Research on the Evaluation System of Innovative Ability of Graduate Students in Energy Disciplines in the Context of the “Dual Carbon” Strategy of China

Abstract

On the basis of analyzing the current situation and common challenges in cultivating the innovative abilities of energy graduate students in the new era of ecological civilization construction, peak carbon dioxide emissions, and carbon neutrality, a comprehensive evaluation index system for the innovative ability of energy graduate students was established using the analytic hierarchy process (AHP) and entropy weight method. The four main components of this system are course learning, academic exchange, innovation performance, and innovation practice. By incorporating survey data from a particular university’s 2022 cohort of energy graduate students, an empirical exploration was undertaken to identify the factors influencing their innovation ability. The findings reveal that, overall, energy discipline graduate students possess a solid grasp of specialized knowledge. However, notable disparities exist in the individual innovation abilities of these students, with doctors exhibiting significantly superior innovation abilities compared to masters. Furthermore, academic masters tend to possess a higher level of innovation ability than their professional counterparts. The insights gained from this research offer valuable implications for enhancing the cultivation of innovation abilities among graduate students in energy disciplines and allied fields.

1. Introduction

At the UN General Assembly in 2020, President Xi Jinping declared that China aims to achieve carbon peak by 2030 and neutrality by 2060. China’s green development has reached new heights with the proposal of the carbon peak and carbon neutrality (“Dual Carbon”) goal. This will significantly support China’s economic and social development, comprehensive green transformation, and sustainable development, highlighting China’s role as a major player in the creation of a global ecological civilization and the fight against climate change. General Secretary Xi Jinping reiterated at the Central Financial and Economic Commission’s ninth meeting in 2021 that reaching carbon peak and carbon neutrality requires a significant and comprehensive shift in the economy and society. He emphasized that these goals should be integrated into the overall framework of the development of an ecological civilization, and efforts must be made to achieve carbon peak by 2030 and carbon neutrality by 2060 on schedule.

The entire society must raise awareness of “Dual-Carbon” and translate the new development idea of green and low-carbon into reality in light of the new stage of development under the objective of “Dual-Carbon.” Higher education institutions, as engines of fundamental research and sources of innovation, must take the lead in integrating the “Dual Carbon” goals into graduate education. This is essential not only to supply highly skilled professionals and scientific and technological support for the energy transition but also to meet the broader objectives of sustainable development [1]. The Ministry of Education released the Action Plan for Carbon Peak and Carbon Neutral Science and Technology Innovation in Colleges and Universities in July 2021. It stated that colleges and universities should leverage their strengths in highly skilled professional cultivation, discipline building, and basic research; accelerate the creation of a “Dual-Carbon” science and technology innovation system; and incorporate the idea and practice of “Dual-Carbon” into the entire highly skilled professional cultivation process.

In recent years, the global community has entered a critical phase of accelerating the energy transition to address the urgent challenges posed by climate change, environmental degradation, and resource depletion. The 2015 Paris Agreement established a clear direction for global climate action by committing signatories to limiting global warming to well below 2 °C, and preferably to 1.5 °C. Achieving this target requires deep decarbonization across all sectors, especially energy production and consumption. Consequently, countries worldwide are adopting renewable energy technologies, phasing out fossil fuels, and investing in low-carbon infrastructure, all of which demand a highly skilled workforce equipped with innovative competencies. Alongside the energy transition, the concept of the circular economy has gained global momentum as a complementary strategy to achieve sustainability. Unlike the traditional linear model of “take, make, dispose,” a circular economy emphasizes resource efficiency, waste minimization, and closed-loop production systems. This systemic change requires interdisciplinary knowledge and innovation in areas such as green manufacturing, sustainable design, energy efficiency, and waste valorization. As such, higher education institutions around the world are being called upon to prepare students to contribute to these transitions by integrating sustainability, systems thinking, and innovation into curricula and research agendas.

Energy, as the lifeblood of modern society, plays a central role in both economic growth and sustainable development [2]. Since the beginning of the 21st century, China’s rapid economic growth has led to a substantial increase in energy resource demand. China’s total primary energy consumption has surged from 1.46 billion tons of standard coal in 2000 to 5.39 billion tons in 2022, surpassing expectations and placing significant pressure on ecological civilization construction and international climate negotiations [3]. In this new era, we find ourselves at a critical juncture in modernization, where energy plays an even more vital role in ensuring the development of ecological civilization, social progress, harmony, and the well-being of the people. China’s energy development is transitioning from mere expansion to a focus on quality improvement and efficiency enhancement. Given the strategic importance of energy disciplines in the construction of economic and ecological civilizations, it becomes imperative to further enhance the innovation capabilities of postgraduate students in the context of the “Dual-Carbon” era, ultimately contributing to the successful realization of a green China.

