Three-stage evaluation method for low-carbon efficiency of airline company

Abstract

The invention discloses a three-stage evaluation method for the low-carbon efficiency of an airline company, and belongs to the technical field of low carbon. In the first stage, the method based on the cloud model is adopted to preliminarily evaluate the carbon efficiency of the airline; in the second stage, a random forest machine learning algorithm is adopted to evaluate and sort the relative importance of a plurality of indexes influencing emission; and in the third stage, dynamic efficiency analysis is performed by adopting a relaxation-based measurement directional distance function model in combination with a GML index, so that a multi-dimensional low-carbon efficiency evaluation system is obtained, a comprehensive and explainable method is provided for evaluating the low-carbon efficiency of the aircraft industry, and research results provide strategic significance for airline company managers, supervisors and policy formulators. And the operation practice is consistent with a long-term decarburization target and a sustainable aviation target.

Description

Technical Field

[0001] The present invention relates to the field of low-carbon technology, and in particular to a three-stage evaluation method for the low-carbon efficiency of an airline company. Background Art

[0002] Amidst intensifying global climate change and accelerating decarbonization, the aviation industry faces significant challenges. Its high reliance on fossil fuels and lack of near-term alternatives make it challenging to reduce carbon emissions. Despite advances in aircraft technology and fuel efficiency, global aviation CO2 emissions continue to climb as travel demand grows. Coupled with increasing carbon accountability requirements under international regulations such as CORSIA and regional schemes like the EU Emissions Trading Scheme, the aviation industry urgently needs to assess and improve its low-carbon efficiency.

[0003] Traditional low-carbon efficiency metrics, such as fuel intensity or carbon emissions per kilometer, provide limited insights because they fail to reflect the multidimensional nature of operational efficiency. To overcome this limitation, researchers are increasingly using data envelopment analysis (DEA) methods. DEA can integrate multiple input and output factors to assess environmental and technical efficiency, and its flexibility and objectivity have led to its widespread application in the energy and transportation sectors. In particular, the application of relaxation-based measurement methods (SBMs) and directed distance functions (DDFs) makes it possible to incorporate undesirable outputs such as carbon dioxide into the efficiency evaluation framework, thereby evaluating efficiency more comprehensively.

[0004] In view of this, this paper proposes a three-stage analytical framework to conduct a more comprehensive and in-depth assessment of the low-carbon efficiency of airlines. Summary of the Invention

[0005] The purpose of the present invention is to provide a three-stage evaluation method for the low-carbon efficiency of an airline company to solve the problems in the background technology.

[0006] To achieve the above objectives, the present invention provides a three-stage evaluation method for airline low-carbon efficiency, comprising the following steps:

[0007] S1. Conduct a preliminary uncertainty assessment of airline carbon efficiency using a cloud model-based approach to obtain a benchmark judgment reference;

[0008] S2. Use the random forest machine learning algorithm to evaluate and rank the relative importance of multiple operational indicators that affect carbon dioxide emissions, and retain the most important operational indicators;

[0009] S3. Based on the results of S1 and S2, the low-carbon efficiency evaluation indicator framework is determined. A relaxation-based measurement directed distance function model is used to combine the global Malmquist-Lenberg index and the comprehensive emission reduction index to conduct low-carbon efficiency analysis and obtain a multi-dimensional low-carbon efficiency evaluation system.

[0010] Preferably, the specific steps of S1 are: using cloud model parameters to capture the volatility and distribution of carbon efficiency indicators, and then evaluating the relative performance, stability and comparative competitiveness of the carbon efficiency indicators; cloud model parameters include expected value, entropy and super entropy.

[0011] Preferably, the specific steps of S2 are:

[0012] S21. Construct a decision tree to perform feature importance analysis; the root node of the decision tree is operating revenue, the dependent variable is carbon dioxide emissions, and the independent variables include available seat kilometers, revenue passenger kilometers, operating costs, fuel consumption, number of employees, number of flights, fleet size, and number of passengers operated;

[0013] S22. Calculate the average impurity reduction and retain the independent variables with high importance scores based on the average impurity reduction.

[0014] Preferably, in S22, the calculation formula for the average impurity reduction is:

[0015]

[0016] Where, MDI j represents the average impurity reduction of feature j, T is the total number of trees in the random forest, is the set of nodes in all trees that use feature j to split, ω v ΔI v represents the weighted impurity reduction of node v.

