Colleges’ performance assessment of university based on grey relational analysis

Abstract

A new three-dimensional college performance assessment index system is established. The grey relational method is used to evaluate college performance in a university and the CRITIC method of variation coefficient is used to weight the assessment indices. The performance of 15 colleges in NH University are assessed by using the index system and the grey method, and the results can supply some important information for management optimization and resource distribution of NH University. It also shows that the index system and grey assessment model proposed in this paper have good potential to solve the similar problem.

Keywords

Performance assessment university Grey relational analysis

1 Introduction

With the economic growth, education, especially higher education developed quickly in China. The influence of Chinese universities in the world has increased significantly. This is not only due to the increased investment in education caused by Chinese economic development, but also to the continuous reform of the university management system.

From the end of last century, Chinese universities began to set up colleges and then Power and responsibility began to shift from the management departments of the universities to the colleges. The colleges make more and more decisions about their own development and affairs. These colleges in universities become core sectors because they are the main units of teaching and scientific research. Nowadays, a university normally has dozens of colleges in China. Only colleges operate with good performance can promote the high-quality development of universities. College performance assessment, is the ground-work for university management, including the most important activities such targeting, resource allocating and control.

2 Literature review

On the performance assessment of education, it can be traced back to the 1970 s. At that time, the theory and method of organizational performance management, which is widely used in enterprises, was introduced into the field of university assessment. The assessment results were even directly used as the basis of resource allocation such as funds in some countries [1]. This kind of government investment policy based on performance assessment has brought a great impact on American higher education institutions and prompts university managers to continuously improve their management [2]. In the late 1980 s and early 1990 s, the concept of performance assessment began to be introduced into the field of higher education in China, for example in talent management [3], etc.

After entering the 21st century, the Chinese government actively advocates that the reform in various fields should give full play to the decisive role of the market in resource allocation and pay more attention to the quality of development and the efficiency of resource allocation, which greatly promotes the performance assessment in the field of higher education, because the universities have to strive for resources through competition and market mechanism. If universities cannot prove that they have good self-assessment and monitoring mechanism, they may incur external doubts and external quality intervention [4]. Therefore, in the face of the dual pressure from external concern and self-development, universities began performance assessment to improve management.

College performance assessment in the university is different from the comprehensive ranking of the University carried out by the third-party institutions, and also different from the assessment of the University organized by the education administrative department [5]. It is a kind of self-restraint and management behavior carried out spontaneously and actively by the university in response to the increasingly fierce competition. The core purpose of college performance assessment includes: problem identification, competition, effective motivation, and improvement of both quality and efficiency. A reasonable and distinctive performance assessment can form a positive competitive atmosphere in the university and greatly strengthen the effectiveness of incentives [6]. So many universities conduct such self-assessment every year in China [7].

However, college performance assessment of universities has always been a problem both in theoretical research and practical work. It is difficult to establish a relatively unified scientific standard and generally accepted assessment procedures. Many researches mainly focus on the design and selection of indices [6 , 8–13]. While, some other scholars rethink on the problems and deficiencies in the practice of college performance assessment. The existing performance assessment at the overall level of the university is difficult to really guide resource allocation [14]. Combined with the practice of Tongji University, Fanxiudi [15] proposed that college performance assessment should reflect the original intention and ensure the positive effect of the assessment results. Wu Guo Jun [16] pointed out that the performance assessment index in Lanzhou University did not consider the diversity of colleges and departments, and the index system failed to cover all the contents of university management. Yang Kangkai, Cai Zongmo and Zhang Haisheng [17] believed that the internal management paradigm of university urgently needed to establish a classified and balanced governance performance assessment index system.

The method of college performance assessment is another hot issue. At present, the methods mainly include comprehensive score method, balanced score method, comprehensive index method, efficiency coefficient method, input-output analysis method, data envelopment analysis method, grey correlation analysis method and AHP method, etc. [18 –22].

In general, college performance assessment is still open. A strict framework and complete index system of college performance assessment should be established. And in practice, a simple, feasible and reliable method is more popular. Therefore, this paper will build a new index system of college performance assessment, and grey relational analysis as the basic assessment method. This paper is organized as follows. Section 2 builds college performance assessment system and the assessment models; the actual data of NH University in 2019 will be used as a case study in Section 3; In section 4, we further analyze and discuss the results of empirical analysis; Section 5 concludes and introduces some possible future work.

3 College performance assessment index system

3.1 Thoughts and framework of college assessment system

College performance assessment is not only of performance measurement but also an orientation for the colleges, which indicates that what are the most important for the development for a university. Referring to the existing research results on the performance assessment of universities, colleges and enterprises, and taking full account of the characteristics of college evaluation, this paper constructs an index system from three dimensions: strategy and objectives, resources and capabilities, achievements and impact.

