Carbon Emission Reduction Assessment of Ships in the Grand Canal Network Based on Synthetic Weighting and Matter-Element Extension Model

Abstract

Vessel traffic is an important source of global greenhouse gas emissions. The carbon emissions from ships in the canal network are directly linked to the environmental performance of China’s inland waterway transportation, contributing to the achievement of global carbon reduction goals. Therefore, systematically assessing the carbon emission reduction levels of ships in canal networks is essential to provide a robust foundation for developing more scientific and feasible emission reduction strategies. To address the limitations of current evaluations—which often focus on a single dimension and lack an objective, quantitative representation of the mechanisms driving carbon emission and their synergistic effects—this study took a comprehensive approach. First, considering the factors influencing ship carbon emissions and emission reduction strategies, an evaluation index system was developed. This system included 6 first-level indexes and 22 s-level indexes, covering aspects such as energy utilization, technical equipment, and economic benefits. Second, a novel combination of methods was used to construct an evaluation model. Qualitative weights, determined through the interval binary semantic method, were integrated with quantitative weights calculated using the CRITIC method. These were then combined and assigned using a game-theory-based comprehensive assignment method. The resulting evaluation model, built upon the theory of matter-element topology, represents a significant methodological innovation. Finally, the evaluation method was applied to the empirical analysis of ships operating in Jiangsu section of the Beijing–Hangzhou Grand Canal. This application demonstrated the model’s specificity and feasibility. The study’s findings provide valuable insights for improving carbon emission reduction levels for inland ships and advancing the sustainable development of the shipping industry.

1. Introduction

The transportation sector is a significant contributor to global carbon emissions, with the shipping industry presenting a persistent global challenge in carbon management. As a critical component of the transportation sector, shipping accounts for over 80% of global trade and transportation activities. Often referred to as the artery of global trade, the shipping industry is essential to the global economy but is also a substantial source of environmental impact. Data indicate that ships worldwide contribute approximately 1 billion tons of carbon emissions annually, accounting for 3.3% of global carbon emissions [1]. This considerable contribution accelerates climate change and has attracted increasing attention from regulatory bodies and environmental advocates. The Beijing–Hangzhou Grand Canal serves as a vital inland waterway in China, handling substantial freight volumes and playing a crucial role in national economic growth and regional development [2]. In recent years, annual freight traffic on the canal has consistently surpassed 300 million tons, underscoring its importance within China’s inland waterway transport system. However, this rapid growth has also introduced significant environmental challenges, particularly in carbon emissions [3], highlighting the urgent need to assess and strengthen carbon reduction strategies for ships.

Reducing carbon emissions is at the core of promoting green and sustainable shipping practices, addressing the pressing environmental challenges within the shipping industry. Emissions can be significantly mitigated through the adoption of clean energy ships, optimization of shipping routes, improvement of transport efficiency, and implementation of carbon capture and storage technologies [4,5,6]. The systematic evaluation of these carbon reduction measures is crucial not only for the sustainable development of the shipping industry but also for providing essential data to policymakers for enacting stricter environmental regulations. Therefore, conducting in-depth research on the green transformation of the shipping sector and exploring the carbon reduction potential along the Beijing–Hangzhou Grand Canal holds immense practical value. Such efforts align with global initiatives to reduce emissions and promote sustainable economic growth. By thoroughly analyzing the current carbon emissions landscape and exploring effective reduction strategies, more practical and feasible solutions can be developed to advance environmental protection and green development.

Current research on carbon emission reduction in shipping often focuses on specific, single-dimensional aspects, such as energy consumption, carbon reduction technologies, energy efficiency indexes, or cost implications [7,8,9,10,11]. Some studies integrate economic and energy-saving benefits [12,13,14,15] into their assessments or consider carbon intensity alongside environmental factors [16], resulting in more comprehensive analyses. However, these evaluations are often insufficiently systematic and fail to fully capture the multi-dimensional impact of ship emissions or the synergistic effects of various emission reduction measures. Consequently, their conclusions may lack depth and scientific rigor. Many researchers relied on energy consumption indexes to construct carbon emission models, which are then combined with analytical models such as input–output analysis [17], DPSIR models [18], obstacle factor analysis [19], and time-varying double-difference models [20]. While these approaches reflected emission reduction levels from certain perspectives or assessed emissions throughout a ship’s entire life cycle [21], they typically relied on isolated data points and could not provide a clear picture of a ship’s emission reduction status or actionable future strategies.

Various evaluation methods have been employed across different fields, including the analytical hierarchy process (AHP) [22], cloud modeling [23], the entropy power method [24], fuzzy theory, and network analysis [25]. More recently, emerging theories such as Markov chains [26], object-element theory [27], and material-element topology [28] have enhanced evaluation models, further optimized previous approaches, and provided a stronger foundation for the theoretical model proposed in this paper.

To address the limitations of current evaluation methods in the maritime sector, this paper proposes a comprehensive system for assessing the carbon emission reduction levels of ships within canal networks. To overcome the shortcomings of interval binary semantic qualitative weighting and CRITIC quantitative weighting, a game-theory-based composite weighting method was applied. This innovative approach integrated the advantages of both methods to derive a more accurate composite weight. Unlike conventional one-dimensional analyses, this study adopted a systematic approach that captured the multidimensional impacts of ship emissions and the synergistic effects of emission reduction measures. Additionally, the matter-element extension theory was employed to construct an evaluation model specifically designed to assess the carbon emission reduction levels of ships operating within the Grand Canal network.

