Applying Concept Hierarchy Development to Multi-attribute Decision-making Method for Product Conceptual Design
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摘要: 为了解决目前产品概念设计方案中系统层级结构考虑欠缺以及多属性之间无相互联系的问题，提出一种基于概念层次开发（Concept hierarchy development，CHD）的产品概念设计多属性决策方法。首先，通过CHD理论将各备选产品概念设计方案的图像划分为模块部件、角度视图、物理属性三个设计层次开发，构建每个层次开发中多属性准则之间的相似度比较矩阵。进而利用毕达哥拉斯模糊集（Pythagorean fuzzy sets，PFS）和前景理论（Prospect theory，PT）相结合的方法，得到各决策专家及设计准则的权重分配，从而实现客观合理的产品概念设计多属性决策。最后以响堂山佛像益智玩具的产品概念设计方案为例，验证了该方法的可行性和有效性。Abstract: In order to solve the problem of poorly considering a system′s hierarchical structure in the current product conceptual design plan and the lack of interrelationship between multiple attributes, a multi-attribute decision-making method for product concept design based on concept hierarchy development (CHD) was proposed. Based on the CHD theory, the method divides the image of each candidate product′s conceptual design plan into three design levels: module component, angle view, and physical attribute.The similarity comparison matrix betweenmulti-attribute criteria at each level of development was constructed. The method of combining the Pythagorean fuzzy set (PFS) and theprospect theory (PT) was used to obtain the weight distribution of decision experts and attribute criteria and realize the objective and reasonable multi-attribute decision-making for product conceptual design. Finally, the feasibility and effectiveness of the method was verified by taking product conceptual design schemes of Xiangtangshan Buddha educational toys as example.
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表 1 产品概念设计方案1各图像权重
权重 佛头 佛身 背刻 模块部件权重 0.778 0.903 0.396 角度视图权重 前0.653，侧0.524，顶0.302 前0.852，侧0.459，顶0.751 前0.624，侧0.315，顶0.367 物理属性权重 材质 0.572 色彩 0.638 造型 0.826 纹理 0.269 
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表 2 5个备选方案相似度决策矩阵
方案 模块部件 角度视图 物理属性 D2 0.348 0.552 0.869 D3 0.526 0.668 0.389 D4 0.824 0.421 0.524 D5 0.459 0.269 0.877 D6 0.375 0.284 0.358
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表 3 方案1模块部件设计层次得分矩阵
专家 Y1 Y2 Y3 Y4 Y5 Y6 N1 0.8 0.6 0.8 0.7 0.5 0.4 N2 0.4 0.3 0.6 0.7 0.5 0.8 N3 0.6 0.4 0.6 0.7 0.9 0.5 N4 0.7 0.6 0.8 0.3 0.5 0.6 N5 0.8 0.7 0.5 0.5 0.6 0.3 N6 0.7 0.5 0.7 0.6 0.8 0.9 N7 0.8 0.6 0.5 0.4 0.7 0.6 N8 0.5 0.8 0.4 0.3 0.6 0.7
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表 4 决策专家评价矩阵