The first dimension is strategy and objectives. Each university has its own unique vision, strategy and goals, which is the mission of the university. Colleges must be highly consistent with the university by strategy and objectives. Education is a public product. Clear strategies and goals not only reflect the development ideas of the college, but also reflect the public welfare of education.

The second dimension is resources and capabilities. The colleges have more and more autonomy in the university, which means that enough resources and strong capabilities are necessary for a college to operate, realize the goals and compete with the others. The most important resources and capabilities are the human resources, certainly teachers and researchers for a college. In addition, internationalization is the general trend of university development. International cooperation is an ability that can promote the long term development of colleges and universities. So this dimension includes two sub-dimensions, teachers and researchers, and international cooperation.

The third dimension is achievements and impact, which are the current results and contribution of the colleges. This aspect is more concerned by the public. Research and education is primary and fundamental for a college. These are the main achievements of a college and the two sub-dimensions.

The first two dimensions, strategy and objectives, resources and capabilities, focus on the operation and sustainable development of the colleges. And the third one, achievements and impact, focuses on the current achievements of the colleges. And the framework of the three dimensions is shown in Fig. 1.

Fig. 1

Three dimensional framework of college performance assessment.

3.2 Assessment index system

According to the general principles of index system construction and the above mentioned framework in Fig. 1, the five dimension or sub-dimensions are used as the first-level indices to establish a college performance assessment index system.

After two rounds of surveys, the assessment index system is established. At the first round, 72 experts were investigated and listed the indicators by themselves; And these indicators are cleared, standardized and then 43 indices are obtained as candidates; at the second round, the 43 indices are sent to the experts again, and they crossed the most important 30 indicators; if the indicator has won the selections of two thirds, it will be included in the final index system; and 18 indices are selected to form the index system for college performance assessment, as shown in Table 1.

Table 1
Assessment indicators system

First -level indicators Secondary indicators

Strategies and objectives Z₁ Clear development strategy (u₁)

Achievable and Valuable goals (u₂)

Teachers’ recognition of strategy (u₃)

Consistency with university goals (u₄)

Education Z₂ Quality of undergraduate cultivation (u₅)

Quality of graduate cultivation (u₆)

Management of teaching (u₇)

Teachers and Researchers Z₃ Number of the Teachers and Researchers (u₈)

Outstanding Teachers and Researchers (u₉)

Staff development (u₁₀)

Research Z₄ Research funds (u₁₁)

Important Research Achievements (u₁₂)

International cooperation Z₅ Connections with foreign universities (u₁₃)

International mutual visiting (u₁₄)

International Staffs(u₁₅)

International Research Cooperation (u₁₆)

International academic reputation (u₁₇)

International students (u₁₈)

First -level indicators	Secondary indicators
Strategies and objectives Z₁	Clear development strategy (u₁)
	Achievable and Valuable goals (u₂)
	Teachers’ recognition of strategy (u₃)
	Consistency with university goals (u₄)
Education Z₂	Quality of undergraduate cultivation (u₅)
	Quality of graduate cultivation (u₆)
	Management of teaching (u₇)
Teachers and Researchers Z₃	Number of the Teachers and Researchers (u₈)
	Outstanding Teachers and Researchers (u₉)
	Staff development (u₁₀)
Research Z₄	Research funds (u₁₁)
	Important Research Achievements (u₁₂)
International cooperation Z₅	Connections with foreign universities (u₁₃)
	International mutual visiting (u₁₄)
	International Staffs(u₁₅)
	International Research Cooperation (u₁₆)
	International academic reputation (u₁₇)
	International students (u₁₈)

4 College performance assessment model based on grey correlation method

4.1 The construction of grey relational assessment model

Grey relational analysis is an important branch of grey system theory, which is active in research and widely used. Its basic idea is to judge whether the connection between different sequences is close according to the similarity degree of sequence geometry. The closer the broken line geometry of a sequence is, the greater the correlation between the corresponding sequences is, and vice versa [23]. The main purpose of grey relational analysis is to measure the incidence between the sequence of each assessment object and the ideal sequence, and then to compare and sort the assessment objects. At the same time, the grey relational model is a mature assessment model which is conducive to the combination of qualitative analysis and quantitative analysis. It does not require that the data of the assessment objects must obey a typical probability distribution. It has the significant advantages of being able to better solve the problem that the assessment index is difficult to accurately quantify statistics and overcome the influence of human factors, and has strong reliability. Grey relational analysis is widely used in performance assessment, for example applied to supply chain performance [24], airport performance [25], R&D performance at Chinese universities [26], Financial performance assessment [27], mergers and acquisitions performance [28], hospital performance [29], Performance in Civil Aircraft [30], Green Supply Chain Management [31], Key Performance Indicators of an Emerging Biotechnology and Medicine Enterprise, etc. [32 –35]. In view of the advantages of grey relational analysis, it is also used in this paper.