[0017] Preferably, in said S3, the low-carbon efficiency evaluation indicator framework includes input indicators, ideal outputs and non-ideal outputs;

[0018] Among them, input indicators include the number of employees, the number of aircraft and flights, operating costs, and fuel consumption; ideal outputs include operating income and revenue passenger kilometers; and non-ideal outputs include carbon dioxide emissions.

[0019] Preferably, in S3, the specific process of performing low-carbon efficiency analysis is:

[0020] S31, using a relaxation-based measured directed distance function model to simultaneously expand ideal outputs and shrink non-ideal outputs;

[0021] S32. Use a comprehensive emission reduction index to statically assess the environmental and operational efficiency of airlines;

[0022] S33. Use the Global Malmquist-Lenberg Index to decompose productivity changes over time into efficiency changes and technological progress for dynamic assessment.

[0023] Preferably, in said S31, the relaxation-based measurement orientation distance function model is expressed as:

[0024]

[0025] Where ρ is the inefficiency index, N is the number of input indicators, is the slack variable for the nth input, x n is the actual value of the nth input, M is the number of ideal output types, K is the number of non-ideal output types, represents the slack variable of the mth ideal output, y m represents the actual value of the mth ideal output, represents the slack variable for the kth non-ideal output, b k represents the actual value of the kth non-ideal output;

[0026] The constraints of the relaxed measurement orientation distance function model are:

[0027]

[0028] Where x i is the input vector of period i, y i is the ideal output vector of period i, b i is the non-ideal output vector of period i; X, Y, and B are matrices composed of all decision-making units, s - Represents the slack variable of input, s b represents the slack variable of non-ideal output, λ is the weight of other decision-making units, λ∈R n .

[0029] Preferably, in said S32, the comprehensive emission reduction index is expressed as:

[0030] IESERI i =1-(θ E +θ c );

[0031] Where, IESERI i represents the comprehensive emission reduction index of the i-th airline, θ E is the energy relaxation, θ c Relax for CO2 emissions.

[0032] Preferably, in said S33, the GML index is expressed as:

[0033]

[0034] Preferably, in S33, the efficiency change is expressed as:

[0035]

[0036] Where, represents the relaxation-based measured orientation distance function at period i;

[0037] Technological progress is expressed as:

[0038]

[0039] Therefore, the present invention provides a three-stage evaluation method for the low-carbon efficiency of airlines. Through a three-stage collaborative framework, it significantly improves the comprehensiveness and scientific nature of the low-carbon efficiency evaluation of the aviation industry. In the first stage, a cloud model is used to deal with the uncertainty of carbon efficiency indicators. The expected value, entropy and hyperentropy parameters are used to quantify the volatility and distribution characteristics, intuitively presenting the stability differences of different airlines and providing a reliable benchmark reference for subsequent analysis. In the second stage, a random forest algorithm is introduced to screen out key operating indicators through a decision tree structure and feature importance ranking, effectively reducing dimensional redundancy and enhancing the interpretability of the indicator system. In the third stage, the SBM-DDF model and the GML index are combined to construct a multi-dimensional dynamic evaluation system: the SBM-DDF model optimizes ideal output and non-ideal output simultaneously through slack variables, and uses a comprehensive emission reduction index to quantify the environmental and operational collaborative efficiency. The λ index reveals industry benchmarks and provides managers with improvement paths. The GML index decomposes efficiency changes and technological progress, dynamically tracking the root causes of productivity evolution. The three-stage design is progressive and can assist policymakers in implementing precise policies. The resulting evaluation system not only overcomes the limitations of traditional single-dimensional indicators, but also adapts to industry fluctuations, providing explainable and operational decision-making support for the aviation industry's decarbonization strategy.

