Rare earth secondary resource recycling comprehensive evaluation method based on TOPSIS model

Abstract

The invention provides a rare earth secondary resource recycling comprehensive evaluation method based on a TOPSIS model. The method comprises the steps that 1, a typical rare earth secondary resource recycling technology comprehensive evaluation index system is established; 2, determining a four-dimension evaluation index accounting method to perform corresponding data collection calculation; 3, determining the subjective weight of each index by using the AHP, and determining the objective weight of each index by using the entropy weight; 4, calculating the comprehensive weight of the indexes and obtaining the calculated value of each weighted index; 5, comprehensive evaluation of the typical rare earth secondary resource recycling technology is conducted through improved TOPSIS. According to the rare earth secondary resource recycling comprehensive evaluation method based on the TOPSIS model, the advantages and disadvantages of the typical rare earth secondary resource recycling technology can be comprehensively and objectively evaluated, and technology screening and upgrading of the typical rare earth secondary resource recycling industry are facilitated.

Description

Technical Field

[0001] The invention relates to the technical field of comprehensive evaluation of solid waste utilization and disposal technology, and in particular to a comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on a TOPSIS model. Background Art

[0002] With the gradual expansion of industrial production and the popularization of new industries, the mining, application and waste treatment of strategic materials have been widely valued. Rare earths, as a type of metal with extremely important strategic position in my country, are not only related to the lifeline of my country's military defense and aerospace, but also critical in the electronics industry, clean production and other fields. However, due to the excessive mining of rare earths in the early stage, the shortage of supply chain and the pollution of ecological environment by the corresponding waste cannot be underestimated. Therefore, we should respond to the national call, build a multi-level resource recycling system, and develop a green economy. In this context, the evaluation and optimization of typical rare earth secondary resource recovery issues and related processes have become the focus of attention.

[0003] According to statistics, less than 1% of rare earth resources are currently recycled worldwide. However, with the increasing demand for rare earth resources in various emerging industries, in order to solve the problems related to rare earth resource reserves, the scale of my country's rare earth secondary resource recycling industry has gradually expanded, the state has gradually increased its support for related enterprises, and the recycling process has gradually been innovated and improved. However, due to the diversity and multi-combination of current technologies, the practical application of recycling technology and the expansion of production to form a large-scale commercial scale require multi-dimensional consideration and evaluation to ensure that it is applicable to economic, ecological, resource, social and other aspects. So far, most scholars have conducted research from the perspective of economic level and environmental impact assessment: Academician Zuo Tieyong systematically introduced the material cycle and environmental impact assessment of my country's non-ferrous metal industry, and analyzed the operating efficiency of the non-ferrous metal industry by using the life cycle method. Hongyue Jin conducted a life cycle assessment study on the recycling of scrapped NdFeB magnets for electric vehicles, comparing the environmental impact of transforming scrapped NdFeB magnets into new magnets with the environmental impact of producing original magnets. Hitachi of Japan used the rare earth magnets in compressors as the object and applied the life cycle impact assessment method based on endpoint modeling to two rare earth recycling technologies. Hong Jinglan's research group conducted a life cycle assessment on three disposal options for waste rare earth phosphor recycling. However, current research does not have evaluation indicators applicable to a variety of rare earth wastes, does not take into account green feasibility and social application, and has a single perspective.

[0004] There are many models for technology evaluation, including subjectively weighted analytic hierarchy process, objectively weighted entropy weight method, TOPSIS, VIKOR, grey correlation method, etc. In the "Optimal method for saline layer CO2 geological storage injection scheme based on AHP-EWM-TOPSIS" invented by Liu Shuyang and others from China University of Petroleum, a subjective and objective weighting method was adopted, and TOPSIS was used to obtain the optimal CO2 injection scheme. Li Shuhua and others from Hefei University of Technology invented "A lightweight design method for cast aluminum integrated engine hood based on FAHP-TOPSIS" to design and process the cast aluminum integrated engine hood, using FAHP to construct a fuzzy judgment matrix to determine the indicator weights, and using the TOPSIS method to determine the distance between the good and bad solutions of the optimization target and conduct a comprehensive evaluation. Liu Xiaojing and others from Beijing University of Technology invented "A comprehensive evaluation method for waste circuit board utilization and disposal technology based on AHM-entropy weight-VIKOR model", using the AHM-entropy weight method to determine the subjective and objective weights of the indicators, and using VIKOR to evaluate the comprehensive performance of different waste circuit board utilization and disposal technologies. At present, the evaluation index system for technology is mostly the separate adaptation of evaluation methods such as VIKOR, TOPSIS, and gray correlation. The decision results obtained may ignore some important factors, such as the dependence between indicators, the irrationality of weight distribution, or excessive reliance on certain mathematical formulas. This limitation will lead to misleading results or decisions that are not suitable for actual situations; the evaluation indicators are mostly concentrated on the economic and environmental levels, and the indicators with characteristics such as the technology itself and sustainability are not reflected. At present, there is a lack of relevant comprehensive evaluation methods for rare earth secondary resource recycling technology, resulting in insufficient data accuracy and incomplete evaluation. In order to promote the technological upgrading of the rare earth secondary resource recycling industry, it is necessary to improve data accuracy and adopt a comprehensive and reasonable comprehensive evaluation method. Summary of the invention

[0005] The purpose of the present invention is to provide a comprehensive evaluation method for rare earth secondary resource recycling based on the TOPSIS model, which can comprehensively and objectively evaluate the advantages and disadvantages of typical rare earth secondary resource recycling technologies and contribute to the technical screening and upgrading of the typical rare earth secondary resource recycling industry.

[0006] The purpose of the present invention can be achieved by the following technical measures: a comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model, the comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model comprises:

[0007] Step 1: Establish a comprehensive evaluation index system for typical rare earth secondary resource recycling technologies;

[0008] Step 2: Determine the calculation methods of the four-dimensional evaluation indicators and collect and calculate the corresponding data;

[0009] Step 3: Use AHP to determine the subjective weight of each indicator and entropy weight to determine the objective weight of each indicator;

[0010] Step 4: Calculate the comprehensive weight of the indicators and obtain the calculated values ​​of each indicator after weighting;

[0011] Step 5: Comprehensively evaluate typical rare earth secondary resource recycling technologies through the improved version of TOPSIS.