Suppose there are m colleges as the objects of performance assessment, and there are n indices in the performance assessment index system, let x_i (j) indicate the value of the jth index corresponding to the ith College, and X_i indicate the assessment index sequence of the ith College. Thus, the matrix X_m×n can be established as following, wherein 1 ⩽ i ⩽ m, 1 ⩽ j ⩽ n. $X_{m \times n} = [\begin{matrix} x_{1} (1) & x_{1} (2) & x_{1} (3) & \dots & x_{1} (n) \\ x_{2} (1) & x_{2} (2) & x_{2} (3) & \dots & x_{2} (n) \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ x_{m} (1) & x_{m} (2) & x_{m} (3) & \dots & x_{m} (n) \end{matrix}]$ (1)

Matrix X_m×n represents the values of each index of the colleges, that is, the data for college performance assessment.

According to Fig. 2, a grey assessment model is constructed based on the data in Equation (1). And it has two parts. The left part shows the calculation of grey relational analysis and the right is the weights of the indices. At the bottom, the results, the weighted grey relational analysis will be obtained. And the processes of grey relational analysis and weights are illustrated.

Fig. 2

Calculation flow chart of grey relational assessment method.

4.2 Grey relational analysis

Grey relational analysis includes 4 steps, as follows [36].

Step1: Nondimensionalization of assessment data. The indices of college performance assessment are benefit indexes, that is, the larger its value is, and the better its performance is. And the biggest one the column is set to 1, the others are set to their proportion to that. So the nondimensionalization matrix B_m×n of X_m×n can be obtained. $B_{m \times n} = [\begin{matrix} b_{1} (1) & b_{1} (2) & b_{1} (3) & \dots & b_{1} (n) \\ b_{2} (1) & b_{2} (2) & b_{2} (3) & \dots & b_{2} (n) \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ b_{m} (1) & b_{m} (2) & b_{m} (3) & \dots & b_{m} (n) \end{matrix}]$ (2) wherein $b_{i} (j) = \frac{x_{i} (j)}{{maxx}_{i} (j)}$

Obviously, 0≤b_i(j)≤1.

Step2: Determination the reference sequence. Select the maximum value of each index, that is, the largest one of each column of B_m×n, to form the ideal vector B₀ as the reference sequence, wherein $\begin{matrix} B_{0} = & [max b_{m} (1), max b_{m} (2), \\ max b_{m} (3), \dots, max b_{m} (n)] \end{matrix}$

Step3: Calculation of grey correlation coefficient. Calculate the grey relational coefficient between each index value b_i(j) of college i and the corresponding index of the reference sequence B₀ by the following equation.

$\begin{matrix} γ (b_{0} (j), b_{i} (j)) \\ = \frac{min_{i} min_{j} | b_{0} (j) - b_{i} (j) | + ξ max_{i} max_{j} | b_{0} (j) - b_{i} (j) |}{| b_{0} (j) - b_{i} (j) | + ζ max_{i} max_{j} | b_{0} (j) - b_{i} (j) |} \end{matrix}$ (3)

Where in, ξ is the distinguishing coefficient, ξ ∈ (0, 1), usually ξ = 0.5.

Step4: Calculation of weighted grey relational degree. If the weight of each index of college performance assessment is ω = (ω₁, ω₂, ω₃, ⋯ , ω_n), then the grey relational degree γ (X₀, X_i) between the evaluated college X_i and the idea sequence X₀ is calculated by the following formula. $γ (X_{0}, X_{i}) = \sum_{j = 1}^{n} ω_{j} γ (b_{0} (j), b_{i} (j))$ (4)

4.3 The determination of the weight of college performance assessment index

In this study, CRITIC(Criteria Importance Though Intercrieria Correlation) method is used to determine the weight of each index of college performance assessment. CRITIC method is a kind of objective weighting method based on data, which mainly determines the index weight by mining the information contained in the assessment indices. This method takes into account both the variability and the conflict of the indices, which helps to overcome the uncertainty of the traditional grey relational analysis method, and makes the calculation result more objective and reasonable. In order to eliminate the influence of dimension, the modified CRITIC method replaces the standard deviation with the coefficient of variation when calculating the weight. For the assessment matrix X_m×n, the detailed steps to determine the weights of assessment indicators are as follows [37]:

Step1: Calculate the average value, ${\bar{x}}_{i} (j)$ ,of index j. ${\bar{x}}_{i} (j) = \frac{1}{n} \sum_{i = 1}^{m} x_{i} (j)$ (5)

Step2: Calculate standard deviation of correlation coefficient S_j of index j. $S_{j} = \sqrt{\frac{1}{n} (x_{i} (j) - {\bar{x}}_{i} (j))} 2$ (6)