[0040] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is an overall flow chart of an embodiment of the present invention;

[0042] Figure 2 This is a cloud model diagram of carbon emissions per revenue ton-kilometer in an embodiment of the present invention, where (a) is Ryanair, (b) is Qantas, (c) is EasyJet, and (d) is Air New Zealand;

[0043] Figure 3 This is a cloud model diagram of carbon emissions per unit of operating income in an embodiment of the present invention, where (a) is Ryanair, (b) is Qantas, (c) is EasyJet, and (d) is Air New Zealand;

[0044] Figure 4 Schematic diagram of the True branch of the decision tree according to an embodiment of the present invention;

[0045] Figure 5 This is a schematic diagram of the False branch of the decision tree according to an embodiment of the present invention;

[0046] Figure 6 This is a heat map of the correlation between carbon emissions and variables in the embodiment of the present invention;

[0047] Figure 7 This is a sensitivity analysis chart of carbon dioxide emission variables for an embodiment of the present invention, where (a) is available seat kilometers, (b) is the number of aircraft, (c) is the number of employees, (d) is the number of flights, (e) is operating costs, (f) is operating revenue, (g) is revenue passenger kilometers, (h) is revenue ton-kilometers, and (i) is the number of passengers;

[0048] Figure 8 This is a comparison chart of low-carbon efficiency based on the SBM-DDF model according to an embodiment of the present invention;

[0049] Figure 9 This is a GML score trend graph of an embodiment of the present invention;

[0050] Figure 10 This is a GEC scoring trend chart of an embodiment of the present invention;

[0051] Figure 11 This is a GTC scoring trend chart of an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0053] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0054] Example

[0055] like Figure 1 As shown, the present invention provides a three-stage evaluation method for airline low-carbon efficiency. This method uses data from official disclosures of some international airlines and industry databases (during the period of 2018-2022) to combine uncertainty modeling, data-driven indicator selection, and frontier-based dynamic analysis to conduct a comprehensive low-carbon efficiency assessment.

[0056] This example uses a total of 14 indicators, which are divided into operational, financial, environmental, and capacity categories. The use of these indicators in the three analysis stages is shown in Table 1;

[0057] Table 1 Complete indicator framework for each analysis stage

[0058]

[0059] The specific steps are as follows:

[0060] S1. Using a cloud-based model approach, conduct a preliminary uncertainty assessment of airline carbon efficiency to obtain a benchmark judgment reference, specifically:

[0061] (1) Three cloud model parameters are used to capture the volatility and distribution of carbon efficiency indicators. The cloud model parameters include:

[0062] Expected value (Ex): the central value that best represents a qualitative concept, such as the average carbon efficiency level of airlines;

[0063] Entropy (En): A measure of the fuzziness and randomness of a concept, reflecting the range of acceptable values ​​under that concept;

[0064] Excess entropy (He): The uncertainty of entropy itself, which indicates the degree of dispersion or aggregation of cloud droplets (data points).

[0065] These parameters intuitively reflect the degree of certainty or variability associated with each indicator. In this example, the cloud model is used to visualize the following two key indicators:

[0066] Carbon emissions per revenue tonne kilometre (RTK) (low carbon transport efficiency): measures the amount of carbon dioxide emitted per kilometre of passenger or freight transport; e.g. Figure 2 As shown, EasyJet and Ryanair have dense and compact cloud droplets, with concentrations far below the industry average (dashed line), indicating good environmental performance. In contrast, Qantas and Air New Zealand have more dispersed cloud structures and a wider range, indicating greater volatility in emission intensity. Furthermore, cloud distribution that significantly deviates from the industry average indicates overall inefficient aircraft utilization or energy intensity.

[0067] Carbon emissions per unit of operating income (low-carbon economic performance): represents the carbon emission efficiency of generating operating income; e.g. Figure 3 As shown, EasyJet, Qantas and Air New Zealand have low and stable emissions per unit of revenue, and are classified as high-carbon profitability efficiency airlines; while companies whose cloud droplet centers are at or above the industry average and whose cloud layers are widely distributed perform poorly in this dimension.

[0068] (2) Evaluate the relative performance of carbon efficiency indicators (how close the operator's expected value Ex is to the optimal low-carbon target), stability (measured in En and He), and comparative competitiveness (through visual clustering of cloud droplets). The cloud model provides a benchmark judgment with perceptible uncertainty before applying more rigorous quantitative models.

[0069] This step addresses the inherent uncertainty and ambiguity of environmental and operational data. The introduced cloud model provides a method for converting qualitative concepts into quantitative assessment methods under conditions of uncertainty, randomness, and ambiguity. It is an important tool for capturing the heterogeneity and stability of airlines' carbon performance.

