Comprehensive evaluation method and system based on improved information entropy

Abstract

The invention belongs to the technical field of data analysis, and particularly discloses a comprehensive evaluation method and system based on improved information entropy, and the method comprises the following steps: collecting original data of indexes of each evaluation object, and carrying out the normalization processing of the original data, and obtaining a normalized matrix of the indexes; calculating the information entropy of each index according to the obtained normalized matrix, introducing a correlation coefficient and an independent coefficient between the indexes to improve the information entropy, and calculating the index weight of correlation coefficient-information entropy; calculating a normalized matrix; calculating the Euclidean distance between each evaluation object and the positive and negative ideal solutions according to the obtained normalized matrix; and calculating a comprehensive evaluation value of each evaluation object according to the obtained Euclidean distance. According to the comprehensive evaluation method and system based on the improved information entropy, the influence of repeatability between indexes on the evaluation result is considered, the stability and accuracy of the comprehensive evaluation result can be improved, and the comprehensive evaluation result is more reasonable.

Description

Technical Field

[0001] The present invention relates to the technical field of data analysis, and in particular to a comprehensive evaluation method and system based on improved information entropy. Background Art

[0002] As a scientific decision support tool, the comprehensive evaluation method provides decision makers with a systematic analysis framework to help them understand problems from multiple perspectives and avoid decision errors caused by one-sidedness. It can comprehensively reflect multiple aspects of things by comprehensively analyzing multiple indicators, overcome the limitations of single indicator evaluation, and make the evaluation results more comprehensive and objective. The comprehensive evaluation method is widely used in many fields such as economy, society, and environment, such as enterprise economic benefit evaluation, social development level evaluation, and environmental quality assessment, providing decision makers with a quantitative decision-making basis and improving the scientificity and effectiveness of decision-making. In addition, the comprehensive evaluation method effectively solves the problem that a single indicator cannot fully reflect the overall situation of things by converting multiple indicators into a comprehensive indicator, making the evaluation results more accurate and reliable. The scientificity, objectivity, and comprehensiveness of the comprehensive evaluation method make it an important tool for solving complex decision-making problems, and it plays an important role in improving decision-making quality, optimizing resource allocation, and promoting sustainable development. Therefore, the research and application of the comprehensive evaluation method has important value and significance for both academia and practice.

[0003] Prior art document 1 (CN118898429A) provides an offshore decision-making scheme evaluation method based on subjective and objective weighting of a directed graph model by introducing fuzzy mapping functions and information entropy into weight calculation. Prior art document 2 (CN118468603A) uses the entropy weight method to determine the information entropy weight, and proposes a method for optimizing the saline CO2 geological storage injection scheme based on HP-EWM-TOPSIS. Prior art document 3 (CN118764900A) reduces the subjectivity in the evaluation process and improves the objectivity of the evaluation through the application of the information entropy weight method. Prior art document 4 (CN118673564A) calculates the information entropy and weight of the influencing factors, and proposes a method for identifying urban ventilation corridors supported by air flow costs. Information entropy is used in the prior art to calculate the weight of indicators, but the influence of the repeatability between indicators on the evaluation results is not taken into account, resulting in the instability and non-uniqueness of the final comprehensive evaluation results. Summary of the invention

[0004] In order to solve the deficiencies in the prior art, the present invention provides a comprehensive evaluation method and system based on improved information entropy, which takes into account the influence of repeatability between indicators on the evaluation results, can improve the stability and accuracy of the comprehensive evaluation results, and make the comprehensive evaluation results more reasonable.

[0005] The present invention adopts the following technical solution.

