Abstract: Comprehensive evaluation refers to the process of conducting a holistic and overall evaluation of an object under evaluation by utilizing multi-dimensional index data. As evaluation issues become increasingly complex, it is becoming more difficult for a single expert to make accurate judgments. To ensure the comprehensiveness and accuracy of evaluation, more and more evaluation issues require the participation of multiple experts, thus forming group evaluation. Especially when dealing with complex systematic evaluation issues, the adoption of group evaluation to solve such problems has become a widely held consensus. One urgent problem to be solved in group evaluation is how to determine the weight coefficients based on the evaluation index preference information provided by multiple experts. As one of the representatives of subjective weighting methods, the sequential relation analysis (G1) method has gained wide attention and extensive application since its introduction due to its simplicity, ease of operation, and the need for no judgment matrix. Currently, the G1 method is gradually being applied to group evaluation, but there are still few studies on how to determine index weights using this method when facing group evaluation issues.
Based on existing research and aiming to ensure experts’ confidence in group evaluation results, this paper proposes a G1 method for group evaluation that follows the principle of “the minority is subordinate to the majority.” Firstly, an iterative algorithm is designed to determine the sequential relationship of evaluation indicators based on the evaluation information provided by experts. Secondly, the concept and measurement method of the ordered rate of sets are proposed to determine expert weights, and the evaluation indicator weights are solved by aggregating the individual evaluation indicator preference information of experts. Thirdly, a method is provided to determine the ratio of the importance of any two adjacent evaluation indicators in the group evaluation indicator sequence based on the evaluation indicator preference information provided by individual experts. The evaluation indicator weights are solved by aggregating the group’s evaluation indicator preference information. Then, two methods are presented to calculate the comprehensive weights of evaluation indicators for group evaluation. One is to solve the evaluation indicator weights based on the preferences of the evaluation demander from two perspectives, and the other is to maximize the overall differences between the evaluated objects by constructing a nonlinear programming model. Finally, an example is used to introduce the application process of the proposed method, and a comparative analysis is conducted with existing research results.
The results show that: (1)The index weights calculated by the proposed method are very close to those obtained by other methods in the literature. Additionally, as the proposed method does not require constructing a judgment matrix, and the information aggregation method is not limited to nonlinear weighting, it can be seen as a more generalized form of other methods, demonstrating its rationality to a certain extent. (2)By solving the evaluation indicator weights from two individual indicator preference information and group indicator preference information, respectively, while considering the preference of the evaluation demander, the proposed method considers more comprehensive information and improves the accuracy and satisfaction of the evaluation results. (3)Different preferences of the evaluation demander in selecting preference coefficients lead to different final weights of evaluation indicators which indicates that considering different evaluation demander preferences has a significant impact on determining weights in the proposed method and verifying its effectiveness. Compared with existing research results, the proposed method extends the G1 method itself to group evaluation situations, rather than simply using it as a method to determine indicator weights in group evaluation. At the same time, the proposed method addresses the issue of determining evaluation indicator weights when the relative importance ratio between adjacent evaluation indicators in the group sequence is missing which makes the application scope of the G1 method more extensive.
In future studies, the proposed method will be further extended to the evaluation of uncertain evaluation situations represented by fuzzy numbers, interval numbers, etc. At the same time, the application of the G1 method in group evaluation will be further explored.

Key words: group evaluation, sequential relation analysis, iterative algorithm, set sequential rate, the biggest overall difference

摘要： 针对评价指标权重的确定问题,本文将序关系分析(G1)法拓展至群体评价,提出一种面向群体评价的序关系分析法。首先,基于专家给出的评价信息,设计一种迭代算法求解群体的评价指标序关系;其次,提出集合有序率概念和测度方法用于确定专家权重,并通过集结专家个体的评价指标偏好信息求解评价指标权重;再次,根据专家个体给出的评价指标偏好信息,给出群体评价指标序关系中任意两相邻评价指标的重要性程度比值的确定方法,并通过集结群体的评价指标偏好信息求解评价指标权重;最后,给出两种求解最终面向群体评价的评价指标综合权重的方法,一是根据评价需求者对两角度求解评价指标权重的偏好求解,二是以使被评价对象间的整体差异最大为目标,通过构建非线性规划模型求解。文末通过一个算例对本文提出的方法进行说明并与其它文献方法进行对比分析。

关键词: 群体评价, 序关系分析法, 迭代算法, 集合有序率, 整体差异最大