Step3: Calculate variation coefficient, E_j, of index j. $E_{j} = \frac{S_{j}}{{\bar{x}}_{i} (j)}$ (7)

Step4: Calculate weight W_j of index j. $W_{j} = \frac{E_{j}}{\sum_{j = 1}^{m} E_{j}}$ (8)

5 Case study

NH University established in 1950 s, and it was an institute of science and technology in China at the beginning. Now, it develops for about 70 years and become a university with 15 colleges who has utterly different subjects and disciplines. Nowadays, the colleges are the engines of the development of the University. In order to promote the colleges to develop, NH University need to assess the performance of the colleges. Based on the data collected of the 15 colleges in NH University in 2019 (Table 2), this study empirically assesses their performance by using the method of section 3. Some statistical data are supplied the administrative sections, and some are obtained by questionnaire filled by the relevant administrative sections and colleges organized by the University. The data is shown in Table 2.

Table 2
Sample data

Strategies and objectives Education Teachers and Researchers Research International cooperation

u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ u₁₆ u₁₇ u₁₈

X₁ 19.00 28.01 27.72 19.58 21.00 21.00 8.50 74.21 75.37 92.88 40.00 21.00 28.00 62.62 66.00 6.00 16.00 19.00

X₂ 18.80 27.75 28.25 20.03 19.00 19.00 7.00 68.54 76.03 90.37 24.00 14.24 24.00 79.80 43.70 10.00 14.00 12.00

X₃ 19.60 28.10 27.79 19.33 25.00 25.00 9.50 75.97 70.40 94.70 36.00 18.30 28.00 53.92 28.20 6.00 20.00 16.00

X₄ 18.20 28.29 27.33 17.81 17.00 17.00 8.00 66.34 62.81 92.84 40.00 30.00 25.00 60.26 40.40 10.00 16.00 17.00

X₅ 19.20 28.31 28.32 20.89 25.00 25.00 9.50 79.24 74.89 93.40 32.00 15.28 24.00 56.56 24.80 10.00 16.00 18.00

X₆ 18.80 27.66 27.22 18.22 10.00 15.00 7.50 67.04 74.50 91.92 40.00 26.29 27.00 60.14 25.50 6.00 18.00 9.00

X₇ 18.60 27.26 26.39 17.66 14.00 13.00 10.00 61.08 75.96 92.98 16.00 11.91 28.00 52.20 20.40 10.00 16.00 14.00

X₈ 18.60 28.26 27.30 19.21 10.00 7.00 5.50 55.29 64.92 87.48 40.00 15.35 23.00 43.00 2.20 2.00 16.00 10.00

X₉ 19.60 28.40 28.32 21.59 20.00 23.00 9.50 74.81 57.72 94.38 36.00 23.46 28.00 58.25 12.00 6.00 12.00 20.00

X₁₀ 18.40 28.10 26.91 18.17 5.00 5.00 5.50 49.79 44.01 94.10 16.00 10.37 24.00 60.89 7.00 2.00 4.00 5.00

X₁₁ 18.80 27.74 27.28 17.50 7.00 9.00 6.50 48.02 52.18 89.16 16.00 10.08 24.00 43.50 5.00 6.00 8.00 7.00

X₁₂ 18.00 26.81 26.21 17.04 7.00 9.00 5.50 61.53 50.36 93.11 24.00 9.17 24.00 53.14 0.00 6.00 12.00 7.00

X₁₃ 18.60 27.73 27.09 15.08 7.00 15.00 7.00 55.21 59.01 89.71 20.00 14.19 27.00 49.72 8.00 2.00 8.00 7.00