[0006] In a first aspect, the present invention provides a comprehensive evaluation method based on improved information entropy, comprising the following steps: collecting the original data of the indicators of each evaluation object, and normalizing the original data to obtain a normalized matrix of the indicators; calculating the information entropy of each indicator based on the obtained normalized matrix, and introducing the correlation coefficient and independence coefficient between the indicators to improve the information entropy, and calculating the indicator weight of the correlation coefficient-information entropy; calculating the normalized matrix based on the obtained correlation coefficient-information entropy weight and the normalized matrix; calculating the Euclidean distance between each evaluation object and the positive and negative ideal solutions based on the obtained normalized matrix; and calculating the comprehensive evaluation value of each evaluation object based on the obtained Euclidean distance.

[0007] Preferably, the calculation method of the normalized matrix is:

[0008]

[0009] Among them, z ij represents the normalized value of the jth indicator of the i-th evaluation object; x ij Represents the original data value of the jth indicator of the i-th evaluation object; are the maximum and minimum values ​​of the jth index respectively; the normalized matrix Z = [z ij ].

[0010] Preferably, the information entropy of each indicator is calculated as follows:

[0011]

[0012] in, m represents the total number of evaluation objects.

[0013] Preferably, the correlation coefficient and the independence coefficient are described according to the following formula:

[0014]

[0015]

[0016] Among them, r kj represents the correlation coefficient between the kth and jth indicators; v j represents the independence coefficient between the kth and jth indicators; z ik and z ij are the normalized scores of the kth and jth indicators of the i-th evaluation object in the normalized matrix Z respectively; and are the means of the normalized values ​​of the kth and jth indicators in the matrix Z, respectively; n represents the total number of indicators.

[0017] Preferably, the calculation method of the index weight of the correlation coefficient-information entropy is:

[0018]

[0019] Among them, w j Represents the indicator weight of correlation coefficient-information entropy,

[0020]

[0021] Preferably, the calculation method of the normalized matrix is:

[0022] C=[c ij ]

[0023] c ij =w j ·z ij

[0024] Where C represents the normalized matrix.

[0025] Preferably, the calculation method of the positive ideal solution and the negative ideal solution is:

[0026]

[0027] in, is a positive ideal solution; is a negative ideal solution; They respectively represent the maximum and minimum values ​​of the jth indicator of all evaluation objects in the normalized matrix.

[0028] Preferably, the Euclidean distance between each evaluation object and the positive and negative ideal solutions is calculated as follows:

[0029]

[0030] in, represents the Euclidean distance between the i-th evaluation object and the positive ideal solution, Represents the Euclidean distance between the i-th evaluation object and the negative ideal solution.

[0031] Preferably, the calculation method of the comprehensive evaluation value of each evaluation object is:

[0032]

[0033] Among them, ρ i Represents the comprehensive evaluation value of the i-th evaluation object.

[0034] In a second aspect, the present invention provides a system utilizing the aforementioned comprehensive evaluation method based on improved information entropy, comprising: a data collection module for collecting the original data of the indicators of each evaluation object; a normalization processing module for normalizing the collected original data; an indicator weight construction module for obtaining a normalized matrix according to the normalization processing, obtaining the information entropy of the indicator and the indicator weight of the correlation coefficient-information entropy after introducing the correlation coefficient and independent coefficient between the indicators to improve the information entropy; an evaluation module for determining the Euclidean distance between each evaluation object and the positive and negative ideal solutions based on the indicator weight and the normalization matrix, and obtaining the comprehensive evaluation value of each evaluation object.

[0035] The beneficial effect of the present invention is that, compared with the prior art, the index weight method based on information entropy of the present invention takes into account the influence of the repeatability between indicators on the evaluation results, and improves the information entropy index weight by introducing the independent coefficient between indicators, so that the comprehensive evaluation results are more reasonable and the accuracy of the evaluation results is effectively improved. And by implementing examples to illustrate and verify the improvement of the traditional information entropy weight calculation method by this method, it can solve the problem of evaluation information duplication caused by the correlation between evaluation indicators, making the final comprehensive evaluation results unstable and non-unique. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of a comprehensive evaluation method based on improved information entropy in the present invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only embodiments of a part of the present invention, rather than all embodiments. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the protection scope of the present invention.