2. Research Progress

This section provides a comprehensive literature review on innovation ability cultivation for graduate students under the ‘Dual Carbon’ strategy, highlighting both domestic and international perspectives. Currently, there is an abundance of research on innovation and entrepreneurship education Ref. [4] as well as the cultivation of innovation abilities in higher education institutions both domestically and internationally. However, there is a noticeable gap in studies that specifically address the cultivation of postgraduates’ innovation abilities within the context of the “Dual-Carbon” initiative. Wu [5] conducted a comprehensive review of the current state of postgraduate education, considering the perspective of carbon neutrality. This paper aims to consolidate the research landscape pertaining to postgraduate students’ awareness of “Dual-Carbon” and the cultivation of their innovation abilities. The analysis is conducted along the central themes of first-class university construction and the cultivation of first-class talent. In particular, we highlight several innovative competencies that are especially critical to addressing challenges associated with the “Dual-Carbon” transition. These include systems thinking and interdisciplinary integration—enabling students to understand the complex interactions between energy, environment, and policy. Competencies in technological innovation, such as the development of low-carbon technologies, renewable energy systems, and energy efficiency solutions, are also essential. Moreover, data-driven decision-making, digital modeling, and the ability to translate scientific research into practical applications (i.e., research-to-market competence) are increasingly important [6]. These competencies align with the urgent demand for highly skilled professionals capable of driving the carbon neutrality agenda and realizing sustainable development goals at both national and global levels.

Chinese scholars have engaged in relevant explorations. Lv [7] examined the efficacy of the University of Melbourne in the pursuit of world-class university status, analyzing its experiences, challenges, and future development trends. The study provided insights and suggestions for the ongoing effort to establish world-class universities in China. Liang et al. [8] analyzed Switzerland’s approach to constructing first-class universities, focusing on innovative, highly skilled professional cultivation and a commitment to excellent teaching quality. Xu [9] explored foreign countries’ policy models for building world-class universities and proposed recommendations for enhancing China’s university research output and facilitating the transformation of research achievements. Guo et al. [10] systematically reviewed the evolution and characteristics of Japan’s first-class universities, offering inspiration and suggestions for China’s world-class university construction. Ji et al. [11] conducted research on Harvard University, Cambridge University, and the University of Tokyo, noting that interdisciplinary, highly skilled professional cultivation has become a global higher education trend. Addressing challenges in postgraduate training within the context of “Double First-Class” construction, Cheng et al. [12] conducted a questionnaire survey on postgraduate students, analyzing the significance of interdisciplinary cross-cultivation and exploring strategies to promote interdisciplinary training.

Majors (disciplines) related to “Dual-Carbon” technology have been established by the initial 42 universities engaged in the “Double First-Class” construction in China. Nineteen scientific research institutions actively conduct research on “Dual-Carbon” technology [13]. In the Yangtze River Delta region, 25 “Double First-Class” universities have introduced majors related to “Dual-Carbon”, leading to the establishment of the “Yangtze River Delta University Alliance for Sustainable Development”. Additionally, the “Initiative for Promoting Carbon Peak and Carbon Neutral Universities Action” has been unveiled. To support “Double First-Class” construction, it is imperative to expedite the reform of postgraduate education, develop first-class disciplines, deploy cutting-edge equipment, implement top-tier management practices, establish a multi-level quality assurance system for cultivating postgraduate innovative abilities, adhere to the laws governing postgraduate growth and education, and instill “Dual Carbon” consciousness and innovative abilities into the collective awareness and behavior of universities, mentors, and postgraduates [14,15]. The cultivation of postgraduate innovation abilities and the “Double First-Class” construction of universities are mutually reinforcing. “Double First-Class” construction presents a strategic opportunity for enhancing postgraduate innovation abilities, while the development of postgraduate innovation abilities can serve as a driving force for “Double First-Class” construction.

Following China’s announcement of the “30–60” goal in 2020, numerous domestic scholars have conducted related research. He et al. [16] focused on graduate students from forestry colleges and universities, analyzing the existing cultivation model for majors related to “Double Carbon” under the context of “Double First-Class”. They discussed its advantages and disadvantages, proposing corresponding suggestions. Gao et al. [17] discussed the training mode of masters in the built environment under the “Double First-Class” framework. Wang et al. [18] investigates the training programs of master’s in environmental fields at select “Double First-Class” universities in China. They examined common issues in the training system for master’s in environmental fields at universities and put forward targeted improvement measures and suggestions. The concept of “Dual-Carbon” in the graduate curriculum is still in its infancy in China and has not yet been developed into a unified and comprehensive system. Although some universities have made exploratory efforts, a systematic and interdisciplinary curriculum framework that fully integrates carbon neutrality education remains underdeveloped domestically [19]. In contrast, several international universities have already taken meaningful steps to incorporate carbon neutrality and sustainability into graduate education. For example, Stanford University has launched the Doerr School of Sustainability, offering interdisciplinary programs on climate and energy systems. Imperial College London integrates climate change mitigation, carbon management, and environmental policy into its MSc in Environmental Technology [20]. Similarly, the University of Cambridge offers an MPhil in Environmental Policy with a strong emphasis on decarbonization strategies and global climate governance.