X₁₄ 19.20 28.01 27.75 20.41 18.00 19.00 7.00 55.26 61.65 90.99 36.00 17.34 28.00 59.92 4.70 6.00 10.00 18.00

X₁₅ 18.60 27.81 27.92 19.06 0.00 2.00 5.50 60.20 51.79 89.62 32.00 18.60 24.00 63.04 2.00 2.00 2.00 0.00

	Strategies and objectives	Education	Teachers and Researchers	Research	International cooperation
X₁	19.00	28.01	27.72	19.58	21.00	21.00	8.50	74.21	75.37	92.88	40.00	21.00	28.00	62.62	66.00	6.00	16.00	19.00
X₂	18.80	27.75	28.25	20.03	19.00	19.00	7.00	68.54	76.03	90.37	24.00	14.24	24.00	79.80	43.70	10.00	14.00	12.00
X₃	19.60	28.10	27.79	19.33	25.00	25.00	9.50	75.97	70.40	94.70	36.00	18.30	28.00	53.92	28.20	6.00	20.00	16.00
X₄	18.20	28.29	27.33	17.81	17.00	17.00	8.00	66.34	62.81	92.84	40.00	30.00	25.00	60.26	40.40	10.00	16.00	17.00
X₅	19.20	28.31	28.32	20.89	25.00	25.00	9.50	79.24	74.89	93.40	32.00	15.28	24.00	56.56	24.80	10.00	16.00	18.00
X₆	18.80	27.66	27.22	18.22	10.00	15.00	7.50	67.04	74.50	91.92	40.00	26.29	27.00	60.14	25.50	6.00	18.00	9.00
X₇	18.60	27.26	26.39	17.66	14.00	13.00	10.00	61.08	75.96	92.98	16.00	11.91	28.00	52.20	20.40	10.00	16.00	14.00
X₈	18.60	28.26	27.30	19.21	10.00	7.00	5.50	55.29	64.92	87.48	40.00	15.35	23.00	43.00	2.20	2.00	16.00	10.00
X₉	19.60	28.40	28.32	21.59	20.00	23.00	9.50	74.81	57.72	94.38	36.00	23.46	28.00	58.25	12.00	6.00	12.00	20.00
X₁₀	18.40	28.10	26.91	18.17	5.00	5.00	5.50	49.79	44.01	94.10	16.00	10.37	24.00	60.89	7.00	2.00	4.00	5.00
X₁₁	18.80	27.74	27.28	17.50	7.00	9.00	6.50	48.02	52.18	89.16	16.00	10.08	24.00	43.50	5.00	6.00	8.00	7.00
X₁₂	18.00	26.81	26.21	17.04	7.00	9.00	5.50	61.53	50.36	93.11	24.00	9.17	24.00	53.14	0.00	6.00	12.00	7.00
X₁₃	18.60	27.73	27.09	15.08	7.00	15.00	7.00	55.21	59.01	89.71	20.00	14.19	27.00	49.72	8.00	2.00	8.00	7.00
X₁₄	19.20	28.01	27.75	20.41	18.00	19.00	7.00	55.26	61.65	90.99	36.00	17.34	28.00	59.92	4.70	6.00	10.00	18.00
X₁₅	18.60	27.81	27.92	19.06	0.00	2.00	5.50	60.20	51.79	89.62	32.00	18.60	24.00	63.04	2.00	2.00	2.00	0.00

5.1 Calculation of grey relational coefficients

First, the data is nondimensionalized and normalized, and the ideal sequence is obtained. $\begin{matrix} B_{0} = & [max b_{15} (1), max b_{15} (2), max b_{15} (3), \\ \dots, max b_{15} (18)] = [1, 1, 1 \dots, 1] \end{matrix}$

Secondly, according to Equation (2), calculate the grey relational coefficients between each index of colleges B_i and the ideal sequence B₀. It is shown in Table 3.

Table 3
Grey relational coefficients between each index of the colleges and idea sequence

Strategies and objectives Education Teachers and Researchers Research International cooperation