[0038] Embodiment 1 of the present invention provides a comprehensive evaluation method based on improved information entropy. The correctness and effectiveness of the comprehensive evaluation method in the present invention are illustrated through the embodiment of the present invention. At the same time, it is illustrated that TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) based on the entropy weight method will produce certain evaluation errors when performing comprehensive evaluation.

[0039] The comprehensive evaluation method based on improved information entropy provided by the present invention comprises the following steps:

[0040] Step 1: Collect the original data of each evaluation object's indicators, and normalize the original data to obtain the normalized matrix of the indicators.

[0041] Specifically, for the evaluated object p i Index t of (i=1,2,3) j (j=1,2,3) for normalization:

[0042]

[0043] In the formula, z ij represents the normalized value of the jth indicator of the i-th evaluation object; x ij Represents the original data value of the jth indicator of the i-th evaluation object; are the maximum and minimum values ​​of the j-th indicator respectively.

[0044] Define Z = [z ij ] is the normalized matrix. The results are shown in Table 1, where all indicators are positive indicators, that is, the larger the value, the better the evaluated object.

[0045] Table 1 Normalized matrix

[0046]

[0047] Step 2: According to the normalized matrix obtained in step 1, the information entropy of each indicator is calculated, and the correlation coefficient and independence coefficient between indicators are introduced to improve the information entropy, and the indicator weight of correlation coefficient-information entropy is calculated.

[0048] Specifically, 1) give the information entropy E of the jth index j The calculation method is:

[0049]

[0050] In the formula, m represents the total number of evaluation objects. 2) The correlation coefficient and independence coefficient between indicators are introduced to improve the information entropy and obtain the indicator weight of correlation coefficient-information entropy.

[0051] The correlation coefficient indicates the degree of linear correlation between two indicators, and the independence coefficient indicates the degree of independence between indicators, which is obtained through complementarity with the correlation coefficient.

[0052] Specifically, the correlation coefficient r between the kth and jth indicators is kj The calculation formula is:

[0053]

[0054] In the formula, r kj represents the correlation coefficient between the kth and jth indicators; zik and z ij are the normalized scores of the kth and jth indicators of the i-th evaluation object in the normalized matrix Z respectively; and are the means of the normalized values ​​of the kth and jth indicators in the matrix Z, respectively.

[0055] The independence coefficient v between the kth and jth indicators j The calculation formula is:

[0056]

[0057] In the formula, v j represents the independence coefficient between the kth and jth indicators; n represents the total number of indicators.

[0058] Therefore, the index weight of the correlation coefficient-information entropy of the jth index is given as:

[0059]

[0060] In the formula,

[0061] In a preferred embodiment of the present invention, m = 3, n = 3. Through the normalized matrix Z and the above calculation method, the index weights of the correlation coefficient-information entropy can be obtained as w1 = 0.1522, w2 = 0.4239, and w3 = 0.4239 respectively.

[0062] Step 3: Calculate the normalized matrix according to the correlation coefficient-information entropy weight in step 2 and the normalized matrix in step 1.

[0063] 1) Normalized matrix C = [c ij ], c ij It represents the jth indicator element of the i-th evaluation object, and its calculation method is:

[0064] c ij =w j ·z ij (4)

[0065] The results are shown in Table 2.

[0066] Table 2 Normalized matrix

[0067]

[0068] 2) According to the normalized matrix, determine the positive ideal solution c * With the negative ideal solution c 0 .

[0069] Positive ideal solution Negative ideal solution They represent the maximum and minimum values ​​of the jth index of all evaluation objects in the normalized matrix. The positive and negative ideal solution results are shown in Table 2.

[0070] Step 4: Based on the normalized matrix obtained in step 3, calculate the Euclidean distance between each evaluation object and the positive and negative ideal solutions.