[0070] S2. Use the random forest machine learning algorithm to evaluate and rank the relative importance of multiple operational indicators that affect carbon dioxide emissions, and retain the most important operational indicators;

[0071] To improve the robustness of traditional DEA-based efficiency evaluation methods and reduce the dimensionality of input-output variables, a random forest machine learning algorithm was introduced to reveal the complex nonlinear relationship between explanatory variables and emission results. This algorithm identifies the most important determinants of CO2 emissions from a range of operational indicators, ensuring that subsequent steps are based on the most statistically relevant factors. This improves the rigor and interpretability of low-carbon efficiency evaluations. Specifically,

[0072] S21, build a decision tree to perform feature importance analysis; Figure 4 、 Figure 5 As shown, the root node of the decision tree is operating revenue, indicating that financial scale is the most valuable predictor. The dependent variable is CO2 emissions, and the independent variables include available seat kilometers (ASKs), revenue passenger kilometers (RPKs), operating costs, fuel consumption, number of employees, number of flights, fleet size, and number of passenger operations. The splitting of the independent variables further demonstrates the multivariate complexity of emissions behavior, as these variables directly affect fuel consumption and emissions. Notably, several branches include the number of employees and RTK, which serve as refinement variables for blade-level predictions, helping the model accurately capture intra-group variation.

[0073] The decision tree confirms that an airline's CO2 emissions are determined by a complex interaction between financial scale, transport capacity, and operational efficiency. The role of operating revenue at the top of the decision tree further demonstrates that, in addition to considering technical and operational factors, economic performance is also necessary when assessing carbon efficiency. Upon inspection, the decision tree achieved low squared errors at most terminal nodes, indicating high predictive accuracy for the training data.

[0074] S22. Calculate the mean impurity reduction (MDI), and retain the independent variables with high importance scores based on the mean impurity reduction;

[0075] Among them, whenever a feature j is used to split a node in a tree in the random forest, it will increase the purity of the node (that is, reduce the impurity, such as Gini impurity or information entropy); the reduction in impurity (weighted by the number of samples in the node) is accumulated to obtain the "importance contribution" of this feature in the entire tree. Finally, this contribution is averaged across all trees to obtain the MDI value of feature j, which is calculated as follows:

[0076]

[0077] Where, MDI j represents the average impurity reduction of feature j, T is the total number of trees in the random forest, is the set of nodes in all trees that use feature j to split, ω v represents the weight of node v, ΔI v represents the reduction in impurity when node n is split, ω v ΔI v represents the weighted impurity reduction of node v;

[0078] After calculation, four variables with higher importance scores were retained: operating revenue, available seat kilometers (ASK), revenue passenger kilometers (RPK) and fuel consumption.

[0079] This embodiment also analyzes the correlation between emissions and operational variables, and uses MATLAB to generate a correlation heat map between carbon emissions and variables based on the Pearson correlation coefficient. Figure 6 The data shows a strong positive correlation between CO2 emissions and airline operating scale and economic indicators. Specifically, available seat kilometers (ASK, r = 0.90), revenue passenger kilometers (RPK, r = 0.89), operating revenue (r = 0.88), and operating costs (r = 0.85) all show high correlations, indicating that emissions are significantly affected by the scope and intensity of operations.

[0080] Moderate correlations were found between workforce and capacity indicators, including number of employees (r=0.63), number of passengers carried (r=0.60), fleet size (r=0.58), and number of flights (r=0.52). These correlations suggest that capacity size and organizational structure have an indirect but real impact on emissions. Revenue tonne-kilometers (RTK) have a relatively weak correlation with CO2 emissions (r=0.36).

[0081] In addition, a sensitivity analysis of the dominant factors affecting emissions was performed. In MATLAB, a stacked ensemble model with random forest and linear regression was trained to independently perturb each input variable in 20% increments ranging from ±20% to ±200%. The corresponding changes in predicted emissions were recorded for both positive and negative perturbations of all variables. Figure 7 The results show that operating revenue, operating costs, and ASK show the highest emissions sensitivity, with positive perturbations leading to significant increases in predicted emissions. This result is consistent with previous correlation analysis and decision tree analysis, reinforcing the explanation that financial and capacity-related indicators are the main drivers of emissions.

[0082] S3. Based on the results of S1 and S2, a low-carbon efficiency evaluation indicator framework is determined. A relaxation-based measurement directed distance function model is used to analyze low-carbon efficiency, combining the global Malmquist-Lenberg index and the comprehensive emission reduction index, to obtain a multi-dimensional low-carbon efficiency evaluation system.