u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ u₁₆ u₁₇ u₁₈

B₁ 0.942 0.973 0.959 0.843 0.758 0.758 0.769 0.887 0.983 0.963 1.000 0.625 1.000 0.699 1.000 0.556 0.714 0.909

B₂ 0.925 0.956 0.996 0.874 0.676 0.676 0.625 0.787 1.000 0.916 0.556 0.488 0.778 1.000 0.597 1.000 0.625 0.556

B₃ 1.000 0.979 0.964 0.827 1.000 1.000 0.909 0.924 0.871 1.000 0.833 0.562 1.000 0.607 0.466 0.556 1.000 0.714

B₄ 0.875 0.992 0.935 0.741 0.610 0.610 0.714 0.754 0.742 0.962 1.000 1.000 0.824 0.671 0.563 1.000 0.714 0.769

B₅ 0.961 0.993 1.000 0.939 1.000 1.000 0.909 1.000 0.971 0.973 0.714 0.505 0.778 0.632 0.445 1.000 0.714 0.833

B₆ 0.925 0.950 0.928 0.762 0.455 0.556 0.667 0.765 0.961 0.945 1.000 0.802 0.933 0.670 0.449 0.556 0.833 0.476

B₇ 0.907 0.926 0.880 0.733 0.532 0.510 1.000 0.686 0.998 0.965 0.455 0.453 1.000 0.591 0.420 1.000 0.714 0.625

B₈ 0.907 0.990 0.933 0.819 0.455 0.410 0.526 0.623 0.774 0.868 1.000 0.506 0.737 0.520 0.341 0.385 0.714 0.500

B₉ 1.000 1.000 1.000 1.000 0.714 0.862 0.909 0.899 0.675 0.993 0.833 0.696 1.000 0.649 0.379 0.556 0.556 1.000

B₁₀ 0.891 0.980 0.910 0.760 0.385 0.385 0.526 0.574 0.543 0.987 0.455 0.433 0.778 0.678 0.359 0.385 0.385 0.400

B₁₁ 0.925 0.955 0.932 0.725 0.410 0.439 0.588 0.559 0.614 0.895 0.455 0.430 0.778 0.524 0.351 0.556 0.455 0.435

B₁₂ 0.860 0.899 0.871 0.704 0.410 0.439 0.526 0.691 0.597 0.968 0.556 0.419 0.778 0.599 0.333 0.556 0.556 0.435

B₁₃ 0.907 0.955 0.920 0.624 0.410 0.556 0.625 0.622 0.691 0.905 0.500 0.487 0.933 0.570 0.363 0.385 0.455 0.435

B₁₄ 0.961 0.973 0.962 0.902 0.641 0.676 0.625 0.623 0.725 0.927 0.833 0.542 1.000 0.667 0.350 0.556 0.500 0.833

B₁₅ 0.907 0.960 0.973 0.810 0.333 0.352 0.526 0.675 0.611 0.903 0.714 0.568 0.778 0.704 0.340 0.385 0.357 0.333

	Strategies and objectives	Education	Teachers and Researchers	Research	International cooperation
B₁	0.942	0.973	0.959	0.843	0.758	0.758	0.769	0.887	0.983	0.963	1.000	0.625	1.000	0.699	1.000	0.556	0.714	0.909
B₂	0.925	0.956	0.996	0.874	0.676	0.676	0.625	0.787	1.000	0.916	0.556	0.488	0.778	1.000	0.597	1.000	0.625	0.556
B₃	1.000	0.979	0.964	0.827	1.000	1.000	0.909	0.924	0.871	1.000	0.833	0.562	1.000	0.607	0.466	0.556	1.000	0.714
B₄	0.875	0.992	0.935	0.741	0.610	0.610	0.714	0.754	0.742	0.962	1.000	1.000	0.824	0.671	0.563	1.000	0.714	0.769
B₅	0.961	0.993	1.000	0.939	1.000	1.000	0.909	1.000	0.971	0.973	0.714	0.505	0.778	0.632	0.445	1.000	0.714	0.833
B₆	0.925	0.950	0.928	0.762	0.455	0.556	0.667	0.765	0.961	0.945	1.000	0.802	0.933	0.670	0.449	0.556	0.833	0.476
B₇	0.907	0.926	0.880	0.733	0.532	0.510	1.000	0.686	0.998	0.965	0.455	0.453	1.000	0.591	0.420	1.000	0.714	0.625
B₈	0.907	0.990	0.933	0.819	0.455	0.410	0.526	0.623	0.774	0.868	1.000	0.506	0.737	0.520	0.341	0.385	0.714	0.500
B₉	1.000	1.000	1.000	1.000	0.714	0.862	0.909	0.899	0.675	0.993	0.833	0.696	1.000	0.649	0.379	0.556	0.556	1.000
B₁₀	0.891	0.980	0.910	0.760	0.385	0.385	0.526	0.574	0.543	0.987	0.455	0.433	0.778	0.678	0.359	0.385	0.385	0.400
B₁₁	0.925	0.955	0.932	0.725	0.410	0.439	0.588	0.559	0.614	0.895	0.455	0.430	0.778	0.524	0.351	0.556	0.455	0.435
B₁₂	0.860	0.899	0.871	0.704	0.410	0.439	0.526	0.691	0.597	0.968	0.556	0.419	0.778	0.599	0.333	0.556	0.556	0.435
B₁₃	0.907	0.955	0.920	0.624	0.410	0.556	0.625	0.622	0.691	0.905	0.500	0.487	0.933	0.570	0.363	0.385	0.455	0.435
B₁₄	0.961	0.973	0.962	0.902	0.641	0.676	0.625	0.623	0.725	0.927	0.833	0.542	1.000	0.667	0.350	0.556	0.500	0.833
B₁₅	0.907	0.960	0.973	0.810	0.333	0.352	0.526	0.675	0.611	0.903	0.714	0.568	0.778	0.704	0.340	0.385	0.357	0.333

5.2 Calculate the weights of the indices

According to the determination steps of index weights in section 3.2, the weight of each index is shown as follows

$\begin{matrix} W_{j} = (\begin{matrix} 0.003 0.005 0.005 0.017 0.063 0.070 0.015 0.031 0.194 \\ 0.099 0.082 0.099 0.111 0.096 0.043 0.030 0.033 0.005 \end{matrix}) \end{matrix}$

5.3 Calculate grey relational degree and sort

Apply the equation (5) to calculate the grey relational degree and rank the colleges. The higher the grey relational degree is, the closer the college performance is to the ideal sequence, and vice versa. The grey relational degree and sorting are shown in Table 4.