[0012] The purpose of the present invention can also be achieved by the following technical measures:

[0013] Step 1 includes:

[0014] Step 11, by analyzing the influencing factors, determine the grading indicators of the comprehensive evaluation index system of typical rare earth secondary resource recycling technology of the AHP entropy weight improved version of TOPSIS model, and divide the index system criterion layer into 4 indicators: A1 green feasibility, A2 economic benefit, A3 environmental impact, and A4 technology social application;

[0015] Step 12: further refine the criteria layer indicators.

[0016] In step 12, the criteria level indicators are refined into 17 indicators:

[0017] A1 Green feasibility includes two aspects: technical environmental protection and energy conservation operability, including A11 resource depletion, A12 fossil fuel depletion, A13 resource recovery rate, A14 total rare earth recovery rate, and A15 total energy consumption per unit product;

[0018] A2 economic benefits include A21 operating costs and A22 main and by-product profits;

[0019] A3 Environmental impacts include A31 acidification effect, A32 eutrophication, A33 freshwater ecotoxicity potential, A34 greenhouse effect, A35 human toxicity potential, A36 photochemical pollution potential, and A37 terrestrial ecotoxicity potential;

[0020] A4 technology social application includes A41 technology innovation, A42 technology flexibility, and A43 technology scalability.

[0021] In step 2, A1 green feasibility includes cost-based indicators A11 resource depletion, A12 fossil fuel depletion, A15 total energy consumption per unit product and benefit-based indicators A13 resource recovery rate, A14 total rare earth recovery rate. The calculation method is as follows:

[0022] ① Resource depletion refers to the depletion of non-renewable resources or elements consumed in the production of a unit of rare earth main product, including the production stage of raw and auxiliary materials. The numerical value refers to the characteristic value of the ADP indicator calculated by the life cycle assessment software, and the unit is kg Sbeq;

[0023] ② Fossil fuel depletion refers to the non-renewable resources or fossils consumed to produce a unit of rare earth main product, including the raw and auxiliary materials production stage. The numerical value refers to the ADP indicator characteristic value calculated by the life cycle assessment software, and the unit is MJ;

[0024] ③ Resource recovery rate refers to the resource recovery efficiency of the main rare earth product produced per unit, in %, and the calculation formula is as follows:

[0025]

[0026] Among them, W i，m is the mass of the main product and by-product m obtained by producing a unit of rare earth main product using the i-th recycling technology, W i，r is the quality of the raw material r used by the recycling technology i;

[0027] ④ The total rare earth yield refers to the total rare earth yield of the main rare earth product produced per unit, in %, and the calculation formula is as follows:

[0028]

[0029] Among them, W i，1 is the mass of each rare earth element 1 in the rare earth primary product produced by the i-th recycling technology, corresponding to the processed rare earth secondary resources, W i，s is the mass of the sth rare earth element produced by technology i;

[0030] ⑤ Total energy consumption per unit product refers to the energy generated and utilized by the recycling technology to produce a unit of rare earth main product, in units of tce / t, and the calculation formula is as follows:

[0031]

[0032] Among them, W i，e is the amount of energy e consumed by the i-th recycling technology to produce a unit of rare earth main product, E i，e is the conversion coefficient of the e-th energy.

[0033] In step 2, A2 economic benefits include cost-based indicators A21 and benefit-based indicators A22. The calculation method is as follows:

[0034] ① The operating cost is the resource and energy input cost of the recycling technology, and the calculation formula is as follows:

[0035]

[0036] Among them, C R，i，t is the unit price of the rth material and energy consumed by the i-th recycling technology to produce a unit of rare earth main product, W i，t The mass of the tth material energy consumed by technology i;

[0037] ② Economic benefits are derived from the sales of main and by-products and subsidy income, and the calculation formula is as follows:

[0038]

[0039] Among them, C i，p W represents the price of the main product, by-product or disposal subsidy p obtained by producing a unit of rare earth main product using the i-th recycling technology, i，p It represents the quality of the product and by-product p obtained by the i-th recycling technology.

[0040] In step 2, A3 environmental impact represents the impact of typical rare earth secondary resource recycling technology on the ecological environment and the environmental impact caused by the disposal of terminal solid waste. Among them, the seven indicators A31-A37 are all cost indicators. The calculation method is as follows:

[0041] ① The acidification effect value is the AP indicator characteristic value calculated by the life cycle assessment software, in kg SO2 eq;

[0042] ② Eutrophication value is the characteristic value of EP index calculated by life cycle assessment software, unit is kgPhosophate eq;

[0043] ③ Freshwater ecotoxicity potential is the characteristic value of FAETP index calculated by life cycle assessment software, unit: kgDCB eq;

[0044] ④ The greenhouse effect value is the GWP indicator characteristic value calculated by the life cycle assessment software, in kg CO2 eq;

[0045] ⑤Human toxicity potential is the characteristic value of HTP index calculated by life cycle assessment software, unit: kg DCB eq;

[0046] ⑥ Photochemical pollution potential is the characteristic value of POCP index calculated by life cycle assessment software, unit: kgEthene eq;

[0047] ⑦ Terrestrial ecotoxicity potential is the characteristic value of TETP indicator calculated by life cycle assessment software, unit: kg DCBeq.

[0048] In step 2, A4 technology social application is a scoring value, and the scoring range is between 0 and 1. The closer the value is to 1, the higher the benefit. A41-A43 are all benefit indicators, and the calculation method is as follows:

[0049] ①Technological innovation is scored based on the novelty of the technology, materials or processes used in the recycling path, as well as whether it breaks through the bottleneck of traditional technology, improves recycling efficiency or reduces costs;

[0050] ② Technical flexibility is scored based on the ability to adapt to different conditions and changing needs, the degree to which parameters can be adjusted during operation, and the degree to which performance is optimized under different process conditions;

[0051] ③ The scalability of the technology is scored and judged based on the feasibility of environmental protection measures and policies, market acceptance, and obstacles to the implementation of the technology during the industrialization process;

[0052] The relevant parameter data of each evaluation indicator are collected through monitoring and testing, element mass balance, industry data, environmental impact assessment reports, and literature. The data are processed according to the calculation methods of 17 indicators to obtain the initial evaluation indicator data set.