2. Methodology

2.1. Construction Principles of the Evaluation Index System

Ship navigation within canal waterway networks is influenced by numerous systems, each shaped by a variety of factors that can impact carbon emission reduction levels. To ensure the accuracy and reliability of the evaluation indexes for assessing the carbon emission reduction levels of ships in these networks, certain key principles must be adhered to: (1) orientation, (2) scientific rigor, (3) comprehensiveness, (4) comparability, and (5) mutual independence.

2.2. Evaluation Indexes and System Framework

Current research on carbon emission reduction in the shipping industry primarily focuses on two key areas: carbon emission measurement and the benefits of emission reduction strategies. Carbon emission measurement typically emphasizes energy consumption, while the benefits of emission reduction are assessed in terms of costs and technological advancements. However, these approaches often fail to capture the full scope of influencing factors. External environmental conditions, regulatory oversight, and corporate operations also play critical roles in the effectiveness of emission reduction efforts.

Building upon existing research, this paper proposed a comprehensive evaluation system. It incorporated a broader range of factors, including external environments, regulatory frameworks, and enterprise operations, all of which significantly influence the carbon emission reduction of ships. The evaluation system was divided into three core components: carbon emission conditions, benefits of emission reduction strategies, and external factors. Carbon emission conditions focused primarily on energy utilization and technical equipment, while emission reduction strategies emphasized regulatory and operational aspects. External factors accounted for waterway environmental conditions. As a result, this framework was further refined into six primary factors: energy utilization, technological equipment, economic considerations, regulatory frameworks, operational efficiency, and waterway conditions, each of which is detailed below.

2.2.1. Energy Utilization

A substantial portion of a ship’s energy consumption is dedicated to propulsion, with most energy derived from fossil fuels. This includes the fuel used by main engines, auxiliary engines, and boilers. Different types of ships exhibit distinct energy consumption patterns depending on their design and function, which in turn lead to differences in carbon emissions. For example, large ocean-going cargo ships primarily use heavy fuel oil, while coastal or inland vessels are more likely to use lighter fuels or diesel.

When constructing an evaluation system, emissions from various types of equipment must be independently accounted for to ensure accuracy. This includes calculating carbon emission coefficients for main and auxiliary engines separately and evaluating boiler efficiency as a key indicator. Optimizing energy consumption across these elements allows for significant reductions in carbon emissions and identifies critical areas for improvement.

2.2.2. Technical Equipment

Technological advancements are often interrelated with operational strategies. For instance, the installation of energy-saving devices requires corresponding operational techniques. Therefore, evaluating the carbon emission reduction levels of ships must include both the individual effects of energy-saving equipment and a comprehensive analysis of the overall technological applications.

Second-level indexes for this evaluation included the efficiency of energy-saving technologies, the proportion of emission reduction equipment, the coverage rate of emission reduction devices, and their utilization rate. This structured approach ensured that all aspects of emission reduction technologies were thoroughly evaluated, providing insights into current performance and opportunities for improvement.

2.2.3. Economic Benefit

Ships primarily serve trade and tourism sectors, making operational economic efficiency a critical factor in carbon emission reduction, especially in key networks like the Beijing–Hangzhou Grand Canal. Economic benefits were evaluated in two main areas: the costs of implementing carbon reduction strategies and the economic gains from reduced emissions.

Key indexes included the energy cost per unit turnover, the labor cost per unit turnover, carbon emissions per unit turnover, and the carbon trading revenue rate. This dual focus ensured a balanced assessment of cost efficiency and economic benefits derived from carbon reduction initiatives.

2.2.4. Regulation

Regulations play a pivotal role in driving carbon reduction efforts and fostering environmental awareness. Effective regulatory measures can encourage the development of carbon reduction technologies and promote low-carbon practices across the industry.

The regulatory evaluation focused on two perspectives: enterprises and management departments. For enterprises, key considerations included the disclosure of the carbon emissions and compliance with regulations. For management authorities, the focus was on the completeness of regulatory frameworks, the coverage of monitoring systems, and the transparency of carbon reporting. Key indicators included the extent of regulatory implementation and the number of non-compliance incidents.

2.2.5. Operations

Operational practices significantly impact carbon emissions during navigation and berthing. For example, hull fouling increases drag and fuel consumption, while prolonged berthing times contribute to unnecessary energy use. Reducing these inefficiencies can lower emissions.

Key operational indexes included the frequency of hull cleaning, the average berthing time, the shore power utilization rate, and speed deviation. Additionally, adopting clean energy at ports and maintaining optimal operating speeds were critical factors in improving operational efficiency and reducing emissions.

2.2.6. Waterway Network

The condition of the waterway environment directly affects energy consumption during navigation. Well-maintained waterways reduce resistance, enabling greater fuel efficiency and the use of larger, more efficient vessels. Conversely, complex waterway conditions can increase operational challenges and energy consumption.

Secondary indexes for waterway evaluation included the proportion of waterway classifications, navigation techniques, and the level of congestion. These factors provided a comprehensive view of how waterway conditions influence carbon emissions.

In summary, this paper constructed a comprehensive evaluation framework comprising six primary indexes and 22 secondary indexes to assess the carbon emission reduction levels of ships within canal waterway networks. A detailed summary of the evaluation framework is presented in

Table 1. Evaluation index system.