[0083] Based on a variety of analytical methods (including correlation diagnostics, random forest feature ranking, decision tree interpretability, sensitivity testing, and cloud model visualization), the results consistently show that variables reflecting scale, revenue, and transport output, particularly ASK, RPK, operating income, and fuel consumption, are the most influential predictors of emissions. Meanwhile, capacity-related indicators and labor indicators play an important, but relatively small, role, while freight indicators such as RTK have low explanatory power.

[0084] Therefore, as shown in Table 2, the low-carbon efficiency evaluation indicator framework includes input indicators, ideal outputs, and non-ideal outputs; input indicators include the number of employees, the number of aircraft and flights, operating costs, and fuel consumption; ideal outputs include operating income and revenue passenger kilometers; and non-ideal outputs are carbon dioxide emissions.

[0085] Table 2 Low-carbon efficiency evaluation indicator framework

[0086]

[0087] This indicator system ensures consistency between methodological design and empirical relevance. It captures the multidimensionality of airline operations while maintaining model simplicity and interpretability. The selected variables provide a solid foundation for assessing the low-carbon efficiency of different airlines and lay the foundation for SBM-DDF-GML modeling.

[0088] The specific process of conducting low-carbon efficiency analysis is as follows:

[0089] S31. A relaxation-based measured directed distance function (SBM-DDF) model is used to simultaneously expand ideal outputs and reduce non-ideal outputs. Specifically:

[0090] The SBM-DDF model can evaluate the environmental and operational efficiency of airlines by constructing a non-radial, non-directional directed distance function, taking into account both ideal and non-ideal outputs. Inefficiency is decomposed into specific inefficiency indicators related to energy consumption and carbon dioxide emissions, thereby constructing the Integrated Efficiency and Emission Reduction Index (IESERI).

[0091] Data envelopment analysis (DEA) evaluates the relative efficiency of decision-making units (DMUs) by comparing them with the empirical production frontier. Particularly relevant to emissions analysis is the non-radial data envelopment analysis based on slack measure (SBM), which takes into account the slack of inputs and outputs, that is, it can handle situations where certain inputs or outputs do not decrease or increase proportionally, and can more accurately measure efficiency in complex operating environments. At the same time, it allows for the inclusion of undesirable outputs such as carbon dioxide emissions, quantifying the degree of resource and emission inefficiency, and providing actionable insights for improving environmental performance. The directed distance function (DDF) extends the DEA framework, allowing for the simultaneous expansion of ideal outputs and reduction of non-ideal outputs, thereby capturing the trade-offs faced by airlines in improving operational performance and environmental impact.

[0092] The establishment process of the SBM-DDF model is as follows:

[0093] Assume that the input and output structure of airline i in period t is:

[0094] Input: x∈R N ;

[0095] Ideal output: y∈R M ;

[0096] Non-ideal output: b∈R K .

[0097] Definitions - 、s + and s b Denote the slack variables of input, ideal output and non-ideal output respectively. Define λ∈R n represents the intensity vector, and the direction vector is defined as g = (-x, y, -b).

[0098] The non-radial and non-directional SBM-DDF model is expressed as:

[0099]

[0100] Where ρ is the inefficiency index, N is the number of input indicators, is the slack variable for the nth input, x n is the actual value of the nth input, M is the number of ideal output types, K is the number of non-ideal output types, represents the slack variable of the mth ideal output, y m represents the actual value of the mth ideal output, represents the slack variable for the kth non-ideal output, b krepresents the actual value of the kth non-ideal output; the denominator of the SBM-DDF model is used to measure the average input slack (inefficiency) relative to each input x n , the denominator will be the ideal output y m and non-ideal output b k Combined with the slack (deficiency or surplus) of the model, the model as a whole maximizes efficiency by minimizing excess inputs and deficiencies in desirable outputs while reducing undesirable outputs.

[0101] The inefficiency index ρ can be further decomposed into three parts to provide a more refined efficiency assessment:

[0102] Inefficient investment:

[0103]

[0104] Inefficient ideal output:

[0105]

[0106] Inefficient and non-ideal output:

[0107]

[0108] The constraints of the relaxed measurement orientation distance function model are:

[0109]

[0110] Where x i is the input vector of period i, y i is the ideal output vector of period i, b i is the non-ideal output vector of period i; X, Y, and B are matrices composed of all decision-making units, s - Represents the slack variable of input, s b represents the slack variable of non-ideal output, λ is the weight of other decision-making units, λ∈R n .