专家 A1 A2 A3 A4 A5 N1 〈0.7,0.2〉 〈0.6,0.5〉 〈0.3,0.4〉 〈0.8,0.2〉 〈0.6,0.1〉 N2 〈0.5,0.3〉 〈0.7,0.5〉 〈0.8,0.5〉 〈0.6,0.2〉 〈0.4,0.7〉 N3 〈0.4,0.5〉 〈0.8,0.1〉 〈0.6,0.4〉 〈0.5,0.6〉 〈0.7,0.3〉 N4 〈0.6,0.2〉 〈0.4,0.4〉 〈0.7,0.5〉 〈0.6,0.2〉 〈0.5,0.6〉 N5 〈0.9,0.1〉 〈0.3,0.6〉 〈0.5,0.7〉 〈0.7,0.4〉 〈0.7,0.3〉 N6 〈0.5,0.6〉 〈0.4,0.7〉 〈0.5,0.2〉 〈0.2,0.1〉 〈0.3,0.6〉 N7 〈0.3,0.8〉 〈0.6,0.2〉 〈0.2,0.4〉 〈0.5,0.3〉 〈0.4,0.5〉 N8 〈0.2,0.1〉 〈0.7,0.6〉 〈0.5,0.5〉 〈0.6,0.2〉 〈0.4,0.4〉
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表 5 犹豫度矩阵
专家 A1 A2 A3 A4 A5 N1 0.663 0.624 0.866 0.566 0.794 N2 0.812 0.510 0.332 0.775 0.592 N3 0.768 0.592 0.173 0.624 0.648 N4 0.775 0.825 0.510 0.775 0.529 N5 0.424 0.742 0.510 0.592 0.648 N6 0.624 0.592 0.843 0.975 0.387 N7 0.520 0.894 0.894 0.812 0.768 N8 0.911 0.387 0.707 0.775 0.825
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表 6 正理想解距离矩阵
专家 A1 A2 A3 A4 A5 N1 0.167 0.553 0.590 0.108 0.075 N2 0.425 0.490 0.341 0.201 0.851 N3 0.763 0 0.395 0.743 0.191 N4 0.232 0.631 0.384 0.201 0.677 N5 0 0.948 0.780 0.206 0.191 N6 0.401 0.924 0.275 0.555 0.822 N7 1.101 0.179 0.834 0.401 0.667 N8 0.597 1.070 0.543 0.203 0.554
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表 7 负理想解距离矩阵
专家 A1 A2 A3 A4 A5 N1 1.029 0.490 0.375 0.975 0.882 N2 0.777 0.578 0.763 0.860 0.120 N3 0.546 1.022 0.650 0.375 0.776 N4 0.975 0.401 0.691 0.860 0.297 N5 1.194 0.085 0.354 0.732 0.776 N6 0.453 0.120 0.765 0.706 0.033 N7 0.110 0.843 0.277 0.661 0.281 N8 0.353 0.496 0.497 0.858 0.401
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表 8 负前景值价值函数
专家 A1 A2 A3 A4 A5 N1 −0.466 −1.336 −1.414 −0.317 −0.230 N2 −1.060 −1.201 −0.873 −0.548 −1.952 N3 −1.773 0 −0.994 −1.732 −0.524 N4 −0.622 −1.500 −0.969 −0.548 −1.596 N5 0 −2.147 −1.808 −0.560 −0.524 N6 −1.007 −2.099 −0.722 −1.340 −1.894 N7 −2.449 −0.495 −1.918 −1.007 −1.575 N8 −1.429 −0.388 −1.315 −0.553 −1.338
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表 9 正前景值价值函数
专家 A1 A2 A3 A4 A5 N1 1.025 0.534 0.422 0.978 0.895 N2 0.801 0.617 0.788 0.878 0.155 N3 0.587 1.019 0.684 0.422 0.800 N4 0.978 0.447 0.722 0.878 0.344 N5 1.169 0.114 0.401 0.760 0.800 N6 0.498 0.155 0.790 0.736 0.050 N7 0.143 0.860 0.323 0.695 0.327 N8 0.400 0.540 0.539 0.874 0.447
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表 10 概率权重函数
权重函数 $ {\lambda _1} $ $ {\lambda _2} $ $ {\lambda _3} $ $ {\lambda _4} $ $ {\lambda _5} $ $ {\xi ^ + }\left( {{\lambda _j}} \right) $ 0.259 0.254 0.255 0.288 0.249 $ {\xi ^ - }\left( {{\lambda _j}} \right) $ 0.255 0.248 0.249 0.286 0.242
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表 11 总体产品概念设计方案3个设计层次开发得分矩阵
方案 模块部件 角度视图 物理属性 D1 0.703 0.512 0.794 D2 0.716 0.608 0.843 D3 0.670 0.433 0.548 D4 0.841 0.739 0.925 D5 0.462 0.597 0.472 D6 0.652 0.767 0.518
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