[0053] Step 3 includes:

[0054] S31: Invite experts in related fields to use the 1-9 scale method to make a comparison of the importance of two factors. The two numbers that are symmetrical on the diagonal are the reciprocals of each other.

[0055] S32: Invite experts in related fields to compare and score the indicators of the indicator system in pairs according to the importance of the 1-9 scale, and obtain the judgment matrix A of the criterion layer and each indicator = (a ij )

[0056] n×n is as follows, where n is the number of indicators or the number of criterion layers corresponding to each criterion layer:

[0057]

[0058] S33: The judgment matrix is ​​normalized by column, and the calculation formula is as follows:

[0059]

[0060] And ask The sum of each row gives the eigenvector

[0061]

[0062] S34: Normalize the feature vector to obtain the weight vector σ, which is calculated as follows:

[0063]

[0064] Calculate the largest eigenvalue λ of the matrix max

[0065]

[0066] Perform consistency check

[0067]

[0068] in:

[0069] CR is the consistency ratio. When CR < 0.1, it is considered that the judgment matrix A meets the consistency requirements;

[0070] R, is the random consistency index, and its value is related to the matrix order;

[0071] S35: Perform forward normalization processing on the initial evaluation index data set obtained in step 2 to obtain a normalization matrix Y=(y ij ) m×n ,y ij is the jth standardized indicator corresponding to the i-th technology, m is the number of corresponding technical solutions, and n is the number of corresponding evaluation indicators; the larger the value of the cost-type indicator, the worse the performance, and the larger the value of the benefit-type indicator, the better the performance. The calculation formula is as follows:

[0072]

[0073] Among them, r i，j It is an unstandardized indicator. The calculation method is shown in S12. i represents the technical solution and j represents the evaluation indicator. Cost indicators include A11, A12, A15, A21, A31-A37; benefit indicators include A13, A14, A22, A41-A43.

[0074] S36: Calculate the information entropy E of each indicator j and objective weight e j , the calculation formula is as follows: ij is the characteristic weight of the jth evaluation index of the i-th technical solution,

[0075]

[0076] S37: Determine the objective weight of the indicator using the entropy weight method based on standardized data j , the calculation formula is as follows:

[0077]

[0078] Step 4 includes:

[0079] S41: Determine the subjective and objective comprehensive weights w of each indicator j , the calculation formula is as follows:

[0080]

[0081] S42: Based on the subjective and objective comprehensive weight w j And the index value standardization matrix Y = (y ij ) m×n Determine the weighted standardized indicator matrix Z = (zij ) m×n , the calculation formula is as follows:

[0082] z i，j =y ij × j

[0083]

[0084] Step 5 includes:

[0085] S51: Confirm the correct understanding Z + and negative ideal solution Z - , the calculation formula is as follows:

[0086] Positive ideal solution:

[0087]

[0088] Negative ideal solution:

[0089]

[0090] S52: Since the index value has been positively converted, the positive ideal solution is used as the optimal sequence:

[0091]

[0092] S53: Find the weighted standardized index Z corresponding to each technical solution i (k) The two-level minimum and maximum differences with the optimal sequence Z0 are obtained:

[0093]

[0094] s54: Calculate the grey correlation coefficient δ based on the maximum difference and the minimum difference ij :

[0095]

[0096] S55: Use the Euclidean distance to calculate the distance between the object and the positive ideal solution and the negative ideal solution, and use the δ obtained above ij Corrected calculated value:

[0097]

[0098] S56: Use negative ideal solution distance to calculate relative closeness and sort:

[0099]

[0100] The relative closeness is between 0 and 1. The larger the value, the farther away from the negative ideal solution, which means the better the technology.

[0101] The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model in the present invention firstly establishes and improves a typical rare earth secondary resource recycling and utilizing technical indicator system, comprehensively considering four influencing aspects of green feasibility, economic benefits, environmental impact, and technological social application; secondly, determines the accounting method of the indicator and performs data collection and processing; thirdly, uses the analytic hierarchy process (AHP) to determine the subjective weight of the indicator; then, uses the entropy weight to determine the objective weight of the indicator, and further obtains the subjective and objective comprehensive weight of the indicator; finally, uses the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) modified by grey correlation to evaluate the comprehensive performance of the typical rare earth secondary resource recycling and utilizing technology.

[0102] The present invention adopts the grey correlation coefficient to correct the TOPSIS evaluation results. By introducing the grey correlation coefficient, the TOPSIS method can be effectively improved in terms of uncertainty processing, relative change trend consideration, robustness and result accuracy. This combination not only utilizes the distance evaluation advantages of TOPSIS, but also takes into account the advantages of grey system theory in uncertain environments, making the overall evaluation system more robust and scientific; and combines the technical characteristics of rare earth waste recycling and the social level to set a corresponding indicator system. The present invention can comprehensively and objectively evaluate the advantages and disadvantages of typical rare earth secondary resource recycling technologies, which is helpful for the technical screening and upgrading of typical rare earth secondary resource recycling industries. The present invention is suitable for comprehensive evaluation of typical rare earth secondary resource recycling technologies. Comparing the present invention with the prior art, it has the following beneficial effects:

[0103] The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model proposed in the present invention, by combining AHP and entropy weight method, comprehensively considers the subjective judgment of experts and the objective information of actual data, so that the evaluation results are more scientific and accurate. By constructing a comprehensive multi-level evaluation index system, all aspects of rare earth secondary resource recycling and utilization technology are comprehensively reflected from four typical dimensions: green feasibility, economy, environment, and technology social application level. The evaluation method uses the TOPSIS method corrected by the grey correlation coefficient to comprehensively evaluate and prioritize the technical solutions, providing an intuitive reference for decision makers. These methods have their own limitations when used independently, and it is difficult to comprehensively and objectively evaluate the recycling and utilization technology of rare earth secondary resources. The present invention helps to screen rare earth secondary resource recycling and utilization technology from a scientific, comprehensive, and subjective and objective perspective, and promote the iterative upgrading of industrial technology and the effective utilization and management of rare earth strategic resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1It is a flow chart of a specific embodiment of the comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model of the present invention;

[0105] Figure 2 It is a schematic diagram of the index system of the comprehensive evaluation method of typical rare earth secondary resource recycling technology of the present invention. DETAILED DESCRIPTION

[0106] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0107] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations and / or combinations thereof.