[0111] These constraints ensure that the DMU being evaluated is compared to a convex combination of other DMUs. The λ value indicates which efficient DMUs contribute to the efficiency forecast and to what extent. As shown in Table 3, a nonzero λ value indicates that the corresponding airline is a benchmark for the evaluated airline. Analyzing the distribution of λ values ​​among inefficient DMUs can identify industry leaders, observe regional or structural benchmarking patterns, and support strategic learning and peer emulation.

[0112] Table 3 Learning benchmark lambda index values ​​of some airlines in 2018

[0113]

[0114] This example uses the SBM-DDF model to evaluate the low-carbon efficiency of 20 airlines worldwide from 2018 to 2022. The results are as follows: Figure 8 As shown, prior to the COVID-19 pandemic in 2020, most airlines maintained relatively high low-carbon efficiency values. 2018 and 2019 were periods of operational stability, with strong passenger demand and high load factors. In contrast, efficiency values ​​declined significantly in 2020 and 2021, reflecting the severe disruptions caused by the pandemic, including a sharp drop in demand, fleet grounding, and underutilization of operating capacity.

[0115] S32. To assess environmental inefficiency, a comprehensive emission reduction index is used to statically assess the environmental and operational efficiency of airlines. The comprehensive emission reduction index is expressed as:

[0116] IESERI i =1-(θ E +θ c );

[0117] Where, IESERI i represents the comprehensive emission reduction index of the i-th airline, θ E is the energy relaxation, θ c The IESERI value is the relaxation of carbon dioxide emissions. Energy inefficiency and environmental externalities in operations can be captured simultaneously through energy consumption relaxation and carbon dioxide emission relaxation. The higher the IESERI value (the closer to 1), the better the energy conservation and emission reduction effect. The IESERI value range is 0 to 1.

[0118] In this example, the IESERI scores of each airline are shown in Table 4;

[0119] Table 4 IESERI scores of the world's 20 airlines

[0120]

[0121] S33. Traditional DEA and DDF models are limited to static evaluation, while the Global Malmquist-Lenberg (GML) index can dynamically evaluate the changes in total factor productivity over time. Figure 9 Shows the trend of GML scores of various airlines;

[0122] Among them, the GML index is expressed as:

[0123]

[0124] The GML index decomposes productivity changes over time into efficiency change (GEC) and technological progress (GTC) for dynamic assessment. This decomposition provides a richer understanding of whether performance improvements stem from internal efficiency improvements or technological innovation across the industry.

[0125] like Figure 10 As shown in Figure 2, the efficiency change (GEC) reflects the change in the relative efficiency of the decision-making unit (DMU), that is, the degree of improvement of the airline compared with its best-performing peers under the same technical conditions. An increase in GEC (>1) means an improvement in management, resource allocation or economies of scale, while a GEC <1 indicates a decrease in operational efficiency. It is expressed as:

[0126]

[0127] Where, represents the relaxation-based measured orientation distance function at period i;

[0128] like Figure 11 As shown in Figure 2, technological progress (GTC) reflects changes in the production frontier itself, reflecting structural changes in innovation, technology adoption, and productivity across the industry. GTC>1 means technological progress, while GTC<1 reflects innovation lag or elimination, expressed as:

[0129]

[0130] Therefore, the GML index can be decomposed as follows: GML = GEC × GTC; if GML>1, it means that production efficiency has increased; if GML<1, it means that production efficiency has decreased; if GML=1, production efficiency remains unchanged.

[0131] Therefore, the present invention proposes a three-stage assessment method for the low-carbon efficiency of airlines, which integrates cloud model-based visualization, random forest feature selection, and the SBM-DDF-GML model for dynamic efficiency analysis. Even in periods of coexistence of structural trends and external shocks, it can provide a qualitative and quantitative insight into the dominant factors, differences, and evolution of the aviation industry's carbon efficiency. This not only improves the accuracy of the analysis, but also provides support for practical benchmarking and scenario planning for the transition to sustainable aviation.

