基于多源混合评价信息的随机聚合指数及应用

doi:10.16381/j.cnki.issn1003-207x.2022.1903

Abstract

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

CLC Number:

C934

Qiankun Dong, Pingtao Yi, Weiwei Li, Lu Wang. Random-aggregation-based Index Based on Multi-source Hybrid Information and Its Applications[J]. Chinese Journal of Management Science, 2025, 33(7): 128-138.

Figures/Tables 10

References 27

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指数类别	计算方式	值域范围	特质	适用情境
优胜指数	差值	有上限	类似于评价结论中的“序”信息，侧重强调被评价对象之间的优劣关系	更适用于在众多对象中进行择优的管理活动，如候选人投票、城市综合实力排名等
差异指数	比值	无上限	类似于评价结论中的“值”信息，侧重强调被评价对象之间的优劣程度	更适用于凸显被评价对象之间差异的管理活动，如员工绩效考核、多区域的发展水平分析等

被考核人员	E₁	E₂	E₃	E₄	E₅
时期T₁
O₁	3	一般	[3，6]	2(序值)	[0.30,0.49]
O₂	6	好	[2，5]	4(序值)	[0.18,0.57]
O₃	5	差	[3，5]	3(序值)	[0.19,0.37]
O₄	8	稍好	[4，5]	1(序值)	[0.11,0.70]
时期T₂
O₁	4	一般	[4，5]	2(序值)	[0.26,0.50]
O₂	7	稍好	[5，8]	4(序值)	[0.40,0.57]
O₃	7	稍差	[4，5]	3(序值)	[0.20,0.48]
O₄	8	好	[2，3]	1(序值)	[0.30,0.48]
时期T₃
O₁	5	稍差	[4，7]	3(序值)	[0.83,1.12]
O₂	8	一般	[5，8]	4(序值)	[0.52,0.65]
O₃	10	一般	[4，6]	2(序值)	[0.48,0.54]
O₄	9	一般	[6，7]	1(序值)	[0.41,0.89]
时期T₄
O₁	7	稍好	[6，10]	3(序值)	[0.84,0.95]
O₂	10	一般	[3，5]	4(序值)	[0.45,0.84]
O₃	13	稍好	[5，7]	2(序值)	[0.55,0.62]
O₄	11	好	[7，10]	1(序值)	[0.58,1.21]
时期T₅
O₁	9	稍好	[4，6]	4(序值)	[0.36,0.75]
O₂	11	稍好	[3，9]	3(序值)	[0.89,1.34]
O₃	16	好	[5，8]	1(序值)	[0.42,0.70]
O₄	13	稍好	[6，9]	2(序值)	[0.39,0.86]
时期T₆
O₁	14	一般	[5，9]	4(序值)	[0.44,0.62]
O₂	15	差	[8，13]	2(序值)	[0.15,0.69]
O₃	18	好	[6，9]	1(序值)	[0.42,0.85]
O₄	14	稍差	[8，10]	3(序值)	[0.62,1.08]

被考核人员	E₁	E₂	E₃	E₄	E₅
时期T₁
O₁	[0,0]	[0.3,0.5]	[0.25,1]	[0.5,0.75]	[0.44,0.72]
O₂	[0.63,0.63]	[0.75,1]	[0,0.75]	[0,0.25]	[0.23,0.83]
O₃	[0.38,0.38]	[0,0.14]	[0.25,0.75]	[0.25,0.5]	[0.25,0.55]
O₄	[1,1]	[0.5,0.75]	[0.42,0.75]	[0.75,1]	[0,1]
时期T₆
O₁	[2.2,2.2]	[0.3,0.5]	[0.75,1.75]	[0,0.25]	[0.65,0.89]
O₂	[2.4,2.4]	[0,0.14]	[1.5,2.75]	[0.5,0.75]	[0.13,0.99]
O₃	[3,3]	[0.75,1]	[1,1.75]	[0.75,1]	[0.62,1.25]
O₄	[2.2,2.2]	[0.14,0.3]	[1.5,2]	[0.25,0.5]	[0.89,1.64]

时期T₁				时期T₂				时期T₃
0.5	0.230	0.948	0	0.5	0	0.302	0	0.5	0.283	0.040	0
0.770	0.5	0.992	0.005	1	0.5	1	0.436	0.717	0.5	0.115	0
0.052	0.008	0.5	0	0.698	0	0.5	0	0.960	0.885	0.5	0.010
1	0.995	1	0.5	1	0.564	1	0.5	1	1	0.990	0.5
时期T₄				时期T₅				时期T₆
0.5	1	0.111	0	0.5	0	0	0	0.5	0.027	0	0.002
0	0.5	0	0	1	0.5	0.038	0.348	0.973	0.5	0.006	0.474
0.889	1	0.5	0	1	0.962	0.5	0.965	1	0.994	0.5	1
1	1	1	0.5	1	0.652	0.035	0.5	0.998	0.526	0	0.5

时期T₁				时期T₂				时期T₃
1	0.883	1.295	0.623	1	0.691	0.947	0.681	1	0.935	0.843	0.717
1.132	1	1.466	0.705	1.446	1	1.370	0.985	1.069	1	0.901	0.766
0.772	0.682	1	0.481	1.056	0.730	1	0.719	1.186	1.109	1	0.850
1.606	1.418	2.080	1	1.468	1.015	1.390	1	1.395	1.305	1.176	1
时期T₄				时期T₅				时期T₆
1	1.375	0.911	0.734	1	0.654	0.552	0.625	1	0.821	0.672	0.816
0.727	1	0.662	0.533	1.529	1	0.844	0.956	1.217	1	0.818	0.994
1.098	1.510	1	0.806	1.812	1.185	1	1.133	1.488	1.222	1	1.215
1.363	1.875	1.241	1	1.600	1.046	0.883	1	1.225	1.006	0.823	1

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

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指数	时期T₁	时期T₂	时期T₃	时期T₄	时期T₅	时期T₆	修正次数
动态平均算子	-	是	是	是	是	是	5
动态TOPSIS	-	是	是	是	是	是	5
随机聚合指数	-	否	否	否	否	否	0

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