Primary Indexes	Secondary Indexes	Properties of Indexes	Indicator Explanation
Energy utilization (A1)	Carbon emissions from ship’s main and auxiliary engines (C11)	Quantitative	${\displaystyle \frac{\begin{array}{c}{\mathrm{C}\mathrm{O}}_2\mathrm{emission\; factor\; \ast \; fuel\; consumption\; \ast \; average\; low}\\ -\mathrm{level\; heat\; content\; of\; fuel}\end{array}}{\mathrm{Ship’s\; main\; engine\; power}}}$
	Ship clean fuel ratio (C12)	Quantitative	The proportion of clean energy consumption in total energy consumption during ship navigation. Clean energy refers to liquefied natural gas (LNG), propane, butane, methanol, ethanol, ammonia, hydrogen, electricity, and other energy sources.
	Energy recovery rate (C13)	Quantitative	The ratio of recovered energy to the total energy consumption of the ship. Recovery energy refers to the energy that can be re-utilized by the ship through the installation of relevant equipment or optimization of the structure, including steam, thermal, etc.
	Carbon recovery rate (C14)	Quantitative	The ratio of carbon recovery to a ship’s theoretical carbon emissions.
Technical equipment (A2)	Hull energy saving technology level (C21)	Qualitative	It mainly includes the technical level involved in the necessary structure of the hull such as the overall design of the hull and the push system, relying on expert evaluation.
	Emission reduction equipment installation rate (C22)	Quantitative	The proportion of the type of emission reduction equipment that can be installed on a ship to the type of emission reduction equipment currently available on the market (which can be installed on this type of ship). The emission reduction equipment here includes two types of equipment: energy saving equipment and carbon emission reduction equipment.
	Emission reduction equipment coverage (C23)	Quantitative	The ratio of the number of energy-saving equipment on ships to the total amount of equipment on ships.
Economic benefit (A3)	Energy cost per unit of turnover (C31)	Quantitative	The cost of energy consumed by a ship per ton-kilometer, where energy includes all the energy involved in the ship’s navigation, excluding the energy consumed by the ship at port.
	Labor cost per unit turnover (C32)	Quantitative	The average monthly labor cost (excluding labor cost of other business of the enterprise) spent by the enterprise on ship navigation and the ratio of the volume of transportation completed in the month.
	Carbon emissions per unit turnover (C33)	Quantitative	The average unit turnover of a single ship corresponds to carbon emissions.
	Carbon trading revenue rate (C34)	Quantitative	$1+{\displaystyle \frac{\begin{array}{c}\mathrm{Carbon\; emissions\; in\; accordance\; with}\\ \mathrm{relevant\; regulations}-\mathrm{actual\; carbon\; emissions}\end{array}}{\mathrm{Nationally\; mandated\; carbon\; emissions}}}$
Regulation (A4)	Degree of perfection of ship carbon emission system (C41)	Quantitative	Relying on expert evaluation, the evaluation content includes the scientific, comprehensive, and practical aspects of the evaluation of regional carbon emission system.
	Carbon detection coverage (C42)	Quantitative	The ratio of the number of ships equipped with carbon detection equipment to the number of navigable ships in the evaluation area.
	Carbon transparency (C43)	Quantitative	The indicator mainly indicates whether the carbon emissions of the ship are disclosed, and the evaluation content mainly includes the total carbon emissions, EEOI, ship type, sailing area, and other information.
	The number of illegal carbon emissions (C44)	Quantitative	Accounting of the number of illegal carbon emissions recorded by a single ship per unit time.
Operations (A5)	Hull cleaning frequency (C51)	Quantitative	The number of cleaning times per ship per unit time.
	The average berthing time of ships in port (C52)	Quantitative	The average length of time a ship completes a single berthing.
	Ship shore power utilization rate (C53)	Quantitative	The ratio of the annual shore power service time to the total length of the ship berthing.
	Speed difference (C54)	Quantitative	The absolute value of the difference between the actual mean sailing speed and the theoretical economic sailing speed.
Waterway network environment (A6)	Area channel class ratio (C61)	Quantitative	Class I and II routes are identified as low-emission routes, and Class III and IV are identified as high-emission routes. The channel class ratio of the navigation section is the ratio of the mileage of the low-emission section to the mileage of the high-emission section in the navigation area of the ship.
	Navigation and navigation technology level (C62)	Quantitative	Relying on expert evaluation, the evaluation content includes navigation map, navigation system and so on.
	Channel congestion (C63)	Qualitative	The planned navigable time of the ship includes the sailing time of the ship according to the planned sailing speed and the time of the ship passing the lock (excluding the time waiting for the lock).

, providing a systematic approach to evaluate the multiple factors influencing carbon emissions and identifying actionable strategies for improvement.

2.3. Data Processing

2.3.1. Data Standardization

This paper employs min-max normalization to standardize the data that require imputation. This method scales the data into a specific range, ensuring consistency and comparability across different indicators. The data in this article were obtained through research, with a time span of 2018–2023, and AIS data from Jiangsu Province from 2018 to 2023 were obtained for a series of studies.

2.3.2. Data Interpolation

To address gaps in the dataset caused by incomplete data collection, this study adopted the random forest imputation algorithm. As referenced in [29], this method treated missing data features as labels, using the remaining features and original labels to construct a new feature matrix. Initially, the missing values were temporarily filled with zeros. A random regression model was then applied to estimate and impute these values. This approach ensured that the imputation was both robust and reliable, maintaining the completeness and accuracy of the dataset for subsequent calculations.

2.4. Indicator Weight

2.4.1. Interval Two-Tuple Linguistic Qualitative Weighting

Unlike traditional qualitative weighting methods, such as the fuzzy comprehensive evaluation method or the analytic hierarchy process (AHP), the interval two-tuple linguistic method [30] provides greater flexibility in handling uncertainty in evaluation information provided by multiple experts. This method enabled a more comprehensive and accurate representation of expert input.