[0108] In view of the single evaluation method and one-sided evaluation indicators at present, the present invention comprehensively considers the diversity of typical rare earth secondary resources and the complexity of disposal technology, proposes reasonably adapted evaluation indicators and comprehensive evaluation system, formulates corresponding indicator calculation method and model building process, and proposes a comprehensive evaluation method for recycling and utilization of rare earth secondary resources based on TOPSIS model, which is suitable for the comprehensive comprehensive evaluation of various typical rare earth secondary resource comprehensive utilization technologies.

[0109] The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model of the present invention, first, establishes a comprehensive evaluation index system that can reflect the four dimensions of green feasibility, economic benefits, environmental impact, and technology social application of typical rare earth secondary resource recycling and utilization technologies; secondly, determines the calculation method of the index and obtains a standardized matrix of corresponding numerical collation; thirdly, uses AHP to determine the subjective weight of the index, and entropy weight method to determine the objective weight of the index, and further obtains the subjective and objective comprehensive weight of the index; finally, the comprehensive performance of the typical rare earth secondary resource recycling and utilization technology is evaluated by correcting TOPSIS by the grey correlation coefficient. The present invention evaluates the advantages and disadvantages of typical rare earth secondary resource recycling and utilization technologies from a multi-dimensional perspective, which is helpful for the technical upgrading and resource management of the rare earth secondary resource recycling and utilization industry.

[0110] like Figure 1 As shown, Figure 1The flowchart of the comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model of the present invention. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model includes:

[0111] S1: Establish a comprehensive evaluation index system for typical rare earth secondary resource recycling and utilization technologies;

[0112] S2: Determine the calculation methods of the four-dimensional evaluation indicators and collect and calculate the corresponding data;

[0113] S3: Use AHP to determine the subjective weight of each indicator and entropy weight to determine the objective weight of each indicator;

[0114] S4: Calculate the comprehensive weight of the indicators and obtain the calculated values ​​of each indicator after weighting;

[0115] S5: Comprehensive evaluation of typical rare earth secondary resource recycling technologies by using the modified TOPSIS. Comprehensive evaluation of typical rare earth secondary resource recycling technologies by using the grey correlation modified TOPSIS.

[0116] The specific steps of S1 are as follows:

[0117] S11: Determine the grading index of the comprehensive evaluation index system of typical rare earth secondary resource recycling technology of AHP-entropy weight-modified TOPSIS model by analyzing the influencing factors. Divide the index system criterion layer into 4 indicators, including A1 green feasibility, A2 economic benefits, A3 environmental impact, and A4 technology social application;

[0118] S12: The criteria level indicators are refined into 17 indicators:

[0119] The A1 green feasibility includes two aspects: technical environmental protection and energy-saving operability, including A11 resource depletion, A12 fossil fuel depletion, A13 resource recovery rate, A14 total rare earth recovery rate, and A15 total energy consumption per unit product;

[0120] The economic benefits of A2 include the operating costs of A21 and the profits of the main and by-products of A22;

[0121] The A3 environmental impacts include A31 acidification effect, A32 eutrophication, A33 freshwater ecotoxicity potential, A34 greenhouse effect, A35 human toxicity potential, A36 photochemical pollution potential, and A37 terrestrial ecotoxicity potential;

[0122] The social application of A4 technology includes A41 technological innovation, A42 technological flexibility, and A43 technological scalability.

[0123] The specific steps of S2 are as follows:

[0124] S21: A1 green feasibility includes cost-based indicators A11, A12, A15 and benefit-based indicators A13 and A14. The calculation method is as follows:

[0125] ① Resource depletion refers to the depletion of non-renewable resources (elements) consumed in the production of a unit of rare earth main product, including the production stage of raw and auxiliary materials. The numerical value refers to the characteristic value of the ADP (element) indicator calculated by life cycle assessment software such as GaBi and open LCA, and the unit is kg Sb eq;

[0126] ② Fossil fuel depletion refers to the depletion of non-renewable resources (fossils) consumed in the production of a unit of rare earth main product, including the production stage of raw and auxiliary materials. The numerical value refers to the characteristic value of the ADP (fossil) indicator calculated by life cycle assessment software such as GaBi and open LCA, and the unit is MJ;

[0127] ③ Resource recovery rate refers to the resource recovery efficiency of the main rare earth product produced per unit, in %, and the calculation formula is as follows:

[0128]

[0129] Among them, W i，m is the mass of the main product and by-product m obtained by producing a unit of rare earth main product using the i-th recycling technology, W i，r is the quality of the raw material r used by the recycling technology i;

[0130] ④ The total rare earth yield refers to the total rare earth yield (in terms of rare earth elements) of the main rare earth product produced per unit, in %, and the calculation formula is as follows:

[0131]

[0132] Among them, W i，1 is the mass of each rare earth element 1 in the rare earth primary product produced by the i-th recycling technology, corresponding to the processed rare earth secondary resources, W i，s is the mass of the sth rare earth element produced by technology i;

[0133] ⑤ Total energy consumption per unit product refers to the energy generated and utilized by the recycling technology to produce a unit of rare earth main product, in units of tce / t, and the calculation formula is as follows:

[0134]

[0135] Among them, W i，e is the amount of energy e consumed by the i-th recycling technology to produce a unit of rare earth main product, E i，e is the conversion factor of the e-th energy source;

[0136] S22: A2 economic benefits include cost-based indicators A21 and benefit-based indicators A22. The calculation method is as follows:

[0137] ① The operating cost is the resource and energy input cost of the recycling technology, and the calculation formula is as follows:

[0138]

[0139] Among them, C R，i，t is the unit price of the rth material and energy consumed by the i-th recycling technology to produce a unit of rare earth main product, W i，t The mass of the tth material energy consumed by technology i;

[0140] ③ The economic benefits are obtained from the sales of main and by-products and subsidy income, and the calculation formula is as follows:

