CN-121980212-A - Subjective and objective combination weighting evaluation method based on variance optimization

CN121980212ACN 121980212 ACN121980212 ACN 121980212ACN-121980212-A

Abstract

The invention discloses a subjective and objective combination weighting evaluation method based on variance optimization, which comprises the steps of firstly, evaluating the relative importance of each index to obtain subjective weight of each index; the method comprises the steps of constructing a sample-index matrix, calculating the information entropy value of each index to obtain the weight of each index based on the information entropy, eliminating redundant indexes through index association degree and inter-index association degree calculation to realize de-overlapping, calculating the index absolute association degree and normalizing to obtain the objective weight of the index, setting a subjective and objective weight coefficient, carrying out linear addition processing on the subjective and objective weight, enabling the variance to be as small as possible under the premise of constraint condition coefficient sum of 1 to obtain the optimal subjective and objective combined weight of each index, judging the consistency of the subjective and objective weights and the sequencing array of the indexes, and determining the final weight of the index. The invention realizes the complementary advantages of subjective and objective empowerment on the basis of retaining the advantages of the original subjective and objective assessment method, and improves the assessment effect of the assessment model.

Inventors

ZHANG TAO
Ruan Ningye
KONG XIANGHAO
Jia Hanwu
XU XINRUI
LI TING
LI XIAOJUAN
LIU TINGHAO
JIANG YU
LIU BIN

Assignees

中国空间技术研究院

Dates

Publication Date: 20260505
Application Date: 20251212

Claims (10)

1. The subjective and objective combination weighting evaluation method based on variance optimization is characterized by comprising the following steps of: evaluating the relative importance of each index to obtain subjective weight of each index; constructing a sample-index matrix, and calculating the information entropy value of each index to obtain the weight of each index based on the information entropy; According to the weight of each index based on the information entropy, eliminating redundant indexes through index association degree and inter-index association degree calculation to realize de-overlapping, calculating the index absolute association degree and normalizing to obtain the objective weight of the index; setting a subjective and objective weight coefficient, carrying out linear addition processing on the subjective and objective weights, and enabling variance to be as small as possible on the premise that the constraint condition coefficient sum is 1 to obtain the subjective and objective combination weight with optimal indexes; Judging the subjective and objective weights of the indexes and the consistency of the ordered arrays, and determining the final weights of the indexes.
2. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1, wherein a sample-index matrix is constructed, and information entropy values of each index are calculated to obtain weights of each index, specifically: The evaluation index data is standardized to obtain standardized data : In the formula, Represents the value in the evaluation index data, Representing the value of the index which is currently required to be standardized; Calculating information entropy of the index: Wherein, the , Is the index number; Based on an entropy weight method, calculating information entropy of each index, and calculating the weight of each index through an information entropy value: In the formula, Is the first The information entropy value of the individual index(s), Is the first The weight of the individual indicators.
3. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1, wherein the index association degree is calculated: In the formula, Is the first calculated by entropy weight method The weight of the term index is determined, ; Is taken as an index To decision index value Is a degree of index association; Is the first Part sample No. 1 A relevance coefficient of the item index; is the number of samples; In the formula, Is the first The decision index value corresponding to the piece of sample, Is the first Part sample No. 1 The normalized value of the term index is used, Is the first Decision index value in sample The minimum value of the difference of the normalized values of the term index, Is the first Decision index value in sample The maximum value of the difference of the normalized values of the term index, Is a resolution factor.
4. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1, wherein the degree of correlation between indexes is calculated: In the formula, Is taken as an index Index of pair The degree of correlation between the indices of (3), Is the first calculated by entropy weight method The weight of the term index is determined, ; Is the first Index in a sample Index of pair A coefficient of correlation between the indices; In the formula, Is the first Part sample No. 1 The normalized value of the term index is used, Is the first Part sample No. 1 The normalized value of the term index is used, Is a resolution factor.
5. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1, wherein the index is calculated by the index association degree and the inter-index association degree Sum index Degree of overlap in index association degree with respect to decision index value: The index can be calculated by de-overlapping Absolute degree of association of the indices of (a): In the formula, For all and index There are numbers of indicators in overlapping relationship.
6. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 5, wherein the objective weights of the indexes are calculated according to the absolute relevance of the indexes: In the formula, Is the first Objective weight of individual indicators.
7. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1, wherein the subjective and objective weights are subjected to linear addition: In the formula, Is the first Subjective weighting of individual indicators And objective weight K is the subjective and objective combination coefficient.
8. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 7, wherein an optimization problem model is established, and an optimal value of a subjective and objective combination coefficient k is solved; Optimization problem model: In the formula, To the first of the evaluated systems The test value of each index, Is the index number.
9. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1 is characterized by judging whether subjective and objective weights of indexes and a sequencing array are consistent, if sequencing is completely consistent, applying a combination weighting method based on variance optimization, if sequencing is partially consistent, calculating index weights by using an optimal combination weighting method based on variance for indexes with the same sequencing, still using subjective weights for indexes with different sequencing, and if sequencing is completely inconsistent, discarding objective weights, using the subjective weights as final index weights, and determining final weights based on the weight selection criteria.
10. The subjective and objective combination weighting evaluation method based on variance optimization according to claim 1 is characterized in that the relative importance of each index is evaluated by using quantization scales of 1 to 9 according to subjective experience, an index importance comparison matrix is formed, consistency test is conducted on the index importance comparison matrix, an index weight vector is calculated after the consistency test is passed, and finally normalization processing is conducted, so that index subjective weights are obtained.