The evaluation utilized 5-term, 7-term, and 9-term linguistic sets, selected based on the characteristics of the evaluation object. A transformation function converted these linguistic evaluations into two-tuple linguistic variables, which were then integrated to calculate the qualitative weights of each evaluation indicator.

2.4.2. Quantitative Weighting Using the CRITIC Method

The CRITIC (Criteria Importance Through Intercriteria Correlation) method determines the objective weights of indicators by assessing both the contrast intensity among the criteria and the conflicts between them. This article combined the CRITIC method with AHP to complement each other and performed weighted average fusion of the results of each method to obtain more accurate indicator weights. The CRITIC method evaluated the indicator importance based not solely on magnitude but also on variability and intercorrelations among the data. This ensured that the weighting reflected the objective attributes inherent in the data. By extensively collecting data on ship carbon emission reduction indicators and applying the CRITIC weighting calculation theory, this study derived the quantitative weights (θ) for each evaluation indicator. This approach provided a systematic and objective framework for assessing the relative significance of various indicators within the context of carbon emission reduction in canal waterway networks.

(1)

Express the variability of indexes in the form of standard deviation:

$$\left\{\begin{array}{c}\overline{b_{\mathit{ij}}}={\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n{b}_{\mathit{ij}}\\ S_j=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{{(b}_{\mathrm{ij}}-\overline{b_j})}^2}{n-1}}}\end{array}\right.,$$

(1)

where b_ij is the value of each evaluation indicator, while S_j is standard deviation of the j-th indicator.

(2)

Use correlation coefficient to represent indicator conflict, and use correlation coefficient to measure the statistical data correlation of the same algorithm model under different evaluation indexes, reflecting the overlap of algorithm performance information:

$$\left|Ri={\displaystyle \sum _{i=1}^n\left(1-r_{\mathit{ij}}\right)}\right|,$$

(2)

where R_i represents the conflict of evaluation index i, and r_ij is the correlation coefficient between the two indexes.

(3)

Perform information processing:

$$Cj=Sj{\displaystyle \sum _{i=1}^P\left(1-r_{\mathit{ij}}\right)},$$

(3)

where C_j is the evaluation indicator of R_i.

(4)

Calculate objective weights:

$${\theta }_j={\displaystyle \frac{C_j}{{{\displaystyle \sum }}_{j=1}^p{C}_j}}$$

(4)

2.4.3. Game-Theory-Based Composite Weighting

The preceding sections employed both qualitative and quantitative approaches to determine the weights of the evaluation indexes for the carbon emission reduction levels of ships in the canal network. Subsequently, these weights were integrated and optimized using game theory.

(1)

Calculate objective weights:

$$W_i={\alpha }_1{\gamma }_i^T+{\alpha }_2{\theta }_i^T,$$

(5)

where W_i is the indicator i linear combination weight, is the weight of indicator i obtained by interval binary semantic calculation, and is the weight of CRITIC method indicator i.

(2)

Based on the game aggregation theory, the objective function is established with the deviation minimization as the optimization objective.

$$\min {\displaystyle \sum _{p=1}^n{\alpha }_p{W}_p^T}-W_{p2},$$

(6)

$$\left[\begin{array}{cc}{\gamma }_i{\gamma }_i^T& {\gamma }_i{\theta }_i^T\\ {\theta }_i{\gamma }_i^T& {\theta }_i{\theta }_i^T\end{array}\right]\left[\begin{array}{c}{\alpha }_1\\ {\alpha }_2\end{array}\right]=\left[\begin{array}{c}{\gamma }_i{\gamma }_i^T\\ {\theta }_i{\theta }_i^T\end{array}\right],$$

(7)

(3)

The obtained coefficient is normalized.

2.5. Model Construction

Based on the matter-element extension theory, also known as extenics theory [31], this study established the classical domain, node domain, evaluated matter element, and the correlation coefficient matrix for each evaluation indicator. By utilizing the comprehensive weights derived earlier, the comprehensive correlation degree of the evaluated matter element was determined. The confidence levels and grade assignments were then introduced to identify the evaluation grade of the matter element.

2.5.1. Section Domain and Classical Domain

This paper categorized the carbon emission reduction levels of ships within the canal waterway network and defined the scoring value ranges and intervals for each evaluation indicator. These intervals formed the classical domain corresponding to each service level.

$$\mathrm{R}i=\left(N,\hspace{0.33em}c,\hspace{0.33em}v\right)=\left[\begin{array}{ccc}{N}_m& c_{i1}& v_{i1}\\ & c_{i2}& v_{i2}\\ & .& .\\ & .& .\\ & .& .\\ & c_{in}& v_{i\mathrm{n}}\end{array}\right]=\left[\begin{array}{ccc}{N}_m& c_{i1}& a_{i1}{b}_{i1}\\ & c_{i2}& a_{i2}{b}_{i2}\\ & .& .\\ & .& .\\ & .& .\\ & c_{in}& a_{ij}{b}_{ij}\end{array}\right],$$

(8)

where R_i is the i-th characteristic element of the evaluation object, N_m is the evaluation level, c_ij is the evaluation indicator of, and is the value range corresponding to the grade r of the evaluation indicator.

According to the extenics theory and the theorem of node domain, this paper utilized the range of values or scores of various evaluation indexes as the node domain for the grading model of carbon emission reduction levels of ships in the canal waterway network.