These global examples demonstrate that interdisciplinary collaboration, integration of scientific and policy knowledge, and institutional commitment are key to advancing carbon neutrality education. Compared to these initiatives, many Chinese universities are still in the early stages of developing curriculum frameworks that embed the “Dual-Carbon” concept. Although some institutions have included relevant topics in their graduate training programs [21], they often remain fragmented, lacking coordination across disciplines or supporting platforms. Therefore, significant efforts are still needed to construct robust and integrated carbon neutrality training systems tailored to China’s strategic goals and educational context. For most domestic universities and research institutions in the field of “Dual-Carbon”, there is a lack of experience in interdisciplinary research through the cross-fertilization of knowledge with other disciplines. Due to various objective factors and outdated management mechanisms, the single-tutor system still dominates the training mode of postgraduate students in most universities and research institutes, making it difficult to adapt to the interdisciplinary fusion of “Dual-Carbon” related training requirements [22]. From the perspective of existing training methods, not all tutor teams can adjust their concepts promptly, and there is still a delay in assimilating the results of cutting-edge research, making it challenging to meet the needs of constructing the system of relevant disciplines in the field of “Dual-Carbon”. Simultaneously, in terms of resources, information, and platforms, the interaction and collision among various disciplines in the field of “Dual-Carbon” are insufficient. This deficiency affects the pace of these disciplines in keeping up with research frontiers at home and abroad, as well as national policies, hindering the innovative ability of graduate students in universities in “Dual-Carbon”. In the context of “Double First-Class” construction, there is an urgent need for the establishment of interdisciplinary teaching teams in the field of “Dual-Carbon”.

Cultivating innovative abilities by combining theory with practice and emphasizing the practical aspect in the field of “Dual-Carbon” during the postgraduate education stage is a crucial approach to advancing “Double First-Class” construction and strengthening the efficacy of highly skilled professional cultivation in the realm of “Dual-Carbon”. Observing the developmental trajectory of China’s colleges and universities, various institutions are increasingly focusing on the practical teaching dimension. They are innovating the cultivation model by enhancing the laboratory infrastructure for practical courses and establishing collaborative training bases with enterprises, among other approaches [23]. A slight deficiency lies in the fact that existing postgraduate training programs in “Dual-Carbon”-related fields have not yet garnered attention from relevant university departments, failing to formulate a comprehensive and scientific training plan for practical teaching. Particularly at the current master’s degree level, most students rely on their own internship placements for practical exposure, preventing them from fully applying the theories learned in precise applications. This situation affects the effectiveness of practical teaching in the “Dual-Carbon” field.

According to the above-mentioned studies and the challenges of system evaluation on the innovative ability of graduate students, this paper analyzes current gaps in postgraduate innovation training from the perspective of sustainable development and proposes strategies for aligning postgraduate education with both the “Dual Carbon” goals and the broader global sustainability agenda. Considering that existing research rarely provides a systematic and quantitative evaluation of the innovation ability of graduate students in energy disciplines under the “Dual Carbon” goal, this study fills the gap by constructing a comprehensive evaluation system using both AHP and entropy weight methods, combining expert judgment with objective data. The main innovations lie in the dual method weighting and empirical validation based on survey data. The objectives of this study are to (i) establish an evaluation system for the innovative ability of graduate students in energy disciplines; and (ii) verify the adaptation of AHP and entropy weight methods by conducting a questionnaire survey. The structure of this paper is as follows: Section 1 outlines the current progress status and main challenges in the innovative abilities of energy graduate students in the new era of ecological civilization construction, peak carbon dioxide emissions, and carbon neutrality; Section 2 presents the evaluation system and survey design; Section 3 analyzes the results using AHP and entropy methods; Section 4 discusses conclusions and implications.

3. Evaluation System Development for Graduate Students’ Innovative Capacity

In order to overcome the drawbacks associated with a single weighting method, the AHP method and entropy weight method were used in this study to calculate subjective and objective weights, respectively. Subjective weights reflect the personal experience and opinions of the experts, while objective weights overcome the disadvantage of high arbitrariness [24]. The relevant steps are as follows:

3.1. Construction of an Evaluation Index System

Academic research on the innovation ability of graduate students primarily focuses on exploring strategies and pathways for cultivating their innovation ability [25,26,27,28]. However, there is a scarcity of studies on constructing an evaluation system for the innovation ability of science and engineering graduate students, particularly those in energy disciplines. To ensure the scientific validity of the evaluation index system, the authors, building on existing research, sought input from numerous scholars and experts with extensive experience in postgraduate education. They considered the specific characteristics of postgraduate students in energy disciplines within the context of the “Dual-Carbon” strategy in the new era. Through this comprehensive approach, the authors developed an evaluation index system for the innovation ability of graduate students in energy disciplines. This system comprises four secondary indicators and 15 tertiary indicators, as depicted in Figure 1.

To align with the “Dual Carbon” goals, the selected indicators reflect the critical competencies needed for the low-carbon transformation of the energy sector. For instance, indicators such as hosting innovation projects (C9), academic papers (C11), and patents (C13) emphasize technological innovation, which is vital for developing low-carbon technologies. Similarly, participation in national and international conferences (C5, C6) promotes knowledge exchange on carbon neutrality strategies. The evaluation system thus ensures that innovation capacity directly supports the dual-carbon agenda through measurable outputs and interdisciplinary engagement.

