传统理想解法存在与正理想解欧氏距离更近的方案同时与负理想解欧 氏距离也更近的缺陷,现有投影方法存在无法完全度量向量之间的相近程度及投影 值的取值范围无界限的缺陷.为了解决以上问题,文章提出了基于归一化双向投影法 的动态评价方法.首先回顾了双向投影法的相关内容及投影方法存在的缺陷;然后讨论 了归一化投影模型的定义及性质;在此基础上提出了基于归一化双向投影的评价方法 并定义了衡量方案优劣的一致性系数,通过具体的例子与其他投影方法进行分析比较;最 后加入时序数据拓展为动态评价模型,同时考虑指标值的差异性和增长程度,并通过 对2014--2018年我国东部地区创新能力进行评价来验证动态模型的有效性.结果表明 基于归一化双向投影法的动态评价方法在综合评价和多属性决策领域具有一定实用性.

The traditional ideal solution method has the defect that the Euclidean distance of the positive ideal solution is closer, and the Euclidean distance of the negative ideal solution is also closer. The existing projection methods have the defects that they cannot fully measure the similarity between vectors and the range of projection values is unlimited. In order to solve the above problems, a dynamic evaluation method based on the normalized bidirectional projection method is proposed. Firstly, the related content of the bidirectional projection method and the defects of the projection method are reviewed. Then the definition and properties of the normalized projection model are discussed. On this basis, an evaluation method based on normalized bidirectional projection is proposed and the consistency coefficient to measure the advantages and disadvantages of the plan is defined, and specific examples are used to analyze and compare with other projection methods. Finally, time series data is introduced to expand into a dynamic evaluation model, while considering the difference and growth degree of index values, and through the 2014--2018 Eastern China innovation ability evaluation to verify the effectiveness of the dynamic model. The results show that the dynamic evaluation method based on the normalized bidirectional projection method has certain practicability in the field of comprehensive evaluation and multi-attribute decision- making.