The node domain R_pi can be expressed as

$${\mathrm{R}}_{\mathrm{p}i}=\left(N_{pi},c_{pij},v_{pij}\right)=\left[\begin{array}{ccc}{N}_{pi}& c_{pi1}& v_{pi1}\\ & c_{pi2}& v_{pi2}\\ & .& .\\ & .& .\\ & .& .\\ & c_{pin}& v_{pin}\end{array}\right]=\left[\begin{array}{ccc}{N}_{pi}& c_{pi1}& a_{pi1}{b}_{pi1}\\ & c_{pi2}& a_{pi2}{b}_{pi2}\\ & .& .\\ & .& .\\ & .& .\\ & c_{pin}& a_{pij}{b}_{pij}\end{array}\right],$$

(9)

2.5.2. Elementization Based on Matter-Element Theory

For the evaluation of carbon emission reduction levels of ships within the canal waterway network, according to the matter-element theory the first-level indexes were elementized as follows:

$$\left[Carbonreductionevaluation \begin{array}{cc}Energy\hspace{0.33em}utilization& \hfill Evaluationresult1\\ Technical\hspace{0.33em}equipment& \hfill Evaluationresult2\\ Economic\hspace{0.33em}benefit& \hfill Evaluationresult3\\ \mathrm{Re}gulation& \hfill Evaluationresult4\\ Operations& \hfill Evaluationresult5\\ Waterway\hspace{0.33em}network\hspace{0.33em}environment& \hfill Evaluationresult6\end{array}\right],$$

(10)

The materialization of second-level indexes (the same applies to other secondary indexes) was as follows:

$$\left[\mathrm{E}nergyutilization \begin{array}{cc}Carbon\hspace{0.33em}emission\hspace{0.33em}of\hspace{0.33em}ship& \hfill Evaluationresult1\\ \mathrm{Pr}oportion\hspace{0.33em}of\hspace{0.33em}clean\hspace{0.33em}fuel\hspace{0.33em}for\hspace{0.33em}ships& \hfill Evaluationresult2\\ Energy\hspace{0.33em}efficiency& \hfill Evaluationresult3\\ Carbon\hspace{0.33em}re\mathrm{cov}ery\hspace{0.33em}rate& \hfill Evaluationresult4\end{array}\right],$$

(11)

2.5.3. Evaluation Grade Correlation Degree

(1)

Define bounded intervals:

$$v_{ij}=\left[a_{ij}{b}_{ij}\right],$$

(12)

where v_ij is the value interval of evaluation indexes, ${\alpha }_{\mathrm{ij}}$ is the lower bound, and ${\mathrm{b}}_{\mathrm{i}\mathrm{j}}$ is the upper bound.

(2)

Determine the modulus of the bounded interval:

$$\left|v_{ij}\right|=\left|a_{ij}{b}_{ij}\right|,$$

(13)

$$\rho \left(c_{ij},\hspace{0.33em}{v}_{ij}\right)=\left|c_{ij}-{\displaystyle \frac{1}{2}}\left(a_{ij}+b_{ij}\right)\right|-{\displaystyle \frac{1}{2}}\left(b_{ij}-a_{ij}\right),$$

(14)

where $\rho (c_{ij},v_{ij})$ is the correlation function, and k is the distance from C_ij to v_ij.

(3)

Calculate the correlation degree:

$$k_{cij}r\left(v_{ij}\right)=\left\{\begin{array}{c}{\displaystyle \frac{-\rho \left(c_{ij},\hspace{0.33em}{v}_{ij}\right)}{\left|v_{ij}\right|}}\left(c_{ij}\in v_{ij}\right)\\ {\displaystyle \frac{\rho \left(c_{ij},\hspace{0.33em}{v}_{ij}\right)}{\rho \left(c_{ij},\hspace{0.33em}{v}_{ij}\right)-\rho \left(c_{ij},\hspace{0.33em}{v}_{ij}\right)}}\left(c_{ij}\notin v_{ij}\right)\end{array}\right.,$$

(15)

where $K_{C_{ij}r}\left(v_{ij}\right)$ is correlation degree of indicator C_ij under r level.

(4)

Calculate the comprehensive correlation degree:

$$k_{cij}r\left(v_{ij}\right)=k_{cij}r\left(v_{ij}\right){\mathrm{W}}_i,$$

(16)

where $K_{C_{ij}r}\left(v_{ij}\right)$ is the correlation degree of the indicator C_ij at the grade after incorporating the weights.

2.6. Grading of Evaluation Levels

Following the evaluation level classification methods from the transportation field [32], the carbon emission reduction levels of ships in the canal waterway network were divided into five grades. The evaluation results were represented by the set Vi = {level 5, level 4, level 3, level 2, level 1}, where each level indicated a progressively higher state of carbon emission reduction. The status of carbon emission reduction at each level is presented in the

Table 2. Rating of evaluation levels.

Rating	Classical Domain	Emission Reduction Status
Ⅰ	0.9–1	Ships predominantly use clean energy, with highly efficient carbon emission reduction technologies and equipment. The associated costs of emission reduction are extremely low, the regulatory framework is scientific and rigorous, and the management is efficient. Consequently, the overall emission reduction performance is excellent.
Ⅱ	0.6–0.9	Ships primarily rely on clean energy, and emission reduction technologies and equipment are relatively efficient. The regulatory framework is scientific and fairly rigorous, and the management is relatively efficient. Overall, the emission reduction performance is good.
Ⅲ	0.3–0.6	Ships generally utilize clean energy and are equipped with moderately efficient carbon emission reduction technologies and equipment. However, emission reduction costs are relatively high. While the regulatory system is comprehensive, management effectiveness is limited. Despite these challenges, the overall emission reduction performance is above average.
Ⅳ	0.1–0.3	Ships are largely dependent on non-clean energy, and the level of carbon emission reduction technology and equipment is low, resulting in high costs. There are notable issues with the regulatory framework, and management is average. Overall, the emission reduction performance is slightly below average.
V	0–0.1	Ships predominantly consume the non-clean energy and lack fundamental carbon emission reduction equipment and technologies. Emission reduction costs are extremely high, the regulatory system is outdated, and the management is inefficient. As a result, the overall emission reduction performance is poor.