3.2. Questionnaire Design

Through the questionnaire survey (the questionnaire was conducted at Central South University in 2023, targeting both doctoral and master’s students in energy-related disciplines) was distributed via an online platform (e.g., Wenjuanxing), with additional reminders sent via email and class WeChat groups. Participation was voluntary and anonymous. To assess the innovative ability of postgraduate students’, the study conducted a questionnaire assessment of the 15 subdivided indicators. Data for this research were sourced from two main channels. Firstly, relevant experts and scholars performed a two-by-two comparison of the importance of each factor in the evaluation index system using the “1~9 Scale Method” proposed by Saaty. They assigned scores to the indexes based on their relative importance within the same level, using scales of 9, 7, 5, 3, 1, 1/3, 1/5, 1/7, and 1/9. Secondly, following the AHP method, the evaluation index system was scored with values of 9, 7, 5, 3, 1, 1/3, 1/5, 1/7, and 1/9, and the relative importance of each index at the same level was determined. Subsequently, based on the fundamental principles of the AHP method, the weight (W_AHP) for each index was calculated, and a consistency test was applied to the judgment matrix. Valid weights were obtained if the test passed; otherwise, the values needed adjustment until passing the consistency test. Secondly, the fuzzy leveling scoring method was employed for the 2022 graduating class of a university. Each index was scored using the nine-level scale method, and information entropy (e), discrimination factor (d), and weight (W_E) were sequentially calculated according to the basic principles of the entropy value method. Finally, the weights obtained through the AHP method and entropy weight method were synthesized and considered, resulting in more scientific and objective weighting results.

4. Analytical Methods and Results

In this study, 180 questionnaires were prepared and distributed to tutors and graduate students in energy disciplines, resulting in the collection of 167 valid questionnaires and an effective rate of 92.78%. Subsequently, the data from the 167 respondents were analyzed using AHP analysis and the entropy weight method, and a consistency test was conducted. The weight of each index was ultimately calculated.

4.1. Determination of Evaluation Index Weight Based on AHP

The AHP method’s crucial feature is the registration of the corresponding degree of importance between two scenarios, expressed in the form of a ratio through a two-by-two comparison, using the 1–9 scale method. This comparison quantifies the qualitative aspects of each indicator, as illustrated in

Table 1. Comparative scale definitions.

Scale	Significance
1	The former is as important as the latter
3	The former is slightly more important than the latter
5	The former is clearly more important compared to the latter
7	The former is very important compared to the latter
9	The former is absolutely more important compared to the latter
2, 4, 6, 8	Denote the intermediate values of the above neighboring judgments, respectively
Reciprocal	Ratio of the latter to the former

.

According to matrix theory (all calculations and visualizations were performed using MATLAB R2021a and OriginPro 2021), it is known that the weight coefficients of the factors are the eigenvectors w of the judgment matrix, which can be obtained by the following formula:

$$Aw={\lambda }_{\max }w$$

(1)

Generally speaking, the calculation of eigenvectors typically involves methods such as the square root method, power method, arithmetic mean method, geometric mean method, etc. In this study, the square root method is utilized to calculate the weight coefficients of the indicators, and the specific steps are as follows:

(1) The values of each row of the judgment matrix $A={(a_{ij})}_{n\times n}$ are multiplied:

$$M_i=\underset{j=1}{\overset{n}{\Pi }}{a}_{ij},i=1,2,\cdot \cdot \cdot ,n.$$

(2)

(2) Calculate the nth root of matrix M_i:

$$\stackrel{\sim }{w_i}=\sqrt[n]{M_i},i=1,2,\cdot \cdot \cdot ,n.$$

(3)

(3) The vector W is normalized:

$$w_i={\displaystyle \frac{\stackrel{\sim }{w_i}}{{\displaystyle \sum _{i=1}^n\stackrel{\sim }{w_i}}}},i=1,2,\cdot \cdot \cdot ,n.$$

(4)

The matrix $W$ obtained is the judgment matrix, and the eigenvectors of the judgment matrix represent the weight coefficients of the indicators.

(4) Calculate the maximum eigenvalue of the judgment matrix:

$${\lambda }_{\max }={\displaystyle \sum _{i=1}^n\frac{{(AW)}_i}{n{w}_i}}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\frac{{(BW)}_i}{w_i}}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\frac{{\displaystyle \sum _{j=1}^n{a}_{ij}{w}_j}}{w_i}}$$

(5)

where ${(AW)}_i$ is the $i_{th}$ component of $AW$, ${(BW)}_i$ is the $i_{th}$ component of $BW$. B refers to the vector obtained from the summation of weighted components in the judgment matrix, representing the composite importance scores of indicators.

A consistency test is conducted on the judgment matrix. Since subjectivity is involved in the comparison of the importance of the indicators, it is necessary to perform a consistency test on the judgment matrices. The test steps are as follows:

(1) Calculate the consistency indicator:

$$CI={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(6)

(2) Calculate the consistency ratio:

$$CR={\displaystyle \frac{CI}{RI}}$$

(7)

A total of 12 experts were invited to participate in the AHP evaluation process, including 6 professors and 4 associate professors from energy-related disciplines and 2 senior engineers from energy enterprises. All had over 10 years of experience in postgraduate training or energy R&D. They compared the secondary indicators of course learning (B₁), academic exchange (B₂), innovation practice (B₃), and innovation performance (B₄) in Figure 1 in pairs using the proportionality scaling method shown in Table 1 to generate the corresponding judgment matrix A:

$$A=\left(\begin{array}{cccc}1& 0.833& 0.294& 0.455\\ 1.2& 1& 0.455& 0.833\\ 3.4& 2.2& 1& 1.25\\ 2.2& 1.2& 0.8& 1\end{array}\right)$$

