基于直觉模糊网络分析法的产品概念设计理论与应用研究

Product conceptual design determines the quality, cost and reliability, etc. of the final product, which is considered the most important stage in the product life cycle. However, due to the ambiguity of design information and high dynamic of design process, the existing conceptual design methods are difficult to meet all these requirements. Evaluation and decision-making theory of complex system based on analytic network process has been drawn widely attention by scholars in recent years. Previous studies propose that the structure and characteristics of the supermatrix have an important effect on the calculation and results of analytic network process, but it needs for clearer and more convincing answers. Meanwhile, when dealing with uncertain information, intuitionistic fuzzy set indicates information more abundant and flexible than fuzzy set. This project plans to focus on the following important problems by integrating the theories and methods of multi-discipline: a) How to acquire the local weights of intuitionistic fuzzy judgment matrices? b) What are the characteristics and properties of the intuitionistic fuzzy unweighted supermatrix? c) Under what conditions will the weighted supermatrix convege? The interactive network analytic frameworks and models based on intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set will be proposed through data analysis and simulation studies, and they will be applied in product conceptual design. This project is expected to solve the bottleneck problem of intuitionistic fuzzy analytic network process, to promote and further the fuzzy analytic network process, and to improve the evaluation and decision-making effect of complex systems, such as product conceptual design.

产品概念设计决定着最终产品的质量、成本和可靠性等，被认为是产品生命周期中最重要的阶段。由于设计信息的模糊性和设计过程的高动态性，现有的设计方法难以完全满足这些要求。近年来，基于网络分析法的复杂系统评价与决策理论引起了学者们的广泛关注。通过已有研究发现超矩阵的结构和性质对网络分析法的计算和结果具有重要影响，但有待深入研究。由于直觉模糊集在处理不确定信息时，比模糊集具有更强的表示能力和灵活性。本项目拟集成多门学科的理论和方法，针对“如何获取直觉模糊判断矩阵的局部权重？”、“直觉模糊未加权超矩阵的特点和性质有哪些？”、“加权超矩阵在什么条件下会收敛？”等重要问题，开展数据分析和模拟仿真研究，提出基于直觉模糊集和区间值直觉模糊集的交互式网络分析框架和模型，并在产品概念设计中应用。这对解决直觉模糊网络分析法的瓶颈问题，推动和促进模糊网络分析法，改进产品概念设计等复杂系统的评价和决策效果具有重要意义。

如何使复杂环境下的评价和决策更加科学和合理，是学者们一直关注的焦点和努力的方向。在产品概念设计、企业价值评估和项目选择等许多实际问题中，各层次指标内部元素间往往存在依存关系，低层元素对高层元素亦有支配作用，即存在反馈，此时系统的结构更类似于网络结构。近年来，基于网络分析法的复杂系统评价与决策理论引起了学者们的广泛关注。由于直觉模糊集在处理不确定信息时，比模糊集具有更强的表示能力和灵活性。本项目集成多门学科的理论和方法，开展了如下研究工作，并取得了相应的研究成果：如何客观合理的建立复杂系统的指标体系网络结构，提出了科学的程序化方法；根据区间数、三角模糊数判断矩阵权重计算方法和直觉模糊偏好关系，提出了基于直觉模糊集的判断矩阵局部权重计算方法；根据指标体系的网络结构科学构造基于直觉模糊集的未加权超矩阵；总结归纳了直觉模糊超矩阵的收敛条件和直觉模糊极限超矩阵的排序等性质；根据定性可能性理论和模糊多目标规划等知识，提出了相应的启发式求解算法；借鉴和改进求解经典网络分析法的Super Decisions Software和Matlab等数学工具，开发求解直觉模糊网络分析法的软件程序；以产品概念设计、企业价值评估、项目选择为例，具体说明了如何运用直觉模糊网络分析法来解决复杂系统的评价和决策问题。这对解决直觉模糊网络分析法的瓶颈问题，推动和促进模糊网络分析法，改进产品概念设计等复杂系统的评价和决策效果具有重要意义。