Description

Subjective and objective combination weighting evaluation method based on variance optimization Technical Field The invention relates to a subjective and objective combination weighting evaluation method based on variance optimization, and belongs to the technical field of efficiency evaluation. Background In the evaluation field, the traditional evaluation method is long-term faced with the fundamental contradiction that subjectivity and objectivity are difficult to coordinate. The early performance evaluation mainly adopts subjective weighting methods such as expert scoring method, analytic hierarchy process and the like, while the experience value of the field expert can be reflected, the evaluation result is easily influenced by expert knowledge structure and subjective tendency, and has larger uncertainty, and with the development of information technology, objective weighting methods such as entropy weighting method, CRITIC method and the like are gradually raised, and the methods can determine the weight according to the statistical characteristics of the data, but often neglect key factors such as actual environment, actual demand and the like, so that the evaluation result has deviation from the practical requirement. Aiming at the evaluation problem that the traditional evaluation method is difficult to meet high precision and high reliability, the subjective and objective combination weighting evaluation method based on variance optimization not only reserves the knowledge value of expert experience, but also fully utilizes the objective rule of data driving, and provides a new thought and method for solving the technical problem of complex performance evaluation. Disclosure of Invention The invention solves the technical problems of overcoming the defects of the prior art, providing a subjective and objective combination weighting evaluation method based on variance optimization, realizing the complementation of the advantages of subjective weighting and objective weighting by weight combination design on the basis of keeping the advantages of the original subjective and objective evaluation method, and improving the evaluation effect of an evaluation model. The technical scheme of the invention is as follows: A subjective and objective combination weighting evaluation method based on variance optimization comprises the following steps: evaluating the relative importance of each index to obtain subjective weight of each index; constructing a sample-index matrix, and calculating the information entropy value of each index to obtain the weight of each index based on the information entropy; According to the weight of each index based on the information entropy, eliminating redundant indexes through index association degree and inter-index association degree calculation to realize de-overlapping, calculating the index absolute association degree and normalizing to obtain the objective weight of the index; setting a subjective and objective weight coefficient, carrying out linear addition processing on the subjective and objective weights, and enabling variance to be as small as possible on the premise that the constraint condition coefficient sum is 1 to obtain the subjective and objective combination weight with optimal indexes; Judging the subjective and objective weights of the indexes and the consistency of the ordered arrays, and determining the final weights of the indexes. Further, a sample-index matrix is constructed, the information entropy value of each index is calculated, and the weight of each index is obtained, specifically: The evaluation index data is standardized to obtain standardized data : If the forward index requirement satisfaction degree is: In the formula, Represents the value in the evaluation index data,Representing the value of the index which is currently required to be standardized; Calculating information entropy of the index: Wherein, the ,Is the index number; Based on an entropy weight method, calculating information entropy of each index, and calculating the weight of each index through an information entropy value: In the formula, Is the firstThe information entropy value of the individual index(s),Is the firstThe weight of the individual indicators. Further, calculating an index association degree: In the formula, Is the first calculated by entropy weight methodThe weight of the term index is determined,;Is taken as an indexTo decision index valueIs a degree of index association; Is the first Part sample No. 1A relevance coefficient of the item index; is the number of samples; In the formula, Is the firstThe decision index value corresponding to the piece of sample,Is the firstPart sample No. 1The normalized value of the term index is used,Is the firstDecision index value in sampleThe minimum value of the difference of the normalized values of the term index,Is the firstDecision index value in sampleThe maximum value of the difference of the normalized values of