Similarly, the judgment matrix B₁ corresponding to the three tertiary indicators within B₁, the judgment matrix B₂ corresponding to the three tertiary indicators within B₂, the judgment matrix B₃ corresponding to the four tertiary indicators within B₃, and the judgment matrix B₄ corresponding to the five tertiary indicators within B₄ are obtained:

$$B_1=\left(\begin{array}{ccc}1& 0.526& 1.111\\ 1.9& 1& 1.818\\ 0.9& 0.55& 1\end{array}\right)$$

$$B_2=\left(\begin{array}{ccc}1& 0.455& 0.714\\ 2.2& 1& 1.25\\ 1.4& 0.8& 1\end{array}\right)$$

$$B_3=\left(\begin{array}{cccc}1& 0.833& 0.667& 1.25\\ 1.2& 1& 0.909& 1.429\\ 1.5& 1.1& 1& 1.667\\ 0.8& 0.7& 0.6& 1\end{array}\right)$$

$$B_4=\left(\begin{array}{ccccc}1& 1.538& 1.25& 3.333& 0.714\\ 0.65& 1& 0.833& 2& 0.625\\ 0.8& 1.2& 1& 1.667& 0.667\\ 0.3& 0.5& 0.6& 1& 0.333\\ 1.4& 1.6& 1.5& 3& 1\end{array}\right)$$

The consistency of the judgment matrices was tested using Equations (6) and (7), and the results indicated that all the judgment matrices were consistent. Therefore, the weight vector of W_A = (0.133, 0.187, 0.402, 0.278), W_B1 = (0.266, 0.482, 0.252), W_B2 = (0.22, 0.448, 0.332), W_B3 = (0.224, 0.274, 0.316, 0.186), and W_B4 = (0.25, 0.174, 0.188, 0.092, 0.296). The final index weights derived from the AHP method are depicted in Figure 2 and Figure 3.

As seen in Figure 2, the weights of each secondary index are calculated from the judgment matrix. Specifically, innovation practice holds the largest weight (0.402) among all the index, indicating that it has the greatest influence on graduate students’ innovation ability. It is followed by innovation performance and academic exchange, with weights of 0.278 and 0.187, respectively. The least influential index on graduate students’ innovation ability is course learning, with a weight of only 0.133.

The weights of the corresponding indicators in each guideline are presented in Figure 3. As observed in Figure 3a, the most influential aspect of the course study on graduate students’ innovation ability is the study of compulsory specialized courses, with a weight share of almost 1/2 at 0.482. It is followed by the study of public courses, with a weight of 0.266, and the weight of elective specialized courses is 0.252. This distribution of weight aligns with the common approach adopted by most colleges and universities in structuring their graduate programs. In Figure 3b, the weight of national academic conferences in academic communication is the highest, reaching 0.448, followed by international academic conferences with a weight of 0.332, while the weight of on-campus academic forums is only 0.22. Concerning the weight of each indicator in innovation practice, as shown in Figure 3c, the weight of hosting a project is 0.316, followed by participation in projects and disciplinary competitions with weights of 0.274 and 0.224, respectively. The smallest weight is assigned to off-campus practice at 0.186. The weighted ranking of innovation performance is then as follows: dissertation (0.296) > academic papers (0.25) > authorized patents (0.188) > maximum impact factor (0.174) > transformation of results (0.092). Finally, the product of the weight of the secondary and tertiary index is calculated to obtain the combined weight of the index.

4.2. Determination of Evaluation Index Weight Based on Entropy Weight Method

The concept of entropy, originating from thermodynamics, is utilized to gauge the level of disorder within a system. It can also represent the information content of known data and determine its weighting [29]. When the discrepancy between the values of evaluation indicators is significant, the entropy value diminishes, indicating that the indicator conveys a greater amount of information and should thus be assigned a higher weight. Conversely, when the indicator carries less information, its entropy value increases. The data for the entropy weight method come from the respondents’ objective evaluation of the situation. Applying the entropy value method to correct the weights derived from the AHP method can enhance its reliability.

The specific steps for determining the weights of indexes to evaluate graduate students’ innovation ability using the entropy weight method are as follows:

The data should be normalized. Let the matrix $X={(x_{ij})}_{n\times m},(i=1,2,\cdot \cdot \cdot ,n;j=1,2,\cdot \cdot \cdot ,m)$ represent the original data matrix comprising n evaluated objects and m evaluation indicators. Different types of data are standardized according to the following formula:

$$\begin{array}{l}{y}_{ij}={\displaystyle \frac{x_{ij}-\min x_{ij}}{\max x_{ij}-\min x_{ij}}},Positiveindexes\\ y_{ij}={\displaystyle \frac{\max x_{ij}-x_{ij}}{\max x_{ij}-\min x_{ij}}},Negativeindexes\end{array}$$

(8)

(1) Obtain the matrix:

$$Y={(y_{ij})}_{n\times m}$$

(9)

where $y_{ij}$ is the $j_{th}$ evaluation index normalized to the value on the $i_{th}$ evaluation object, and the value $y_{ij}\in [0,1]$.