.

3. Results

This paper used the Jiangsu section of the Beijing–Hangzhou Grand Canal as a case study to evaluate the scientific validity and feasibility of the proposed model for assessing the carbon emission reduction levels of ships in the canal waterway network. The Beijing–Hangzhou Grand Canal, the world’s longest ancient canal, spans 1794 km. The Jiangsu section accounts for 78.3% of the canal’s annual navigable mileage and handles over 100 million tons of cargo annually. This section also features the best navigation conditions and the largest ship traffic volume along the entire canal. Figure 1a,b illustrate the schematic diagram of the Jiangsu section and the topological structure model of its waterway network. The Jiangsu section is divided into the Northern Jiangsu Canal and the Southern Jiangsu Canal by the Yangtze River. The Northern Jiangsu Canal, located in the northern part of Jiangsu Province, accommodates the majority of ship traffic within this section. Therefore, effective management of carbon emissions in this area is critical for realizing the overall carbon reduction benefits of the canal.

3.1. Data Import

This study collected data from shipping enterprises operating along the Jiangsu section of the Beijing–Hangzhou Grand Canal and the mainline of the Yangtze River. The weights of various indicators were calculated, and the previously constructed evaluation model was applied to assess the carbon emission reduction levels of ships in the Jiangsu section. Due to missing and erroneous data encountered during the collection process, the random forest imputation method was employed to address data gaps. The results of the imputation process are illustrated in Figure 2.

3.2. Evaluation of Carbon Emission Reduction Level

The binary set (si, α) was used to represent the evaluation language set for each evaluation object. This study employed three evaluation language sets: the five-element set X = {very unimportant (x₁), unimportant (x₂), average (x₃), important (x₄), very important (x₅)}, the seven-element evaluation language set Y = {totally unimportant (y₁), unimportant (y₂), more unimportant (y₃), average (y₄), more meaningful (y₅), meaningful (y₆), very meaningful (y₇)}, and the nine-element evaluation language set Z = {very low (z₁), very low (z₂), low (z₃), slightly low (z₄), medium (z₅), slightly high (z₆), high (z₇), very high (z₈), extremely high (z₉)}.

A panel of 20 experts in the field participated in the weight evaluation process. The experts were categorized into three groups with weights of 0.3, 0.4, and 0.3. Based on their assessments, an interval binary semantic judgment matrix was constructed, an interval binary semantic judgment matrix was constructed, and binary semantic weights were calculated. The CRITIC method was applied to derive quantitative weights, and a game-theory-based comprehensive assignment method was used to compute the final comprehensive weights. By quantifying evaluation indicators, it was possible to objectively measure the specific impacts of various factors on the overall performance, providing a more data-driven basis for decision-making. The final results are presented in

Table 3. Evaluation indicator weights.