[0141]

[0142] Among them, C i，p W represents the price of the main product, by-product or disposal subsidy p obtained by producing a unit of rare earth main product using the i-th recycling technology, ip represents the quality of the product and by-product p obtained by the i-th recycling technology;

[0143] S23: A3 environmental impact refers to the impact of typical rare earth secondary resource recycling technology on the ecological environment and the environmental impact caused by the disposal of terminal solid waste. Among them, the seven indicators A31-A37 are all cost indicators. The calculation method is as follows:

[0144] ① The acidification effect value is recommended to be calculated using the AP indicator characteristic value of GaBi, Simapro, open LCA and other life cycle assessment software, in units of kg SO2 eq;

[0145] ② Eutrophication values ​​are recommended to be calculated using EP indicator characteristic values ​​from life cycle assessment software such as GaBi, Simapro, and open LCA, in kg Phosophate eq.

[0146] ③ Freshwater ecotoxicity potential: FAETP indicator characteristic value calculated by life cycle assessment software such as GaBi, Simapro, open LCA, etc., in kg DCB eq;

[0147] ④ The greenhouse effect value is recommended to use the GWP indicator characteristic value calculated by life cycle assessment software such as GaBi, Simapro, open LCA, etc., in kg CO2 eq;

[0148] ⑤ The human toxicity potential is recommended to be calculated using the HTP indicator characteristic value of GaBi, Simapro, open LCA and other life cycle assessment software, in kg DCB eq;

[0149] ⑥ The photochemical pollution potential is recommended to be calculated using the POCP indicator characteristic value of life cycle assessment software such as GaBi, Simapro, open LCA, etc., in kg Ethene eq;

[0150] ⑦ For the terrestrial ecotoxicity potential, it is recommended to use the characteristic value of the TETP indicator calculated by life cycle assessment software such as GaBi, Simapro, open LCA, etc., in kg DCB eq;

[0151] S24: A4: Socialized application of technology is a scoring value, ranging from 0 to 1. The closer the value is to 1, the higher the benefit. A41-A43 are all benefit indicators, and the calculation method is as follows:

[0152] ①Technological innovation is scored based on the novelty of the technology, materials or processes used in the recycling path, as well as whether it breaks through the bottleneck of traditional technology, improves recycling efficiency or reduces costs;

[0153] ② Technical flexibility is scored based on the ability to adapt to different conditions and changing needs, the degree to which parameters can be adjusted during operation, and the degree to which performance is optimized under different process conditions;

[0154] ③ The scalability of the technology is judged based on the feasibility of relevant environmental protection measures and policies, market acceptance, and obstacles to the implementation of the technology during the industrialization process;

[0155] S25: Collect relevant parameter data of each evaluation index through monitoring and testing, element mass balance, industry data, environmental impact assessment reports, literature, etc., process the data according to the accounting method of S21-S24 and obtain the initial evaluation index data set.

[0156] The specific steps of S3 are as follows:

[0157] S31: Invite experts in related fields to use the 1-9 scale method to compare the importance of each factor. The two numbers symmetrical on the diagonal are reciprocals of each other, as shown in Table 1.

[0158] Table 11~9 scale meaning comparison table

[0159] Scale meaning 1 The two factors are equally important. 3 When comparing two factors, one is slightly more important than the other. 5 When comparing two factors, one factor is significantly more important than the other 7 When comparing two factors, one is much more important than the other. 9 When comparing two factors, one is extremely more important than the other. 2，4，6，8 The intermediate state of the above scale

[0160] S32: Invite experts in related fields to compare and score the indicators of the indicator system in pairs according to the importance of the 1-9 scale, and obtain the judgment matrix A of the criterion layer and each indicator = (a ij )n×n As shown below, n is the number of indicators or the number of criterion layers corresponding to each criterion layer:

[0161]

[0162] S33: The judgment matrix is ​​normalized by column, and the calculation formula is as follows:

[0163]

[0164] And ask The sum of each row gives the eigenvector

[0165]

[0166] S34: Normalize the feature vector to obtain the weight vector σ, which is calculated as follows:

[0167]

[0168] Calculate the largest eigenvalue λ of the matrix max

[0169]

[0170] Perform consistency check

[0171]

[0172] in:

[0173] CR is the consistency ratio. When CR < 0.1, it is considered that the judgment matrix A meets the consistency requirements.

[0174] R is a random consistency index, and its value is related to the matrix order.

[0175] S35: Perform forward normalization processing on the initial evaluation index data set obtained in S24 to obtain a normalization matrix Y=(y ij ) m×n ,y ij is the jth standardized indicator corresponding to the i-th technology, m is the number of corresponding technical solutions, and n is the number of corresponding evaluation indicators. Among them, the larger the value of the cost-type indicator, the worse the performance, and the larger the value of the benefit-type indicator, the better the performance. The calculation formula is as follows:

[0176]

[0177] where r i，jIt is an unstandardized evaluation index. The calculation method is shown in S12. i represents the technical solution and j represents the evaluation index. Cost-based indicators include A11, A12, A15, A21, A31-A37; benefit-based indicators include A13, A14, A22, A41-A43;

[0178] S36: Calculate the information entropy Ej and objective weight e of each indicator j , p ij is the characteristic weight of the jth evaluation index of the i-th technical solution

[0179] The calculation formula is as follows:

[0180]

[0181] S37: Determine the objective weight of the indicator using the entropy weight method based on standardized data j , the calculation formula is as follows:

[0182]

[0183] The specific steps of S4 are as follows:

[0184] S41: Determine the subjective and objective comprehensive weights w of each indicator j , the calculation formula is as follows:

[0185]

[0186] S42: Based on the subjective and objective comprehensive weight w j And the index value standardization matrix Y = (y ij ) m×n Determine the weighted standardized indicator matrix Z = (z ij ) m×n , the calculation formula is as follows:

[0187] z i，j =y ij × j

[0188]

[0189] The specific steps of S5 are as follows:

[0190] S51: Confirm the correct understanding Z + and negative ideal solution Z - , the calculation formula is as follows:

[0191] Positive ideal solution:

[0192]

[0193] Negative ideal solution:

[0194]

[0195] S52: Since the index value has been positively converted, the positive ideal solution is used as the optimal sequence:

[0196]

[0197] S53: Find the weighted standardized index Z corresponding to each technical solution i (k) The two-level minimum and maximum differences with the optimal sequence Z0 are obtained:

[0198]

[0199] S54: Calculate the grey correlation coefficient δ based on the maximum difference and the minimum difference ij :

[0200]

[0201] S55: Use the Euclidean distance to calculate the distance between the object and the positive ideal solution and the negative ideal solution, and use the δ obtained above ij Corrected calculated value:

[0202]

[0203] S56: Use negative ideal solution distance to calculate relative closeness and sort:

[0204]

[0205] The relative closeness is between 0 and 1. The larger the value, the farther away from the negative ideal solution, which means the better the technology.

