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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (12): 2367-2378    DOI: 10.3785/j.issn.1008-973X.2022.12.006
机械工程     
基于单值中智集和云聚类的产品造型设计决策方法
裴卉宁1(),谭昭芸1,刘鑫宇1,田保珍2
1. 河北工业大学 建筑与艺术设计学院，天津 300401
2. 太原科技大学 机械工程学院，山西 太原 030027
Decision method for product styling design based on single-valued neutrosophic sets and cloud clustering
Hui-ning PEI1(),Zhao-yun TAN1,Xin-yu LIU1,Bao-zhen TIAN2
1. School of Architecture and Art Design, Hebei University of Technology, Tianjin 300401, China
2. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030027, China
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摘要：

为了获得客观、合理的权重分配，综合考虑有限理性心理行为特征和策略操控行为，把决策专家进行科学聚类，提出基于单值中智集（SVNS）和云模型聚类的产品造型设计多属性决策方法. 决策专家构造标准属性和备选方案的成对比较比率平方矩阵获得SVNS，映射真、假、不确定3个隶属度值到单值中智立方体（SVNC）中，筛选各标准属性下备选方案的评估结果，获得标准属性的相对权重. 利用融合多粒度语言的云模型聚类方法集群决策专家，淘汰存在冲突和非理性的决策专家，获得有效的设计决策专家权重. 由标准属性权重和决策专家权重，综合计算各备选方案的总体优先级得分并进行排序. 以汽车造型设计方案为例，验证所提方法的可行性和有效性. 结果表明，所提方法避免了恶意策略操作，有效地解决了复杂和不确定情况下的汽车造型设计多属性决策问题.
关键词： 产品造型设计;  单值中智集(SVNS);  云模型聚类;  多属性决策;  多粒度语言    
Abstract:

A multi-attribute decision method for product styling design based on single-valued neutrosophic sets (SVNS) and cloud model clustering was proposed, in order to obtain an objective and reasonable weight distribution. Decision-making experts were scientifically clustered, considering the limited rational psychological behavior characteristics and strategic manipulation behaviors. The square matrix of the pairwise comparison ratios of the standard attributes and the alternatives was constructed by the decision-making experts to obtain the SVNS. Mapping the three membership values of true, false, and uncertain in the single-valued neutrosophic cube (SVNC), the relative weight of the standard attributes was obtained by screening the evaluation results of the alternatives under each standard attribute. The cloud model clustering method fused with multi-granularity language was used to cluster decision-making experts, conflicting and unreasonable decision-making experts were eliminated to obtain effective design decision-making expert weights. The overall priority score of each alternative was calculated and sorted through the standard attribute weights and the weights of decision-making experts. The feasibility and effectiveness of the proposed method was verified by an example of car styling design scheme. Results show that using the proposed method, dishonest strategic manipulation is avoided and the multiple attribute decision making problem for car styling design in complex and uncertain situations is effectively solved.
Key words: product styling design    single-valued neutrosophic sets (SVNS)    cloud model clustering    multiple attribute decision making    multi-granularity language
收稿日期: 2021-12-29 出版日期: 2023-01-03
CLC:  C 934  
基金资助: 教育部人文社会科学基金资助项目（21YJCZH113）；河北省高等学校科学研究资助项目（SD201091）
作者简介: 裴卉宁（1986—），女，讲师，博士，从事认知工效学、智能设计研究. orcid.org/0000-0002-4741-7175. E-mail： peihuining@hebut.edu.cn
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引用本文:

裴卉宁,谭昭芸,刘鑫宇,田保珍. 基于单值中智集和云聚类的产品造型设计决策方法[J]. 浙江大学学报(工学版), 2022, 56(12): 2367-2378.

Hui-ning PEI,Zhao-yun TAN,Xin-yu LIU,Bao-zhen TIAN. Decision method for product styling design based on single-valued neutrosophic sets and cloud clustering. Journal of ZheJiang University (Engineering Science), 2022, 56(12): 2367-2378.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.12.006    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I12/2367