Index	Domain 1 Experts (5 Pers.)	Domain 2 Experts (9 Pers.)	Domain 3 Experts (6 Pers.)	Binary Semantics	CRITIC	Game-Theory-Derived Weights
	(0.3)	(0.4)	(0.3)
${\mathrm{C}}_{11}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_5,0\left)\right]$	${\left[\right(\mathrm{y}}_7,0),({\mathrm{y}}_7,0\left)\right]$	${\left[\right(\mathrm{z}}_7,0),({\mathrm{z}}_9,0\left)\right]$	0.06859	0.05477	0.06550
${\mathrm{C}}_{12}$	${\left[\right(\mathrm{x}}_5,0),({\mathrm{x}}_4,0\left)\right]$	${\left[\right(\mathrm{y}}_7,0),({\mathrm{y}}_7,0\left)\right]$	${\left[\right(\mathrm{z}}_7,0),({\mathrm{z}}_8,0\left)\right]$	0.06957	0.06968	0.06959
${\mathrm{C}}_{13}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_3,0\left)\right]$	${\left[\right(\mathrm{z}}_3,0),({\mathrm{z}}_7,0\left)\right]$	0.03892	0.05143	0.04172
${\mathrm{C}}_{14}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_5,0\left)\right]$	0.04285	0.05661	0.04593
${\mathrm{C}}_{21}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_5,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_6,0\left)\right]$	${\left[\right(\mathrm{z}}_6,0),({\mathrm{z}}_7,0\left)\right]$	0.05539	0.04422	0.05289
${\mathrm{C}}_{22}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_1,0\left)\right]$	${\left[\right(\mathrm{y}}_3,0),({\mathrm{y}}_4,0\left)\right]$	${\left[\right(\mathrm{z}}_4,0),({\mathrm{z}}_5,0\left)\right]$	0.03211	0.04867	0.03582
${\mathrm{C}}_{23}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_5,0\left)\right]$	0.04649	0.05238	0.04781
${\mathrm{C}}_{31}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_6,0\left)\right]$	${\left[\right(\mathrm{z}}_6,0),({\mathrm{z}}_5,0\left)\right]$	0.04639	0.04061	0.04509
${\mathrm{C}}_{32}$	${\left[\right(\mathrm{x}}_1,0),({\mathrm{x}}_2,0\left)\right]$	${\left[\right(\mathrm{y}}_3,0),({\mathrm{y}}_3,0\left)\right]$	${\left[\right(\mathrm{z}}_3,0),({\mathrm{z}}_5,0\left)\right]$	0.03002	0.03728	0.03165
${\mathrm{C}}_{33}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_2,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_6,0\left)\right]$	0.04309	0.04278	0.04302
${\mathrm{C}}_{34}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_5,0\left)\right]$	0.04431	0.02918	0.04091
${\mathrm{C}}_{41}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_1,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_3,0\left)\right]$	${\left[\right(\mathrm{z}}_3,0),({\mathrm{z}}_6,0\left)\right]$	0.03454	0.03637	0.03495
${\mathrm{C}}_{42}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_2,0\left)\right]$	${\left[\right(\mathrm{y}}_3,0),({\mathrm{y}}_4,0\left)\right]$	${\left[\right(\mathrm{z}}_4,0),({\mathrm{z}}_6,0\left)\right]$	0.03795	0.03489	0.03726
${\mathrm{C}}_{43}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_1,0\left)\right]$	${\left[\right(\mathrm{y}}_2,0),({\mathrm{y}}_2,0\left)\right]$	${\left[\right(\mathrm{z}}_2,0),({\mathrm{z}}_5,0\left)\right]$	0.02585	0.04144	0.02935
${\mathrm{C}}_{44}$	${\left[\right(\mathrm{x}}_1,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_3,0\left)\right]$	${\left[\right(\mathrm{z}}_3,0),({\mathrm{z}}_5,0\left)\right]$	0.03430	0.05007	0.03783
${\mathrm{C}}_{51}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_5,0),({\mathrm{y}}_6,0\left)\right]$	${\left[\right(\mathrm{z}}_6,0),({\mathrm{z}}_6,0\left)\right]$	0.04823	0.04950	0.04852
${\mathrm{C}}_{52}$	${\left[\right(\mathrm{x}}_3,0),({\mathrm{x}}_4,0\left)\right]$	${\left[\right(\mathrm{y}}_6,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_6,0\left)\right]$	0.05285	0.05253	0.05278
${\mathrm{C}}_{53}$	${\left[\right(\mathrm{x}}_4,0),({\mathrm{x}}_4,0\left)\right]$	${\left[\right(\mathrm{y}}_7,0),({\mathrm{y}}_6,0\left)\right]$	${\left[\right(\mathrm{z}}_6,0),({\mathrm{z}}_8,0\left)\right]$	0.06286	0.04328	0.05847
${\mathrm{C}}_{54}$	${\left[\right(\mathrm{x}}_4,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_5,0),({\mathrm{y}}_7,0\left)\right]$	${\left[\right(\mathrm{z}}_7,0),({\mathrm{z}}_8,0\left)\right]$	0.05980	0.04089	0.05556
${\mathrm{C}}_{61}$	${\left[\right(\mathrm{x}}_2,0),({\mathrm{x}}_3,0\left)\right]$	${\left[\right(\mathrm{y}}_3,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_5,0\left)\right]$	0.04222	0.04277	0.04234
${\mathrm{C}}_{62}$	${\left[\right(\mathrm{x}}_1,0),({\mathrm{x}}_2,0\left)\right]$	${\left[\right(\mathrm{y}}_2,0),({\mathrm{y}}_3,0\left)\right]$	${\left[\right(\mathrm{z}}_3,0),({\mathrm{z}}_5,0\left)\right]$	0.02915	0.04191	0.03201
${\mathrm{C}}_{63}$	${\left[\right(\mathrm{x}}_4,0),({\mathrm{x}}_4,0\left)\right]$	${\left[\right(\mathrm{y}}_4,0),({\mathrm{y}}_5,0\left)\right]$	${\left[\right(\mathrm{z}}_5,0),({\mathrm{z}}_7,0\left)\right]$	0.05452	0.03876	0.05099

, and a more intuitive visualization is provided in Figure 3.

The study standardized the data for each evaluation indicator and applied the proposed model for the calculations. The resulting correlation degree values for each indicator are presented in

Table 4. Correlation coefficient and result.

	Ⅰ	Ⅱ	Ⅲ	Ⅳ	V (Substandard)	Rating	Primary Level Indicator Evaluation Level
${\mathrm{C}}_{11}$	−0.369565	0.472222	−0.395833	−0.654762	−0.731481	II	II
${\mathrm{C}}_{12}$	−0.317263	0.289362	−0.532979	−0.733131	−0.792435	II
${\mathrm{C}}_{13}$	−0.366296	0.456600	−0.407550	−0.661457	−0.736689	II
${\mathrm{C}}_{14}$	−0.684499	−0.526749	−0.053498	0.080247	−0.393140	IV
${\mathrm{C}}_{21}$	−0.374372	0.496667	−0.377500	−0.644286	−0.723333	II	II
${\mathrm{C}}_{22}$	−0.381443	0.463768	−0.347826	−0.627329	−0.710145	II
${\mathrm{C}}_{23}$	−0.444444	−0.166667	0.333333	−0.285714	−0.444444	III
${\mathrm{C}}_{31}$	−0.275362	0.204301	−0.596774	−0.769585	−0.820789	II	II
${\mathrm{C}}_{32}$	−0.367816	0.463768	−0.402174	−0.658385	−0.734300	II
${\mathrm{C}}_{33}$	−0.410377	0.236842	−0.177632	−0.530075	−0.634503	II
${\mathrm{C}}_{34}$	−0.386103	0.435014	−0.326260	−0.615006	−0.700560	II
${\mathrm{C}}_{41}$	−0.404762	0.291667	−0.218750	−0.553571	−0.652778	II	III
${\mathrm{C}}_{42}$	−0.594542	−0.391813	0.216374	−0.151020	−0.420613	III
${\mathrm{C}}_{43}$	−0.402985	0.307692	−0.230769	−0.560440	−0.658120	II
${\mathrm{C}}_{44}$	−0.444444	−0.166667	0.333333	−0.285714	−0.444444	III
${\mathrm{C}}_{51}$	−0.442922	−0.152778	0.293333	−0.302857	−0.457778	II	II
${\mathrm{C}}_{52}$	−0.419162	0.135802	−0.101852	−0.486772	−0.600823	II
${\mathrm{C}}_{53}$	−0.367089	0.460317	−0.404762	−0.659864	−0.735450	II
${\mathrm{C}}_{54}$	−0.472991	−0.209486	0.418972	−0.268739	−0.441081	III
${\mathrm{C}}_{61}$	0.446774	−0.553226	−0.888306	−0.936175	−0.950358	I	I
${\mathrm{C}}_{62}$	−0.285714	0.222222	−0.583333	−0.761905	−0.814815	II
${\mathrm{C}}_{63}$	0.149351	−0.149351	−0.787338	−0.878479	−0.905483	I