[0206] The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model of the present invention, first, establishes a comprehensive evaluation index system that meets the impact of typical rare earth secondary resource recycling and utilization technology in four aspects of green feasibility, economic benefits, environmental impact, and technology social application; secondly, determines the four-dimensional evaluation index calculation method to collect and calculate the corresponding data; thirdly, uses AHP to determine the subjective weight of each index and entropy weight to determine the objective weight of each index; then, performs index comprehensive weight calculation and obtains the weighted calculated value of each index; finally, performs a comprehensive evaluation of typical rare earth secondary resource recycling and utilization technology through TOPSIS corrected by grey correlation coefficient. The present invention can comprehensively and objectively reflect the advantages and disadvantages of typical rare earth secondary resource recycling and utilization technology, and is conducive to the iterative upgrading and management improvement of typical rare earth secondary resource recycling and utilization technology. The present invention combines multi-dimensional and multi-attribute influencing factors, uses reasonable weight distribution, provides a clear comparison of technical advantages and disadvantages, and provides an intuitive and reliable basis for decision-making. However, the existing evaluation methods for rare earth secondary resources often ignore the multi-dimensional perspectives and technical characteristics of rare earth secondary resource recycling and utilization technology, resulting in an evaluation index system that is not comprehensive enough and the evaluation results that are not convincing and scientific enough.

[0207] In a specific embodiment of the present invention, the comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model of the present invention specifically includes:

[0208] S1: Establish a typical rare earth secondary resource recycling and utilization technical indicator system such as Figure 2 As shown;

[0209] S2: Determine the evaluation indicators of the four dimensions and calculate the corresponding data collection methods;

[0210] Three typical secondary resources of rare earths are selected (among which the market stock accounts for a large proportion), namely waste NdFeB magnets, waste petroleum catalytic cracking catalysts, and waste polishing powder. Each type of rare earth secondary resource corresponds to two technical routes. The corresponding recycling technologies for waste NdFeB magnets are Technology A1 and Technology A2; the corresponding recycling technologies for waste petroleum catalytic cracking catalysts are Technology B1 and Technology B2; the corresponding recycling technologies for waste polishing powder are Technology C1 and Technology C2. The treatment processes for each type of rare earth waste are compared. The relevant parameter data of each evaluation indicator are collected through monitoring and testing, element mass balance, industry data, environmental impact assessment reports, literature, etc., and the data is processed according to the calculation method of S21-S24 to obtain the initial evaluation indicator data set, as shown in Table 2:

[0211] Table 2 Initial evaluation index dataset

[0212]

[0213]

[0214] S3: Use AHP to determine the subjective weight of each indicator;

[0215] Invite domain experts to compare and score the evaluation indicators in pairs, and calculate the judgment matrix of the criterion layer according to the formula of S32 as follows:

[0216]

[0217] According to the formula S33-S34, the CR value of the criterion layer judgment matrix is ​​calculated = 0.044 < 0.1, passing the consistency test; the results show that the environmental impact has the highest weight, followed by green feasibility and economic benefits, and the weight of technology social application is the lowest; the subjective weight S of the criterion layer is W 准则 =(0.2633, 0.1219, 0.5579, 0.0569);

[0218] Specifically, the judgment matrix and measurement matrix of each attribute indicator layer are as follows:

[0219]

[0220]

[0221] The judgment matrices of each attribute indicator layer calculated according to the formulas S33-S34 all passed the consistency test;

[0222] Table 3 Subjective weight table of comprehensive evaluation index system for typical rare earth secondary resource disposal technology

[0223]

[0224] From the perspective of the criterion layer, the environment accounts for the largest proportion, followed by green feasibility and economic benefits, and finally the level of technological socialization; in the indicator layer, it can be seen from the subjective weights obtained that the greenhouse effect and human toxicity potential in environmental impacts have the largest weights, and the second largest weight also includes the total rare earth recovery rate in green feasibility. This indicator is an evaluation indicator exclusive to typical rare earth waste recycling, which makes the evaluation system adapt to the evaluation object and is more scientific and reasonable.

[0225] According to S35, the initial evaluation index data set is divided into cost type and benefit type according to the index attributes, and the standardized calculation is performed to obtain the standardized matrix Y = (y ij ) m×n ;

[0226] Table 4 Standardized evaluation index dataset

[0227]

[0228]

[0229] Then, the objective weight of the entropy weight method is calculated through S36-S37 to obtain the information entropy Ej and the objective weight ej;

[0230] Table 5 Information entropy and objective weights corresponding to three types of waste AC

[0231]

[0232]

[0233] Combined with the subjective and objective weight calculation, the subjective and objective comprehensive weight w of each indicator is determined according to S41 j ;

[0234] Table 6 Comprehensive weights of three types of waste AC

[0235]

[0236] From S42, we get the subjective and objective comprehensive weight w j And the index value standardization matrix Y = (y ij ) m×n Determine the weighted standardized indicator matrix Z = (z ij ) m×n , as shown in Table 7;

[0237] Table 7 Weighted standardized indicator data sets corresponding to three types of waste

[0238]

[0239]

[0240] According to S51-S56, the positive and negative ideal solutions are determined and the Euclidean distance is calculated, and finally the relative progress Si is obtained, as shown in Table 8;

[0241] Table 8 TOPSIS comprehensive evaluation results and technology ranking

[0242]

[0243] S53 comprehensively evaluates the disposal technologies A1-A2, B1-B2, and C1-C2 of three rare earth secondary resources, namely, waste NdFeB magnets, waste petroleum catalytic cracking catalysts, and waste polishing powder based on TOPSIS, and the calculation results are shown in Table 5. Since each rare earth secondary resource is only comparable to the disposal technology of this type, the disposal technology solutions corresponding to the three rare earth wastes are ranked as follows: waste NdFeB magnets: A1>A2, waste petroleum catalytic cracking catalysts: B1>B2, and waste polishing powder: C1>C2. Each type of rare earth secondary resource can select the best path for waste disposal and recycling.