图 1  基于单值中智集（SVNS）的产品造型设计多属性决策框架
图 2  单值中智集(SVNC)空间划分
图 3  基于云模型聚类的决策专家权重分配框架
图 4  汽车前视图造型设计方案
图 5  汽车前视图造型设计方案的评估标准图例
A $x_i^{(j,m)} / x_l^{(j,m)}$
A1 A2 A3 A4 A5 A6
A1 1 1/5 3 1/2 1/3 4
A2 5 1 7 3 2 9
A3 1/3 1/7 1 1/3 1/5 1/2
A4 2 1/3 3 1 1/2 5
A5 3 1/2 5 2 1 6
A6 1/4 1/9 2 1/5 1/6 1
表 1  备选方案成对比较比率平方矩阵
${D_{\rm{M}}}$ $x_1^m, S_1^m$ $x_2^m, S_2^m$ $x_3^m, S_3^m$ $x_4^m, S_4^m$ $x_5^m, S_5^m$ $x_6^m, S_6^m$ $x_7^m, S_7^m$ $x_8^m, S_8^m$ ${\text{C} }{\text{.r} }.\left( {{\boldsymbol{R}}_{J \times J}^m} \right)$/%
$D_{\rm{M}}^1$ 0.028 3, 90 0.158 8, 85 0.041 8, 100 0.020 4, 80 0.330 6, 100 0.250 9, 95 0.070 4, 85 0.098 9, 90 3.46
$D_{\rm{M}}^2$ 0.067 7, 100 0.153 1, 85 0.030 7, 80 0.022 2, 95 0.345 9, 100 0.231 8, 90 0.045 6, 100 0.103 0, 85 2.49
$D_{\rm{M}}^3$ 0.066 7, 85 0.173 8, 75 0.029 9, 80 0.022 3, 70 0.358 8, 85 0.218 3, 70 0.043 4, 90 0.086 8, 75 5.61
$D_{\rm{M}}^4$ 0.067 1, 85 0.108 3, 90 0.019 7, 80 0.027 8, 90 0.349 2, 85 0.230 2, 75 0.047 1, 95 0.150 6, 95 4.10
$D_{\rm{M}}^6$ 0.063 8, 75 0.106 7, 80 0.018 9, 70 0.028 9, 85 0.359 5, 80 0.225 8, 70 0.048 7, 90 0.147 6, 90 5.20
$\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $
$D_{\rm{M}}^{20}$ 0.068 5, 100 0.148 1, 80 0.030 6, 75 0.021 0, 95 0.367 1, 90 0.221 9, 85 0.044 5, 100 0.098 4, 90 3.15
表 2  各决策专家对各标准的权重、一致性比率和置信度得分
$B$ $x_1^{\left( {j, 1} \right)}, S_1^{\left( {j, 1} \right)}$ $x_2^{\left( {j, 1} \right)}, S_2^{\left( {j, 1} \right)}$ $x_3^{\left( {j, 1} \right)}, S_3^{\left( {j, 1} \right)}$ $x_4^{\left( {j, 1} \right)}, S_4^{\left( {j, 1} \right)}$ $x_5^{\left( {j, 1} \right)}, S_5^{\left( {j, 1} \right)}$ $x_6^{\left( {j, 1} \right)}, S_6^{\left( {j, 1} \right)}$ ${\text{C} }{\text{.r} }.\left( {{\boldsymbol{R}}_{J \times J}^1} \right)$/%
B1 0.102 5, 100 0.413 2, 95 0.050 6, 80 0.152 8, 85 0.247 9, 100 0.032 9, 90 1.99
B2 0.095 5, 85 0.410 6, 65 0.049 1, 45 0.150 5, 60 0.254 6, 75 0.039 6, 75 5.13
B3 0.087 8, 85 0.424 0, 80 0.051 7, 85 0.143 8, 95 0.255 4, 65 0.037 3, 100 3.28
B4 0.096 4, 80 0.411 9, 85 0.049 6, 75 0.145 1, 80 0.255 9, 70 0.041 1, 75 4.96
B5 0.100 8, 95 0.425 6, 100 0.039 1, 90 0.138 4, 85 0.253 7, 95 0.042 5, 70 3.46
B6 0.090 8, 60 0.432 0, 65 0.047 0, 85 0.136 2, 75 0.255 6, 50 0.038 5, 45 7.32
B7 0.096 1, 65 0.424 6, 70 0.049 4, 65 0.142 2, 60 0.255 5, 75 0.032 3, 80 2.76
B8 0.096 3, 85 0.418 4, 100 0.049 4, 80 0.151 5, 90 0.251 2, 60 0.033 2, 85 1.54
表 3  决策专家 $D_{\rm{M}}^1$对各备选方案在各标准下的一致性比率和置信度得分
图 6  单值中智集空间映射
B ${\psi ^ * }_i^j$
A1 A2 A3 A4 A5 A6
B1 0.101 2 0.370 5 0.034 5 0.173 6 0.264 9 0.069 5