(2) Normalize the matrix:

$$R^{\prime }={(y_{ij}^{\prime })}_{n\times m}={\displaystyle \frac{y_{ij}}{{\displaystyle \sum _{i=1}^n{y}_{ij}}}},i=1,2,\cdot \cdot \cdot ,n;j=1,2,\cdot \cdot \cdot ,m.$$

(10)

(3) Calculate the entropy value of each evaluation index:

$$H_j=-{\displaystyle \frac{1}{\ln m}}{\displaystyle \sum _{i=1}^m{y}_{ij}^{\prime }}\ln y_{ij}^{\prime },i=1,2,\cdot \cdot \cdot ,n;j=1,2,\cdot \cdot \cdot ,m.$$

(11)

when $y_{ij}^{\prime }=0$, it needs to be corrected according to $y_{ij}^{\prime }={\displaystyle \frac{1+y_{ij}}{{\displaystyle \sum _{i=1}^m(1+y_{ij})}}}$, and the objective weighting coefficients of the indexes are:

$$W_i={\displaystyle \frac{1-H_j}{m-{\displaystyle \sum _{j=1}^m{H}_j}}}$$

(12)

Substituting the data obtained through the questionnaire into the above equation, the weight for the evaluation index can be obtained (

Table 2. Results of the entropy weight method for calculating the weight of the evaluation index.

Indicators	Entropy (e)	Discrimination Factor (d)	Weight (W)
C1	0.987	0.013	0.03643
C2	0.977	0.023	0.06403
C3	0.989	0.011	0.02995
C4	0.984	0.016	0.04398
C5	0.969	0.031	0.08672
C6	0.978	0.022	0.06154
C7	0.968	0.032	0.08794
C8	0.962	0.038	0.10582
C9	0.962	0.038	0.10641
C10	0.97	0.03	0.08418
C11	0.972	0.028	0.07717
C12	0.982	0.018	0.04929
C13	0.981	0.019	0.05326
C14	0.99	0.01	0.02876
C15	0.969	0.031	0.08452

).

Figure 4 presents a comparison of the weight of the indexes obtained through the AHP method and the entropy weight method. It is evident that the discrepancies in the weight derived from the two methods are mostly within 20%, and even the majority of them remain within 10%. Therefore, it can be concluded that the two weighting methods utilized in this study are deemed reasonable and reliable.

4.3. Determination of Comprehensive Weight of the Evaluation Index Based on the AHP-Entropy Weight Method

The least squares method is employed to optimize the combined weight model, and the subjective and objective weights $W$ and $W_i$ obtained by the AHP-entropy weight method are combined to obtain the weights $W^{*}$:

$$\min F(W^{*})={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m\left\{{\left[(W^{*}-W)b_{ij}\right]}^2+{\left[(W^{*}-W_i)b_{ij}\right]}^2\right\}}}$$

(13)

$$st:{\displaystyle \sum _{j=1}^m{W}^{*}}=1;W^{*}>0,j=1,2,\cdot \cdot \cdot ,m$$

(14)

Considering that there are many factors affecting the innovation ability of graduate students, it is necessary to increase the weight of specific indicators. The subjective and objective methods are combined into the improved entropy method. As shown in the comprehensive multi-indicator evaluation decision model [30], the importance of specific indicators increases, and the improved weight of index $j$ is calculated as follows: (Here, ‘Rj’ denotes the improved weight vector after adjusting for increased importance of specific indicators using the least squares combination of AHP and entropy weights).

$$W{R}_j={\displaystyle \frac{W_j{R}_j}{{\displaystyle \sum _j^n{W}_j{R}_j}}}$$

(15)

The combined weights of the indexes and their rankings obtained using the AHP method and entropy weight method are presented in Figure 5. From Figure 5a, it is observed that when the weights obtained using the AHP method and entropy weight method are small, the final composite weights obtained will be smaller than either of the two, while when the weights obtained using the AHP method and entropy weight method are large, the composite weights will be larger than either of the two. As seen in Figure 5b, among all the indexes, hosting projects (C₉) has the largest weight of 0.17582, followed by participating in projects (C₈) and academic competition (C₇), with weights of 0.15144 and 0.10297, respectively. The three indexes with the smallest weights are the transformation of results (C₁₄), elective professional courses (C₃), and public courses (C₁), with weights of 0.00958, 0.01305, and 0.01678, respectively.

As shown in Figure 6, respondents’ views on the importance of key factors affecting the innovation ability of graduate students in energy disciplines are as follows: innovation practice (0.487) > innovation performance (0.286) > academic exchange (0.18) > course learning (0.047). Innovation practice holds a crucial position in the innovation ability of graduate students in energy disciplines, indicating that, as an engineering specialty, energy disciplines prioritize the practical training of graduate students to enhance their innovation ability. Following closely is innovation performance, weighted at 28.6%, emphasizing the significance of postgraduate research outputs (theses, patents) as essential indicators of innovation capacity. Academic communication is assigned a weight of 18%, indicating that gaining peer recognition also reflects, to some extent, the graduate student’s innovation profile. Course learning contributes approximately 4.7% to the total, highlighting the distinctive feature of graduate education in integrating teaching and scientific research, setting it apart from undergraduate education.