[0244] The invention proposes a comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model, establishes a complete comprehensive evaluation index system for typical rare earth secondary resource recycling and utilization technologies, and comprehensively analyzes from four typical dimensions - green feasibility, economy, environment, and technology socialization, providing a theoretical basis for comprehensive evaluation; calculates and verifies the adaptability and feasibility of the index system and calculation method through three typical rare earth waste materials, waste NdFeB magnets, waste petroleum catalytic cracking catalysts, and waste polishing powder; uses AHP to determine the subjective weights of different criterion layers and different indicator layers, decomposes complex problems into a multi-level, multi-factor structured model, and makes the decision-making process transparent and traceable. And AHP provides a consistency verification mechanism. If there is a large deviation in the judgment, it can prompt the decision maker to re-evaluate to improve the credibility of the weight distribution; based on objective data, the objective weight of the index is determined by using entropy weight. The weight is determined by analyzing the degree of variation of each index, and the error of the subjective weight can be corrected to a certain extent. The combination of the two can provide a comprehensive and reliable weight evaluation in decision analysis to obtain a comprehensive weight that combines subjective and objective factors; the TOPSIS comprehensive evaluation corrected by gray correlation can comprehensively consider the decision-making problems of multiple indicators and multiple criteria. The evaluation scheme is comprehensive, easy to calculate, and the results are highly interpretable. At the same time, positive and negative ideal solutions are considered, which can effectively avoid the one-sidedness of focusing only on advantages or disadvantages. The present invention is conducive to more comprehensive and reasonable screening and management of typical rare earth secondary resource recycling technologies, and is conducive to the green and sustainable development of the rare earth industry, the sustainable development of pollution reduction and carbon reduction, and the improvement of management.

[0245] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions recorded in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0246] Except for the technical features described in the specification, all other technical features are known technologies to those skilled in the art.

Claims

1. A comprehensive evaluation method for recycling and utilization of rare earth secondary resources based on the TOPSIS model, characterized in that: The comprehensive evaluation method for recycling and utilization of rare earth secondary resources based on the TOPSIS model includes: Step 1: Establish a comprehensive evaluation index system for typical rare earth secondary resource recycling technologies; Step 2: Determine the calculation methods of the four-dimensional evaluation indicators and collect and calculate the corresponding data; Step 3: Use AHP to determine the subjective weight of each indicator and entropy weight to determine the objective weight of each indicator; Step 4: Calculate the comprehensive weight of the indicators and obtain the calculated values ​​of each indicator after weighting; Step 5: Comprehensively evaluate typical rare earth secondary resource recycling technologies through the improved version of TOPSIS.

2. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 1, characterized in that: Step 1 includes: Step 11, by analyzing the influencing factors, determine the grading indicators of the comprehensive evaluation index system of typical rare earth secondary resource recycling technology of the AHP entropy weight improved version of TOPSIS model, and divide the index system criterion layer into 4 indicators: A1 green feasibility, A2 economic benefit, A3 environmental impact, and A4 technology social application; Step 12: further refine the criteria layer indicators.

3. According to the comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model of claim 2, in step 12, the criterion layer indicators are refined into 17 indicators: A1 Green feasibility includes two aspects: technical environmental protection and energy conservation operability, including A11 resource depletion, A12 fossil fuel depletion, A13 resource recovery rate, A14 total rare earth recovery rate, and A15 total energy consumption per unit product; A2 economic benefits include A21 operating costs and A22 main and by-product profits; A3 Environmental impacts include A31 acidification effect, A32 eutrophication, A33 freshwater ecotoxicity potential, A34 greenhouse effect, A35 human toxicity potential, A36 photochemical pollution potential, and A37 terrestrial ecotoxicity potential; A4 technology social application includes A41 technology innovation, A42 technology flexibility, and A43 technology scalability.

4. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIs model according to claim 3 is characterized in that: In step 2, A1 green feasibility includes cost-based indicators A11 resource depletion, A12 fossil fuel depletion, A15 total energy consumption per unit product and benefit-based indicators A13 resource recovery rate, A14 total rare earth recovery rate. The calculation method is as follows: ① Resource depletion refers to the depletion of non-renewable resources or elements consumed in the production of a unit of rare earth main product, including the production stage of raw and auxiliary materials. The numerical value refers to the characteristic value of the ADP indicator calculated by the life cycle assessment software, and the unit is kg Sb eq; ② Fossil fuel depletion refers to the non-renewable resources or fossils consumed in the production of a unit of rare earth main product, including the production stage of raw and auxiliary materials. The numerical value refers to the characteristic value of the ADP indicator calculated by the life cycle assessment software, and the unit is MJ; ③ Resource recovery rate refers to the resource recovery efficiency of the main rare earth product produced per unit, in %, and the calculation formula is as follows: Among them, W i，m is the mass of the main product and by-product m obtained by producing a unit of rare earth main product using the i-th recycling technology, W i，r is the quality of the raw material r used by the recycling technology i; ④ The total rare earth yield refers to the total rare earth yield of the main rare earth product produced per unit, in %, and the calculation formula is as follows: Among them, W i，1 is the mass of each rare earth element 1 in the rare earth primary product produced by the i-th recycling technology, corresponding to the processed rare earth secondary resources, W i，s is the mass of the sth rare earth element produced by technology i; ⑤ Total energy consumption per unit product refers to the energy generated and utilized by the recycling technology to produce a unit of rare earth main product, in units of tce / t, and the calculation formula is as follows: Among them, W i，e is the amount of energy e consumed by the i-th recycling technology to produce a unit of rare earth main product, E i，e is the conversion coefficient of the e-th energy.

5. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 4 is characterized in that: In step 2, A2 economic benefits include cost-based indicators A21 and benefit-based indicators A22. The calculation method is as follows: ① The operating cost is the resource and energy input cost of the recycling technology, and the calculation formula is as follows: Among them, C R，i，t is the unit price of the rth material and energy consumed by the i-th recycling technology to produce a unit of rare earth main product, W i，t The mass of the tth material energy consumed by technology i; ③ The economic benefits are obtained from the sales of main and by-products and subsidy income, and the calculation formula is as follows: Among them, C i，p W represents the price of the main product, by-product or disposal subsidy p obtained by producing a unit of rare earth main product using the i-th recycling technology, i，p It represents the quality of the product and by-product p obtained by the i-th recycling technology.

6. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 5, characterized in that: In step 2, A3 environmental impact represents the impact of typical rare earth secondary resource recycling technology on the ecological environment and the environmental impact caused by the disposal of terminal solid waste. Among them, the seven indicators A31-A37 are all cost indicators. The calculation method is as follows: ① The acidification effect value is the AP indicator characteristic value calculated by the life cycle assessment software, in kg SO2eq; ② Eutrophication value is the characteristic value of EP index calculated by life cycle assessment software, unit is kg Phosophateeq; ③ Freshwater ecotoxicity potential is the characteristic value of FAETP index calculated by life cycle assessment software, unit: kg DCBeq; ④ The greenhouse effect value is the GWP indicator characteristic value calculated by the life cycle assessment software, in kg CO2eq; ⑤Human toxicity potential is the characteristic value of HTP index calculated by life cycle assessment software, unit: kg DCB eq; ⑥ Photochemical pollution potential is the characteristic value of POCP index calculated by life cycle assessment software, unit: kg Etheneeq; ⑦ The terrestrial ecotoxicity potential is the characteristic value of the TETP indicator calculated using the life cycle assessment software, with the unit of kg DCB eq.

7. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 6, characterized in that: In step 2, A4 technology social application is a scoring value, and the scoring range is between 0 and 1. The closer the value is to 1, the higher the benefit. A41-A43 are all benefit indicators, and the calculation method is as follows: ①Technological innovation is scored based on the novelty of the technology, materials or processes used in the recycling path, as well as whether it breaks through the bottleneck of traditional technology, improves recycling efficiency or reduces costs; ② Technical flexibility is scored based on the ability to adapt to different conditions and changing needs, the degree to which parameters can be adjusted during operation, and the degree to which performance is optimized under different process conditions; ③ The scalability of the technology is scored and judged based on the feasibility of environmental protection measures and policies, market acceptance, and obstacles to the implementation of the technology during the industrialization process; The relevant parameter data of each evaluation indicator are collected through monitoring and testing, element mass balance, industry data, environmental impact assessment reports, and literature. The data are processed according to the calculation methods of 17 indicators to obtain the initial evaluation indicator data set.

8. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 1, characterized in that: Step 3 includes: S31: Invite experts in related fields to use the 1-9 scale method to make a comparison of the importance of two factors. The two numbers that are symmetrical on the diagonal are the reciprocals of each other. S32: Invite experts in related fields to compare and score the indicators of the indicator system in pairs according to the importance of the 1-9 scale, and obtain the judgment matrix A of the criterion layer and each indicator = (a ij ) n×n As shown below, n is the number of indicators or the number of criterion layers corresponding to each criterion layer: S33: The judgment matrix is ​​normalized by column, and the calculation formula is as follows: And ask The sum of each row gives the eigenvector S34: Normalize the feature vector to get the weight vector W j , the calculation formula is as follows: Calculate the largest eigenvalue λ of the matrix max Perform consistency check in: CR is the consistency ratio. When CR < 0.1, it is considered that the judgment matrix A meets the consistency requirements; R, is the random consistency index, and its value is related to the matrix order; S35: Perform forward normalization processing on the initial evaluation index data set obtained in step 2 to obtain a normalization matrix Y=(y ij ) m×n ,y ij is the jth standardized indicator corresponding to the i-th technology, m is the number of corresponding technical solutions, and n is the number of corresponding evaluation indicators; the larger the value of the cost-type indicator, the worse the performance, and the larger the value of the benefit-type indicator, the better the performance. The calculation formula is as follows: where r i，j It is an unstandardized evaluation index, i represents the technical solution, j represents the evaluation index; cost-type indicators include A11, A12, A15, A21, A31-A37; benefit-type indicators include A13, A14, A22, A41-A43; S36: Calculate the information entropy E of each indicator j and objective weight e j , the calculation formula is as follows: ij is the characteristic weight of the jth evaluation index of the i-th technical solution, S37: Determine the objective weight of the indicator using the entropy weight method based on standardized data j , the calculation formula is as follows:

9. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 8, characterized in that: Step 4 includes: S41: Determine the subjective and objective comprehensive weights w of each indicator j , the calculation formula is as follows: S42: Based on the subjective and objective comprehensive weight w j And the index value standardization matrix Y = (y ij ) m×n Determine the weighted standardized indicator matrix Z = (z ij ) m×n , the calculation formula is as follows: z i，j =y ij ×w j 10. The comprehensive evaluation method for recycling and utilizing rare earth secondary resources based on the TOPSIS model according to claim 9, characterized in that: Step 5 includes: S51: Confirm the correct understanding Z + and negative ideal solution Z - , the calculation formula is as follows: Positive ideal solution: Negative ideal solution: S52: Since the index value has been positively converted, the positive ideal solution is used as the optimal sequence: S53: Find the weighted standardized index Z corresponding to each technical solution i (k) The two-level minimum and maximum differences with the optimal sequence Z0 are obtained: S54: Calculate the grey correlation coefficient δ based on the maximum difference and the minimum difference ij : S55: Use the Euclidean distance to calculate the distance between the object and the positive ideal solution and the negative ideal solution, and use the δ obtained above ij Corrected calculated value: S56: Use negative ideal solution distance to calculate relative closeness and sort: The relative closeness is between 0 and 1. The larger the value, the farther away from the negative ideal solution, which means the better the technology.

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