B2 0.100 3 0.367 3 0.034 9 0.175 5 0.264 7 0.069 9
B3 0.100 7 0.364 0 0.036 0 0.178 0 0.268 3 0.068 6
B4 0.111 0 0.357 5 0.035 0 0.166 4 0.268 6 0.064 5
B5 0.106 1 0.364 2 0.034 4 0.138 4 0.261 2 0.071 6
B6 0.103 4 0.355 7 0.033 9 0.175 1 0.274 9 0.071 9
B7 0.105 6 0.367 3 0.034 1 0.166 9 0.264 0 0.070 6
B8 0.105 7 0.365 4 0.035 3 0.171 3 0.263 2 0.069 4
$ x_i^G $ 0.104 3 0.363 2 0.034 5 0.161 4 0.265 9 0.070 7
表 4  所有备选方案在各标准下的总体优先级得分
A hxy
$ {A_1} $ $ {A_2} $ $ {A_3} $
A1 0.5 0.4, 0.3, 0.5 0.5, 0.6, 0.7
A2 0.6, 0.7, 0.5 0.5 0.7, 0.8, 0.9
A3 0.5, 0.4, 0.3 0.3, 0.2, 0.1 0.5
A4 0.5, 0.6, 0.7 0.2, 0.3, 0.4 0.5, 0.8, 0.7
A5 0.6, 0.8, 0.5 0.3, 0.4, 0.5 0.7, 0.8, 0.9
A6 0.3, 0.2, 0.4 0.1, 0.3, 0.2 0.4, 0.2, 0.3
表 5  决策专家 $ D_M^1 $的部分原始犹豫模糊偏好关系数据
${D_{\rm{M}}}$ $O\left( {{\boldsymbol{R}}_1^{ {H_\gamma } } } \right)$ $O\left( {{\boldsymbol{R}}_2^{ {H_\gamma } } } \right)$ $O\left( {{\boldsymbol{R}}_3^{ {H_\gamma } } } \right)$ $ {\vartheta _\gamma } $ $D_{\rm{L}}^\gamma$ $r$
$D_{\rm{M}}^1$ 0 ?0.333 0 1 0.049 0.071
$D_{\rm{M}}^2$ 0 0 0 0 0.052 0.068
$D_{\rm{M}}^3$ 0 0 ?1 1 0.056 0.064
$D_{\rm{M}}^4$ 0 ?1.333 0 1 0.071 0.049
$\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $
$D_{\rm{M}}^{20}$ 0 0 ?0.667 1 0.042 0.078
表 6  决策专家的意见可靠性推导值
B $g_i^l $
A1 A2 A3 A4 A5 A6
$ {B_1} $ $ g_3^3 $ $ g_5^3 $ $ g_2^3 $ $ g_4^3 $ $ g_4^3 $ $ g_2^3 $
$ {B_2} $ $ g_6^3 $ $ g_7^3 $ $ g_6^3 $ $ g_7^3 $ $ g_7^3 $ $ g_5^3 $
$ {B_3} $ $ g_4^3 $ $ g_5^3 $ $ g_4^3 $ $ g_5^3 $ $ g_5^3 $ $ g_3^3 $
$ {B_4} $ $ g_2^3 $ $ g_4^3 $ $ g_1^3 $ $ g_3^3 $ $ g_3^3 $ $ g_0^3 $
$ {B_5} $ $ g_7^3 $ $ g_8^3 $ $ g_7^3 $ $ g_8^3 $ $ g_8^3 $ $ g_7^3 $
$ {B_6} $ $ g_7^3 $ $ g_8^3 $ $ g_6^3 $ $ g_7^3 $ $ g_8^3 $ $ g_6^3 $
$ {B_7} $ $ g_5^3 $ $ g_6^3 $ $ g_4^3 $ $ g_5^3 $ $ g_6^3 $ $ g_4^3 $
$ {B_8} $ $ g_5^3 $ $ g_7^3 $ $ g_5^3 $ $ g_6^3 $ $ g_6^3 $ $ g_4^3 $
表 7  决策专家对各备选方案在各标准下决策专家的云模型数据
A ${\boldsymbol{R}}$ $t_{xy}^c $
$ {A_1} $ $ {A_2} $ $ {A_3} $ $ {A_4} $ $ {A_5} $ $ {A_6} $
$ {A_1} $ R1 0.128 0 0.162 7 0.097 2 0.139 2 0.170 1 0.093 2
R2 0 0.181 4 0.075 2 0.150 1 0.160 4 0.086 3
R3 0 0.164 2 0.092 5 0.151 5 0.171 3 0.096 1
$\vdots$
$ {A_6} $ R1 0.162 8 0.184 6 0.109 4 0.156 2 0.174 0 0.128 0
R2 0.169 6 0.187 0 0.116 1 0.148 7 0.156 4 0
R3 0.159 9 0.189 2 0.111 0 0.146 3 0.172 1 0
表 8  3个模糊偏好关系下的群决策矩阵
图 7  不同决策方法的总体得分结果对比图
决策方法 e/% t/min
4个备选方案 6个备选方案 4个备选方案 6个备选方案
本研究 4.82 6.91 1.37 1.91
SVNS 5.07 9.30 1.19 1.75
VIKOR 11.13 18.62 0.53 0.84
BWM 12.29 20.46 0.78 0.95
表 9  决策性能结果对比
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