 2012， 20（5）： 173-177.
[3]	刘震，党耀国，钱吴永，等. 基于面板数据的灰色网格关联度模型［J］. 系统工程理论与实践， 2014， 34（4）： 991-996.
	Liu Z， Dang Y G， Qian W Y， et al. Grey grid incidence model based on panel data［J］. Systems Engineering-Theory & Practice， 2014， 34（4）： 991-996.
[4]	徐林明，李美娟，卢锦呈. 考虑决策者偏好的均衡接近度灰关联改进 TOPSIS动态评价方法及其应用研究［J］. 中国管理科学， 2023， 31（3）： 251-258.
	Xu L M， Li M J， Lu J C. Dynamic evaluation method based on grey correlational analysis by the method of balance and approach and improved TOPSIS considering the preference of the decision maker［J］. Chinese Journal of Management Science， 2023， 31（3）： 251-258.
[5]	Rajesh R. A novel advanced grey incidence analysis for investigating the level of resilience in supply chains［J］. Annals of Operations Research，2022，308（1）： 441-490.
[6]	邹凯，包明林，张晓瑜，等. 基于三角模糊软集的多属性灰色关联决策方法［J］. 中国管理科学， 2015， 23（S1）： 23-27.
	Zou K， Bao M L， Zhang X Y， et al. Multiple attribute grey relational decision making method based on triangular fuzzy soft sets［J］. Chinese Journal of Management Science， 2015， 23（S1）： 23-27.
[7]	Liu S， Tang W. On general uncertainty data and general uncertainty variable for reliability growth analysis of major aerospace equipment［J］. Grey Systems： Theory and Application， 2023， 13（2）： 261-276.
[8]	常志朋，程龙生. 基于施密特正交马田系统和Ф_s转换的灰模糊积分关联度决策模型［J］. 控制与决策， 2014， 29（7）： 1257-1261.
	Chang Z P， Cheng L S. Grey fuzzy integral correlation degree decision model based on Mahalanobis-Taguchi Gram-Schmidt and Ф_s transformation［J］. Control and Decision， 2014， 29（7）： 1257-1261.
[9]	Tian G， Hao N， Zhou M， et al. Fuzzy grey choquet integral for evaluation of multicriteria decision making problems with interactive and qualitative indices［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2021， 51（3）： 1855-1868.
[10]	徐选华，赵程伟，何继善，等. 多型异构数据下关联变权空间多属性决策方法［J］. 系统工程理论与实践， 2020， 40（7）： 1895-1905.
	Xu X H， Zhao C W， He J S， et al. Association variable weight space multi-attribute decision method under multi-type heterogeneous data［J］.Systems Engineering- Theory & Practice， 2020，40（7）： 1895-1905.
[11]	刘思峰，方志耕，谢乃明. 基于核和灰度的区间灰数运算法则［J］. 系统工程与电子技术， 2010， 32（2）： 313-316.
	Liu S F， Fang Z G， Xie N M. Algorithm rules of interval grey numbers based on the “Kernel” and the degree of greyness of grey numbers［J］. Systems Engineering and Electronics， 2010， 32（2）： 313-316.
[12]	Wang W， Zhan J， Mi J. A three-way decision approach with probabilistic dominance relations under intuitionistic fuzzy information［J］. Information Sciences， 2022， 582： 114-145.
[13]	Torra V. Hesitant fuzzy sets［J］. International Journal of Intelligent Systems， 2010， 25（6）： 529-539.
[14]	Ma X， Qin J， Martínez L， et al. A linguistic information granulation model based on best-worst method in decision making problems［J］. Information Fusion， 2023， 89： 210-227.
[15]	Grabisch M. K-order additive discrete fuzzy measures and their representation［J］. Fuzzy Sets and Systems， 1997， 92（2）： 167-189.
[16]	Grabisch M， Labreuche C. A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid［J］. Annals of Operations Research， 2010， 175（1）： 247-286..
[17]	常志朋，程龙生，刘家树. 基于马田系统的2可加Choquet积分多属性决策方法［J］. 管理工程学报， 2016， 30（1）： 133-139.
	Chang Z P， Cheng L S， Liu J S. Multi-attribute decision making method based on mahalanobis-taguchi system and 2-additive choquet integral［J］. Journal of Industrial Engineering and Engineering Management， 2016， 30（1）： 133-139.
[18]	Wang X， Triantaphyllou E. Ranking irregularities when evaluating alternatives by using some ELECTRE methods［J］. Omega， 2008， 36（1）： 45-63.
[19]	Zhang K， Dai J. A novel TOPSIS method with decision-theoretic rough fuzzy sets［J］. Information Sciences， 2022， 608： 1221-1244.
[20]	Lin M， Chen Z， Xu Z， et al. Score function based on concentration degree for probabilistic linguistic term sets： An application to TOPSIS and VIKOR［J］. Information Sciences， 2021， 551： 270-290.

Grey Incidence Decision-making Method with Mixed Information Based on 2-additive Choquet Integral and Its Application

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