Table 4
Grey relational degree and total sorting

Strategies and objectives Education Teachers and Researchers Research International cooperation The grey relational degree Total Sorting

X₃ 0.027 0.147 0.296 0.235 0.242 0.946 1

X₅ 0.029 0.147 0.315 0.195 0.224 0.909 2

X₆ 0.025 0.078 0.303 0.265 0.234 0.904 3

X₄ 0.025 0.092 0.262 0.272 0.237 0.888 4

X₉ 0.030 0.119 0.257 0.248 0.229 0.883 5

X₂ 0.027 0.099 0.308 0.180 0.261 0.876 6

X₁ 0.027 0.112 0.313 0.144 0.266 0.861 7

X₇ 0.024 0.084 0.310 0.193 0.242 0.853 8

X₁₄ 0.028 0.097 0.251 0.233 0.227 0.836 9

X₈ 0.026 0.065 0.255 0.213 0.184 0.743 10

X₁₃ 0.022 0.074 0.242 0.193 0.202 0.734 11

X₁₅ 0.026 0.054 0.228 0.201 0.193 0.702 12

X₁₂ 0.023 0.064 0.233 0.173 0.195 0.688 13

X₁₁ 0.024 0.065 0.225 0.166 0.185 0.666 14

_X10 0.025 0.059 0.220 0.166 0.193 0.663 15

Max 0.030 0.147 0.315 0.272 0.266 0.946

Average 0.026 0.090 0.268 0.205 0.221 0.810

	Strategies and objectives	Education	Teachers and Researchers	Research	International cooperation	The grey relational degree	Total Sorting
X₃	0.027	0.147	0.296	0.235	0.242	0.946	1
X₅	0.029	0.147	0.315	0.195	0.224	0.909	2
X₆	0.025	0.078	0.303	0.265	0.234	0.904	3
X₄	0.025	0.092	0.262	0.272	0.237	0.888	4
X₉	0.030	0.119	0.257	0.248	0.229	0.883	5
X₂	0.027	0.099	0.308	0.180	0.261	0.876	6
X₁	0.027	0.112	0.313	0.144	0.266	0.861	7
X₇	0.024	0.084	0.310	0.193	0.242	0.853	8
X₁₄	0.028	0.097	0.251	0.233	0.227	0.836	9
X₈	0.026	0.065	0.255	0.213	0.184	0.743	10
X₁₃	0.022	0.074	0.242	0.193	0.202	0.734	11
X₁₅	0.026	0.054	0.228	0.201	0.193	0.702	12
X₁₂	0.023	0.064	0.233	0.173	0.195	0.688	13
X₁₁	0.024	0.065	0.225	0.166	0.185	0.666	14
_X10	0.025	0.059	0.220	0.166	0.193	0.663	15
Max	0.030	0.147	0.315	0.272	0.266	0.946
Average	0.026	0.090	0.268	0.205	0.221	0.810

6 Case results and discussion

6.1 General analysis

From Table 4, we can see that the average relational degree of the college performance in NH University is 0.810, and the performance of nine colleges is above the average level, which accounts for about 60 percent of the colleges. The colleges X₃,X₅,X_6,,X₄ and X₉ rank the top five, and the first college is higher than the last one by 42 percent.

At the same time, there are also significant differences between different disciplines. Colleges of technology are higher than those of Humanities and Social Sciences, traditional disciplines are higher than emerging disciplines, and research-oriented colleges are higher than teaching-oriented colleges.

From each dimension rthere are also differences between colleges. In the dimension of strategy and objectives rX₉ ranks the first rbut there is little difference in relational degree among the colleges. This shows that the overall level of this dimension in colleges of NH University is relatively good. In other aspects or dimensions—the levels of colleges are still very uneven. In particular rgrey relational coefficients of some colleges with the idea sequence are small. This shows that these colleges still have potential to make efforts to improve in the area. In the sub-dimension of education rcolleges’ grey relational degree of X₁ rX₇ rX₈ rX₁₀ rX₁₁ rX₁₂ rX₁₃ rX₁₄ and X₁₅ are much worse than the average rand they still need to work hard on that. In the sub-dimension of teachers and researchers—there are seven colleges below the average which are X₈ rX₁₀ rX₁₁ rX₁₂ rX₁₃ rX₁₄ and X_15 . This shows that there are still many problems in the construction of teachers and researchers in these colleges and teachers and researchers is the main factor restricting their performance. In the sub-dimension of research rsix colleges are below average which is the same as in International cooperation. These colleges should improve the performance level of these two aspects as soon as possible.

6.2 Category analysis

In order to observe the difference between colleges more intuitively rwe differentiate the colleges according to the grey relational degree. Colleges are classified into five grades as shown in Table 5.