[0071] The calculation formula of the Euclidean distance between each evaluation object and the positive and negative ideal solutions is:

[0072]

[0073] In the formula, represents the Euclidean distance between the i-th evaluation object and the positive ideal solution, Represents the Euclidean distance between the i-th evaluation object and the negative ideal solution.

[0074] The results are shown in Table 3.

[0075] Table 3. Euclidean distances of positive and negative ideal solutions and comprehensive evaluation results

[0076]

[0077] Step 5: According to the Euclidean distance obtained in step 4, calculate the comprehensive evaluation value of each evaluation object. The calculation formula is as follows:

[0078]

[0079] ρ i represents the comprehensive evaluation value of the i-th evaluation object. The results are shown in Table 3.

[0080] It should be noted that the present invention improves the information entropy weight by the independent coefficients between indicators to optimize the evaluation results. In order to illustrate the improvement effect, the above embodiment is recalculated using the information entropy weight method to compare the evaluation results.

[0081] According to the information entropy weight By calculating the weight of each indicator, we can get the indicator weight values ​​of 0.0824, 0.4588, and 0.4588. Then, we can get the normalized matrix through formula (4), and get the positive and negative ideal solutions at the same time, as shown in Table 4.

[0082] Table 4. Standard matrix and positive and negative ideal solutions based on information entropy

[0083]

[0084] Through formula (1.6) and (1.7), the Euclid distance and comprehensive evaluation results can be obtained as shown in Table 1.5.

[0085] Table 5 Euclidean distance based on information entropy and comprehensive evaluation results

[0086]

[0087] As shown in the normalized matrix Table 1, for the index t1, the evaluated object p1 is 0.3 lower than p2, while for t2 and t3, p1 is only 0.04 higher than p2. It should be noted that the results of the t2 index and the t3 index are exactly the same, indicating that the two indexes are completely positively correlated. However, the comprehensive evaluation results (Table 5) show that C1 = 0.06049 > C2 = 0.05449, that is, the object p1 is superior to the object p2. This shows that the TOPSIS method based on information entropy adds points to the object p1 by repeatedly using the relevant evaluation indexes t2 and t3, resulting in a larger comprehensive evaluation value of p1 than p2. This is obviously inconsistent with the actual evaluation results, and there is a problem that the information entropy weight method is incorrect for the evaluation results.

[0088] This problem is caused by the repeated calculation of relevant indexes. By introducing an independent coefficient to consider the correlation between indexes and optimizing the information entropy index weight, this problem is solved. From the evaluation result Table 3, C1 = 0.06018 < C2 = 0.1033, and the result is in line with the actual situation.

[0089] Embodiment 2 of the present invention provides a system using the comprehensive evaluation method based on improved information entropy in Embodiment 1, including: a data collection module, a normalization processing module, an index construction module, and an evaluation module.

[0090] The data collection module is used to collect the original data of the indexes of each evaluation object;

[0091] The normalization processing module is used to perform normalization processing on the collected original data;

[0092] The index weight construction module is used to obtain the information entropy of the index and the index weight of the correlation coefficient - information entropy after improving the information entropy by introducing the correlation coefficient and independent coefficient between indexes according to the normalized matrix obtained by the normalization processing;

[0093] The evaluation module is used to determine the Euclidean distance between each evaluation object and the positive and negative ideal solutions based on the index weight and the normalized matrix, and obtain the comprehensive evaluation value of each evaluation object.

