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中国管理科学

中国管理科学 ›› 2025, Vol. 33 ›› Issue (7): 128-138.doi: 10.16381/j.cnki.issn1003-207x.2022.1903

• • 上一篇    

基于多源混合评价信息的随机聚合指数及应用

董乾坤1,2, 易平涛1,2(), 李伟伟1,2, 王露1,2   

  1. 1.东北大学工商管理学院，辽宁 沈阳 110167
    2.东北评价中心，辽宁 沈阳 110167
  • 收稿日期:2022-08-30 修回日期:2024-05-27 出版日期:2025-07-25 发布日期:2025-08-06
  • 通讯作者: 易平涛 E-mail:ptyi@mail.neu.edu.cn
  • 基金资助:
    国家自然科学基金项目(72171040);国家自然科学基金项目(72171041);国家自然科学基金项目(72301062);辽宁省自然科学基金优秀青年基金项目(2024JH3/10200008);中央高校基本科研业务专项资金项目(N2406013);中央高校基本科研业务专项资金项目(N25ZLL013);中央高校基本科研业务专项资金项目(N25QNR003);中央高校基本科研业务专项资金项目(N25BSS010)

Random-aggregation-based Index Based on Multi-source Hybrid Information and Its Applications

Qiankun Dong1,2, Pingtao Yi1,2(), Weiwei Li1,2, Lu Wang1,2   

  1. 1.School of Business Administration，Northeastern University，Shenyang 110167，China
    2.Northeastern Evaluation Center，Shenyang 110167，China
  • Received:2022-08-30 Revised:2024-05-27 Online:2025-07-25 Published:2025-08-06
  • Contact: Pingtao Yi E-mail:ptyi@mail.neu.edu.cn

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摘要：

随着经济社会的发展，对事物状态进行实时跟踪的现实需求日益增加。针对多信息来源、多数据结构的复杂评价问题，提出了一类随机聚合指数以实时定位被评价对象的发展水平。具体而言，以分层计算的方式，分别给出了基期与报告期评价信息的无量纲化处理方法，为指数在相邻时期的平滑更迭提供数据支撑。在此基础上，依据优胜度矩阵，给出了优胜指数的编制方法，其中，采用“引入参考对象”的新思路确定基点大小，并利用平均优胜增量计算指数值。另外，考虑到被评价对象之间的优劣差异，提出“差异度矩阵”的概念，从坐标投影的视角给出了差异度的随机聚合算法，并详细讨论了差异指数的编制方法。通过公理化检验发现，随机聚合指数与众多经典指数相似，具有恒等性、同度量性、确定性、比例性等特征，这从理论层面证明了随机聚合指数在管理实践中的可行性。选取某企业员工绩效评价问题进行实例分析，结果表明，随机聚合指数能够在不确定混合信息考核环境下对员工之间的相对表现做到准确地跟踪监测。

关键词: 多源混合信息, 综合评价, 随机聚合, 指数计算, 动态分层无量纲化

Abstract:

The flourishing development of the big data era has led to the prevalence of decision situation involving multi-source hybrid information. Random-aggregation-based evaluation theory provides an effective solution for decision problems in such situations. However， existing research on random-aggregation-based evaluation has only focused on the fundamental measurement， neglecting the tracking function for the dynamic development of alternatives. In statistics， the concept of an “index” plays a role in dynamically monitoring the changes of phenomena. Therefore， the main objective of this paper is to study the calculation of random-aggregation-based index.Specifically， it focuses on addressing the following issues： （i） How to normalize multidimensional hybrid information data？ （ii） How to establish benchmarks based on random aggregation conclusions？ （iii） How to calculate the value of random-aggregation-based index？Motivated by the aforementioned issues， the primary contributions of this paper include： （i） A hierarchical dimensionless normalization method is proposed for the base period and reporting period， separately， to achieve a smooth index update. （ii） An index compilation method is presented in terms of the superiority matrix， in which a new idea of “introduction of reference objects” is used to determine the benchmark and the index value is calculated using the increment of the superiority. （iii） The concept of “Difference Matrix” is proposed and its random aggregation is given algorithm from the perspective of coordinate projection， along with discussing the associated index compilation method. （iv） The mathematical test reveals that the proposed indices， similar to the other classical indices， has the properties of identity， commensurability， determination， and proportion.Finally， an example concerning the performance appraisal is analyzed and it is found that the proposed index can accurately track the relative performance among employees in uncertain complex environments. Compared with existing dynamic comprehensive methods， the proposed index can effectively reduce computational workload and minimize result bias.

Key words: multi-source hybrid information, evaluation, random aggregation, index calculation, dynamic hierarchical dimensionless normalization

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