4.4. Comparisons of Current Results with Existing Literature

When comparing our results to those of earlier studies, it must be noted that our finding of doctoral students having significantly higher innovation capacity than master’s students aligns with Olugbenga et al. (2023) [31]. Their research in environmental science disciplines also reported a similar gap, attributing it to doctoral students’ longer research cycles and more in-depth project engagement. However, this is in contrast to Andreas et al. (2022) [32], who found smaller differences in applied energy fields. This discrepancy might be due to the fact that Andreas et al.’s study focused more on professional masters, where practical skills training in applied energy fields could potentially narrow the gap with doctoral students. In terms of the comparison between academic and professional masters, our result that academic masters outperform professional masters in innovation capacity is consistent with Kasworm C et al. (2021) [33]. They noted that academic programs typically emphasize theoretical innovation, while professional programs focus more on practical skills. This also aligns with the global trends observed by Stanford’s Doerr School of Sustainability (2022) [34], which showed that interdisciplinary professional programs often prioritize industry collaboration over academic output.

Regarding the importance of innovation practice, our study found that “hosting projects” had a high weight (0.1758) in the comprehensive weights. This is in line with Li et al. (2023) [35], who highlighted project-based learning as a key driver of engineering innovation. Similarly, MIT’s Energy Initiative (2024) [36] has integrated project participation into graduate curricula to enhance applied innovation, further validating our findings. Our finding that course learning has a relatively low weight (4.7%) in influencing innovation capacity echoes the research of Wang et al. (2022) [37]. They argued that graduate education in energy disciplines should shift from knowledge transmission to research practice, which is also consistent with the reforms at Imperial College London (2023) [38].

One limitation of this study is that the sample is restricted to only one university, Central South University. This may limit the generalizability of our findings, as different universities may have distinct educational resources, teaching philosophies, and student populations [39]. Despite this limitation, our study still provides valuable insights into the innovation capacity evaluation of energy discipline graduate students under the “Dual Carbon” context. The single-university sample allows for in-depth exploration within a specific educational environment, which can serve as a foundation for future multi-university research. Another limitation is that the index system we constructed lacks some “Dual Carbon”–specific indicators. For example, we did not include indicators related to low-carbon technology patents or carbon footprint reduction projects. This may lead to an incomplete evaluation of students’ innovation capacity in the context of “Dual Carbon” [40]. However, our existing index system still captures the main aspects of innovation capacity in energy disciplines, providing a starting point for further improvement. Moreover, our reliance on quantitative methods alone may overlook some qualitative aspects of innovation capacity, such as students’ creative thinking and problem-solving abilities in unstructured situations [41]. Although quantitative data can provide objective and comparable results, integrating qualitative methods could offer a more comprehensive understanding of students’ innovation capacity.

One important future direction of this research is to expand the sample size to include multiple universities across China, preferably 5–10 institutions with diverse educational backgrounds and regional characteristics. This would enable a more comprehensive and representative analysis of the innovation capacity of energy discipline graduate students, enhancing the generalizability of the research results [42]. Another future direction is to refine the evaluation index system by adding “Dual Carbon”–specific indicators. For example, including indicators related to students’ participation in low-carbon technology R&D projects, their achievements in reducing carbon emissions in practical projects, or their understanding and application of carbon trading mechanisms. This would make the evaluation more relevant to the “Dual Carbon” strategy [43]. In addition, future research could combine quantitative data with qualitative research methods, such as in-depth interviews with students, tutors, and industry experts. This would help to uncover the qualitative aspects of innovation capacity, such as the thought processes behind students’ innovative ideas and the impact of mentoring on their innovation development [44]. Furthermore, conducting longitudinal studies to track the innovation capacity of graduate students after graduation would also be beneficial. This could provide insights into how well the skills and knowledge acquired during graduate study translate into real-world innovation and contributions to the energy industry under the “Dual Carbon” scenario [45]. Several questions remain unanswered at present. For example, how do different regional policies related to “Dual Carbon” affect the innovation capacity cultivation of graduate students? How can international cooperation in energy research and education be better integrated into graduate education to enhance students’ global competitiveness in the context of “Dual Carbon”? Future research could focus on these questions to further expand the knowledge in this field.

5. Case Studies and Conclusions

According to the evaluation index system of innovation ability for postgraduates in energy disciplines, we conducted a questionnaire survey with over 50% participation from postgraduates and postgraduate supervisors in energy disciplines. The analysis covers various indices related to course learning, academic communication, innovation practice, and innovation performance of 9 doctoral and 84 master’s graduates from the class of 2022 (including 36 academic masters and 48 professional masters). The following conclusions were drawn from the study:

5.1. Doctors Are Significantly More Innovative than Masters

It has been demonstrated that postgraduate education at different stages effectively cultivates innovation ability. Doctoral students exhibit significantly greater capabilities than master’s students in publishing academic papers, authorizing invention patents, hosting innovative projects, and participating in academic conferences. As illustrated in Figure 7, doctors publish 4.5 more SCI papers per capita than masters. Moreover, all doctors participate in national and international academic conferences in the energy field, while less than one-third of masters do so. Regarding innovation practice, doctors primarily engage in national key R&D programs, the National Natural Science Foundation of China, or major enterprise projects. In contrast, masters are more involved in provincial and ministerial-level projects or enterprise projects, with some participating in national-level projects. This disparity underscores that doctors’ innovation ability is closely linked to their higher project involvement, increased communication with domestic and international peers, a more comprehensive grasp of disciplinary frontiers, and their significant creative contributions to projects. Additionally, concerning coursework, all doctors maintain a GPA of 3.5 or higher, while 98% of masters achieve a GPA of 3.0 or higher, and 52% attain a GPA of 3.5 or higher. This indicates that graduate students in the energy discipline generally possess a better grasp of specialized knowledge in the energy field and a stronger foundation for scientific research. It should be noted that the dataset is limited to a single university, and the doctoral sample size is relatively small (n = 9). Thus, while the observed trends indicate that doctoral students demonstrate stronger innovation performance than master’s students, this conclusion should be interpreted cautiously and validated with larger, more diverse samples in future research.

5.2. Academic Masters Are More Innovative than Professional Masters

Figure 8 presents a comparison between academic and professional masters at all levels. Regarding course learning, 67% of academic masters are above 3.5 (the highest GPA is 4.0), whereas only 43% of professional masters are above 3.5. Concerning academic papers, academic masters publish 0.61 high-level papers per capita, whereas professional masters publish only 0.48 papers, with as many as 73% of professional masters having no academic papers or authorized patents. Additionally, in terms of off-campus practice, 100% of professional masters participate, while fewer academic masters participate. This aligns with the cultivation goals and methods of academic masters, which prioritize academic research, theory, and cultivating research talent, and professional masters, which focus on practical application, comprehensive literacy, and applying knowledge and skills.

5.3. Significant Differences in Individual Graduate Student Innovativeness

Research achievements and comprehensive quality are the areas where the differences in the innovation ability of doctors are more obvious, and there are almost no very obvious differences between doctors in terms of basic courses, specialized courses, and other courses. The comprehensive quality of scientific research is mainly manifested in the ability to engage in scientific research independently, participate in projects, preside over projects, publish academic papers, and authorize invention patents. In terms of high-level publications by the doctoral graduates of the class of 2022 alone, the highest number of publications was nine, and the lowest was three, with a difference of more than three times in the number of SCI publications and more than five times in the maximum impact factor of a single publication. The innovation ability of masters is mainly reflected in the aspects of course study and practical exercises, and there are also differences in published papers and authorized specialties, but not as obvious as the differences of doctors. By analyzing the 2022 master’s graduates, there was a maximum 35% difference in GPA in terms of course learning. In the dissertation, the main differences between masters were in literature review and writing skills, while the differences between doctors were mainly in creative graduate work, a result consistent with the State Council Academic Degrees Office’s training requirements for doctoral and master’s degrees.

In the context of “Dual Carbon”, personalized teaching strategies should focus on embedding carbon neutrality challenges into coursework and research training. Suggested measures include (1) developing case-based courses on carbon-neutral technologies and policy frameworks; (2) creating interdisciplinary innovation labs addressing energy, environment, and sustainability; (3) establishing collaborative mentorship with industry partners engaged in green energy R&D; and (4) introducing “carbon-neutral innovation awards” to incentivize student participation in relevant projects.

In conclusion, the innovation ability of graduate students is dynamic, fluctuating not only during the study period but also undergoing significant changes after graduation and entry into the workforce. The evaluation index system of innovation ability for graduate students in energy disciplines, constructed in this paper under the background of “Dual-Carbon”, can accurately reflect their innovation capacity. It comprehensively quantifies and analyzes the innovation ability of graduate students during their study period, enabling comparisons among different graduate students. This quantification allows for the assessment of students through relatively scientific methods, revealing their innovation ability from various perspectives. This approach aids students and educators in analyzing individual situations, enabling targeted teaching based on each student’s aptitude. The implementation of personalized teaching aims to maximize the development of students’ innovative abilities, contributing to the expeditious realization of China’s ecological civilization construction and the “Dual-Carbon” goals by cultivating high-quality, innovative, and excellent talents.

The dynamic nature of innovation ability was observed through substantial variations in GPA, research outputs, and participation levels among individual students. For example, among doctoral students, SCI publication counts ranged from 3 to 9, and GPA differences reached up to 0.8 points. These fluctuations suggest that innovation ability evolves over time and is influenced by exposure to high-level projects, interdisciplinary mentorship, and international engagement.

The evaluation system can be implemented via periodic assessments (e.g., each semester), allowing supervisors to adjust training plans based on the dynamic profiles of students. Institutions can establish “innovation development profiles” for each student, guiding tailored mentorship and course adjustments.

Key results show that energy graduate students have a solid professional foundation but with individual disparities; doctoral students outperform master’s students, academic master’s surpass professional master’s students, and innovation practice and innovation performance are the most influential factors. The results confirm our initial assumptions that doctoral students outperform master’s students in innovation capability (H1) and that academic master’s students exhibit stronger innovation competencies than professional master’s students (H2), as evidenced by their research outputs and project involvement. Recommendations include universities integrating “Dual-Carbon” into curricula and optimizing training, tutors adopting personalized guidance, and policymakers supporting resource sharing. Limitations involve a single university sample and lack of “Dual-Carbon”-specific indicators; future research should expand samples, add relevant indicators, conduct longitudinal studies, and combine qualitative methods.