[0094] The beneficial effect of the present invention is that, compared with the prior art, the index weight method based on information entropy of the present invention takes into account the influence of the repeatability between indicators on the evaluation results, and improves the information entropy index weight by introducing the independent coefficient between indicators, so that the comprehensive evaluation results are more reasonable and the accuracy of the evaluation results is effectively improved. And by implementing examples to illustrate and verify the improvement of the traditional information entropy weight calculation method by this method, it can solve the problem of evaluation information duplication caused by the correlation between evaluation indicators, making the final comprehensive evaluation results unstable and non-unique.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A comprehensive evaluation method based on improved information entropy, characterized in that: The following steps are involved: Collect the original data of the indicators of each evaluation object, and normalize these original data to obtain the normalized matrix of the indicators; According to the obtained normalized matrix, the information entropy of each indicator is calculated, and the correlation coefficient and independence coefficient between indicators are introduced to improve the information entropy, and the indicator weight of correlation coefficient-information entropy is calculated; Calculate the normalized matrix based on the obtained correlation coefficient-information entropy weight and the normalized matrix; According to the obtained normalized matrix, the Euclidean distance between each evaluation object and the positive and negative ideal solutions is calculated; According to the obtained Euclidean distance, the comprehensive evaluation value of each evaluation object is calculated.

2. The comprehensive evaluation method based on improved information entropy according to claim 1 is characterized in that: The calculation method of the normalized matrix is: Among them, z ij represents the normalized value of the jth indicator of the i-th evaluation object; x ij Represents the original data value of the jth indicator of the i-th evaluation object; are the maximum and minimum values ​​of the jth index respectively; Normalized matrix Z = [z ij ].

3. The comprehensive evaluation method based on improved information entropy according to claim 2 is characterized in that: The calculation method of the information entropy of each indicator is: in, 0≤p ij ≤1, m represents the total number of evaluation objects.

4. The comprehensive evaluation method based on improved information entropy according to claim 3 is characterized in that: The correlation coefficient and independence coefficient are described according to the following formula: Among them, r kj represents the correlation coefficient between the kth and jth indicators; v j represents the independence coefficient between the kth and jth indicators; z ik and z ij are the normalized scores of the kth and jth indicators of the i-th evaluation object in the normalized matrix Z respectively; and are the means of the normalized values ​​of the kth and jth indicators in the matrix Z, respectively; n represents the total number of indicators.

5. The comprehensive evaluation method based on improved information entropy according to claim 4 is characterized in that: The calculation method of the index weight of the correlation coefficient-information entropy is: Among them, w j Represents the indicator weight of correlation coefficient-information entropy, 6. The comprehensive evaluation method based on improved information entropy according to claim 5 is characterized in that: The calculation method of the normalized matrix is: C=[c ij ] c ij =w j ·z ij Where C represents the normalized matrix.

7. The comprehensive evaluation method based on improved information entropy according to claim 6 is characterized in that: The calculation method of the positive ideal solution and the negative ideal solution is: in, is a positive ideal solution; is a negative ideal solution; They respectively represent the maximum and minimum values ​​of the jth indicator of all evaluation objects in the normalized matrix.

8. The comprehensive evaluation method based on improved information entropy according to claim 7 is characterized in that: The calculation method of the Euclidean distance between each evaluation object and the positive and negative ideal solutions is: in, represents the Euclidean distance between the i-th evaluation object and the positive ideal solution, d i 0 Represents the Euclidean distance between the i-th evaluation object and the negative ideal solution.

9. The comprehensive evaluation method based on improved information entropy according to claim 7, characterized in that: The calculation method of the comprehensive evaluation value of each evaluation object is: Among them, ρ i Represents the comprehensive evaluation value of the i-th evaluation object.

10. A system using the comprehensive evaluation method based on improved information entropy according to any one of claims 1 to 9, characterized in that: include: The data collection module is used to collect the original data of the indicators of each evaluation object; A normalization processing module is used to normalize the collected raw data; The indicator weight construction module is used to obtain the normalized matrix according to the normalization process, obtain the information entropy of the indicator and the indicator weight of the correlation coefficient-information entropy after introducing the correlation coefficient and independent coefficient between the indicators to improve the information entropy; The evaluation module is used to determine the Euclidean distance between each evaluation object and the positive and negative ideal solutions based on the indicator weights and the normalized matrix, and obtain the comprehensive evaluation value of each evaluation object.

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