. The larger the value in the table, the more accurately it reflected the degree of compliance with its corresponding level, and a positive value indicated full compliance with the requirements of that level.

4. Discussion

Based on the evaluation results presented in Table 4, the Jiangsu section of the Beijing–Hangzhou Grand Canal achieved a second-level (II) rating in terms of energy utilization, technology and equipment evaluation, and economic benefits. As a key navigable segment of the canal, this section predominantly operates ships powered by liquefied natural gas (LNG), with a smaller proportion relying on diesel fuel. The energy profile is considered relatively clean, and the carbon emission reduction benefits in this region are notable. The well-developed shipping industry in Jiangsu benefits from geographical advantages, advanced emission reduction technologies, and strong economic performance. Consequently, the evaluation results aligned closely with the actual carbon reduction outcomes in terms of energy use, technology, and economic benefits.

However, China’s initiatives toward “carbon emission reduction and carbon neutrality” alongside other green and sustainable development strategies are relatively new. There remain gaps in policy development, regulatory frameworks, and enforcement mechanisms. As a result, the evaluation and supervision of carbon emission reduction for ships in the Jiangsu section are rated at level III, indicating significant room for improvement in these areas. Considering feasibility and cost, strategies can be used to improve loading and unloading efficiency, increase ship electrification rate, optimize energy-saving funds, implement policy subsidies, allocate carbon quotas reasonably, and regulate carbon trading prices. Port carbon reduction relies on the optimization of mechanical energy consumption. Accelerating the process of converting machinery from oil to electricity and improving shore power coverage can effectively reduce port carbon emissions, while optimizing the ship speed has a relatively small impact on the overall system. Increasing fiscal incentives can expand the medium- to long-term space for carbon reduction, especially by increasing special fund investment, which is more effective than increasing the proportion of government environmental protection investment. The carbon emissions trading market has a significant promoting effect on ship carbon reduction and is a key policy tool for achieving the goals of “carbon peak and carbon neutrality”.

Given the long-standing operational history and established infrastructure of the Jiangsu section, it is well positioned to integrate modern carbon emission reduction strategies. Its carbon emission reduction operations for ships can potentially reach level II. The Beijing–Hangzhou Grand Canal, as an artificial waterway, provides excellent canal conditions, particularly in the Jiangsu section, which is classified as a second-level canal. These favorable navigation conditions help to minimize additional carbon emissions during ship operations, supporting a level I rating for the waterway environment in the evaluation.

In summary, the overall carbon emission reduction level of ships in the Jiangsu section of the Beijing–Hangzhou Grand Canal is rated as class II. This reflects good performance in areas such as energy utilization, technological advancements, economic benefits, regulation, operations, and the waterway environment. While the overall carbon reduction level is commendable, there is room for improvement, particularly in regulatory oversight. Continuous advancements in this area are essential for achieving sustainable and high-quality development. Although this research focuses on the canal network, with the Jiangsu section used as a test case, the proposed methodology is adaptable and can be applied to waterways globally.

As the shipping industry is a significant contributor to global greenhouse gas emissions, reducing its carbon footprint through technological innovation and policy reform is imperative. In this context, mitigating emissions from ships becomes a priority. The carbon emission levels of inland ships directly influence the environmental performance of the transportation sector and play a crucial role in achieving global carbon reduction targets. Therefore, systematically evaluating carbon emission reduction levels for inland ships is not only practically significant but also provides a foundation for devising more scientifically sound and feasible emission reduction strategies.

5. Conclusions

This study carried out an empirical analysis using the Jiangsu section of the Beijing–Hangzhou Grand Canal as a case study to validate the scientific soundness and feasibility of the proposed evaluation model. The findings underscored the importance of integrating multiple factors—such as regulatory frameworks, ship operations, and emission characteristics—into a comprehensive evaluation approach, thus providing a broader perspective on carbon reduction strategies in inland waterway transportation. Specifically, the carbon emission reduction performance of ships was influenced not only by direct operational parameters but also by the interplay of external factors, including policy-driven incentives and infrastructural constraints. This highlights the need for a more systemic approach to addressing emissions, one that acknowledges the complexity of real-world conditions. Overall, by providing a detailed analysis of emission patterns and proposing a robust evaluation framework and establishing a more holistic and rational evaluation index system, the study contributes to the development of practical strategies for enhancing the sustainability of waterborne transportation. Meanwhile, to benefit from incorporating real-time data analysis and broader geographic contexts, it can better capture the intricacies of emission dynamics across different canal systems. However, the study also has limitations as it relies on certain assumptions that simplify these complexities. Further research is needed to refine the model and account for more dynamic and interconnected influences.