Table 5
Classification results of performance grade

Performance grade Grey relational degree College number

Excellent Above 0.9 X_3,X_5,X₆ 3

Good [r0.85 r0.9 r) X₄ rX_{9 r}X₂ rX_{1 r}X₇ 5

Medium 0.75 r0.85) X₁₄ 1

Qualified 0.7 r0.75) X₈ rX₁₃ rX₁₅ 3

Unqualified 0.7 or less X_{12 r}X₁₁ rX₁₀ 3

Performance grade	Grey relational degree	College	number
Excellent	Above 0.9	X_3,X_5,X₆	3
Good	[r0.85 r0.9 r)	X₄ rX_{9 r}X₂ rX_{1 r}X₇	5
Medium	0.75 r0.85)	X₁₄	1
Qualified	0.7 r0.75)	X₈ rX₁₃ rX₁₅	3
Unqualified	0.7 or less	X_{12 r}X₁₁ rX₁₀	3

Through the classification rwe can more clearly see which colleges have similar levels of performance rand then analyze the similarities and differences in colleges under the same category.

The Excellent category: X₃ is the college with the highest grey relational degree. But its degrees in five aspects are not the highest. X₃ and X₅ have the same grey relational degree in education. Especially rits degree in Strategies and objectives rTeachers and Researchers lower than X₅ who takes the lead. The reason X₃ ranks first is that X₃ is a traditional engineering college and it has accumulated significant advantages rand develops fast in Research and International cooperation.

The Good category: There are five colleges in this category which has the highest proportion of assessment objects. In this category the colleges have good performance in some dimensions and sub-dimensions: X₉ in Strategies and objectives rEducation); X₁ in Teachers and Researchers rinternational cooperation; X₄ in Research. This category mainly incudes the colleges of technology and engineering rwith earlier establishment and large scale.

The Medium category: This category includes X₁₄ which is a college with unique discipline. Compared with the average rit is above the average in four aspects and close to the average in the other one. Overall rthe college performance in this category has great potential.

The Qualified category: In general rthe level of performance of this category is relatively low. This category only approaches or reaches the average level in very few aspects. Colleges in this category can be roughly divided into two categories. One is the newly established college rthe other is teaching oriented college.

The Unqualified category: This category includes X₁₀ rX₁₁ and X_{12 r} which are liberal arts colleges rand the degree of performance significantly below average in all five aspects. The colleges in this category should seek new development opportunities and fully integrate into the mainstream trend of college development.

6.3 Management enlightenment

College performance assessment index system is constructed by combining qualitative and quantitative analysis. The empirical assessment of NH University in 2019 further verify its effectiveness. This study can be used for reference in the research of performance assessment of internal governance. Based on the assessment results rNH University and its colleges can fully realize its own gap and deficiency. It can point out the development direction for the colleges. In order to improve the strength and competitiveness rNH University can also carry out classified management of colleges and implement differentiated development strategies according to the assessment results.

7 Conclusion and discussion

The colleges are the main body of a university rand its quality and performance play an important role in the realization of the goals of the University. To cope with fierce competition rit has become a common practice for universities to assess and improve college performance. Therefore rresearch on college performance assessment in university is very valuable and useful. The main conclusions are as follows.

(1) A three-dimensional assessment system is established to carry out multi-dimensional and all-round assessment of college performance. On the design of index system rit pays attention to the coordination of the college main goals rfunctions rtasks and achievements rincluding Strategies and objectives rEducation rTeachers and Researchers rResearch and International cooperation. The index system can reflect and compare the current situation and main achievements of colleges comprehensively robjectively and accurately.

(2) The grey relational analysis is used to evaluate college performance. The grey relational assessment combines the qualitative assessment and quantitative assessment organically. At the same time rwe use the CRITIC method of variation coefficient to objectively weight the assessment indices rwhich can fully mine and utilize the information of the assessment data itself rand make the weight calculation results and assessment results more objective and accurate.

(3) Through the performance assessment of 15 colleges in NH University rwe verify the validity of the model. The grey relational assessment model is also helpful for the ranking and classification of the assessment objects. The assessment results are reasonable and with good applicability. It has certain theoretical and practical significance for the college performance assessment of Universities rand it has potential to popularize and widely apply.

To sum up rcollege performance assessment in Universities is carried out by the three-dimensional performance assessment system and the grey relational analysis method. It can ensure the realization of the overall goals reducation quality rand promote the orderly refficient and up to standard operation of the colleges. In addition rthe college performance assessment in the university is a systematic project which needs continuous innovation in theoretical methods and practical paths. The specific assessment index system also needs continuous exploration radjustment rand improvement with the actual situation.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Funding statement

This work was supported by Ministry of Education rHumanities and Social Sciences Fund (Grant No.18YJC710039).

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