[0132] 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 the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A three-stage evaluation method for airline low-carbon efficiency, characterized by: The following steps are involved: S1. Conduct a preliminary uncertainty assessment of airline carbon efficiency using a cloud model-based approach to obtain a benchmark judgment reference; S2. Use the random forest machine learning algorithm to evaluate and rank the relative importance of multiple operational indicators that affect carbon dioxide emissions, and retain the most important operational indicators; S3. Based on the results of S1 and S2, the low-carbon efficiency evaluation indicator framework is determined. A relaxation-based measurement directed distance function model is used to combine the global Malmquist-Lenberg index and the comprehensive emission reduction index to conduct low-carbon efficiency analysis and obtain a multi-dimensional low-carbon efficiency evaluation system.

2. The three-stage evaluation method for airline low-carbon efficiency according to claim 1 is characterized in that: The specific steps of S1 are: using cloud model parameters to capture the volatility and distribution of carbon efficiency indicators, and then evaluating the relative performance, stability and comparative competitiveness of carbon efficiency indicators; cloud model parameters include expected value, entropy and super entropy.

3. The three-stage evaluation method for airline low-carbon efficiency according to claim 1 is characterized in that: The specific steps of S2 are: S21. Construct a decision tree to perform feature importance analysis; the root node of the decision tree is operating revenue, the dependent variable is carbon dioxide emissions, and the independent variables include available seat kilometers, revenue passenger kilometers, operating costs, fuel consumption, number of employees, number of flights, fleet size, and number of passengers operated; S22. Calculate the average impurity reduction and retain the independent variables with high importance scores based on the average impurity reduction.

4. The three-stage evaluation method for airline low-carbon efficiency according to claim 3 is characterized by: In S22, the calculation formula for the average impurity reduction is: Where, MDI j represents the average impurity reduction of feature j, T is the total number of trees in the random forest, is the set of nodes in all trees that use feature j to split, ω v ΔI v represents the weighted impurity reduction of node v.

5. The three-stage evaluation method for airline low-carbon efficiency according to claim 1 is characterized by: In S3, the low-carbon efficiency evaluation indicator framework includes input indicators, ideal outputs, and non-ideal outputs; Among them, input indicators include the number of employees, the number of aircraft and flights, operating costs, and fuel consumption; ideal outputs include operating income and revenue passenger kilometers; and non-ideal outputs include carbon dioxide emissions.

6. A three-stage evaluation method for airline low-carbon efficiency according to claim 5, characterized in that: In S3, the specific process of performing low-carbon efficiency analysis is as follows: S31, using a relaxation-based measured directed distance function model to simultaneously expand ideal outputs and shrink non-ideal outputs; S32. Use a comprehensive emission reduction index to statically assess the environmental and operational efficiency of airlines; S33. Use the Global Malmquist-Lenberg Index to decompose productivity changes over time into efficiency changes and technological progress for dynamic assessment.

7. A three-stage evaluation method for airline low-carbon efficiency according to claim 6, characterized in that: In S31, the relaxed measurement orientation distance function model is expressed as: Where ρ is the inefficiency index, N is the number of input indicators, is the slack variable for the nth input, x n is the actual value of the nth input, M is the number of ideal output types, K is the number of non-ideal output types, represents the slack variable of the mth ideal output, y m represents the actual value of the mth ideal output, represents the slack variable for the kth non-ideal output, b k represents the actual value of the kth non-ideal output; The constraints of the relaxed measurement orientation distance function model are: Where x i is the input vector of period i, y i is the ideal output vector of period i, b i is the non-ideal output vector of period i; X, Y, and B are matrices composed of all decision-making units, s - Represents the slack variable of input, s b represents the slack variable of non-ideal output, λ is the weight of other decision-making units, λ∈R n .

8. The three-stage evaluation method for airline low-carbon efficiency according to claim 6 is characterized in that: In S32, the comprehensive emission reduction index is expressed as: IESERI i =1-(θ E +θ c ); Where, IESERI i represents the comprehensive emission reduction index of the i-th airline, θ E is the energy relaxation, θ c Relax for CO2 emissions.

9. The three-stage evaluation method for airline low-carbon efficiency according to claim 6 is characterized in that: In S33, the efficiency change is expressed as: Where, represents the relaxation-based measured orientation distance function at period i; Technological progress is expressed as:

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