Study on the quality of private university education based on analytic hierarchy process and fuzzy comprehensive evaluation method 1

Abstract

The development of private colleges and universities affects structural reform and changes the trend of higher education. To study the running level of private colleges and universities, an empirical study must be conducted. First, statistical information from 23 Shandong Province private colleges and universities was collected, and an index system of education level with six primary indicators and 13 secondary indicators was constructed. The index data were standardized through a statistical analysis software. Analytical hierarchy process was adopted to determine the weight of the evaluation index and test the consistency of the judgment matrix. A fuzzy comprehensive evaluation model was established, and the building evaluation set was improved. After confirming the membership matrix of the fuzzy relation, multi-index comprehensive evaluation and comprehensive ranking of private higher education level in Shandong Province were carried out. The improved traditional fuzzy comprehensive evaluation method can be used in evaluating the performance of private colleges and analyze scientific rankings. Results of this work have high theoretical significance and application value.

Keywords

Analytical hierarchy process fuzzy comprehensive evaluation model weight

1 Introduction

Private colleges have gradually developed and increased in number in the twenty-first century. These institutions play an important role in the structure of higher education because they can promote the development of higher education. Private colleges and universities have a flexible mechanism. Private universities function through private funding because of its advantages, and they produce many skilled individuals who contribute to society. Moreover, private universities increase the popularity of higher education. In response to the call to establish a high level of private schools by “Outline of the national medium and long term educational reform and development plan,” many Chinese and foreign researchers examined the factors that influence private colleges and evaluate the system of private higher institutions. Few studies focus on the comprehensive running level of private colleges and universities. To study the comprehensive strength of private universities in Shandong Province, this paper established a system to evaluate private colleges and universities in the context of Shandong Province by using fuzzy comprehensive evaluation. Generally, in the process of establishing the model, the evaluation set was improved from the 3–5 evaluation standard approach. But in this paper, a total of 23 evaluation standards were established according to the data obtained from 23 colleges and universities, and a comprehensive ranking of 23 private universities was produced. Results provide a scientific basis to allow investors and the public to objectively know the development status of private universities in Shandong Province. The results indicated that the development direction of every college and university differed from each other. Thus, the competitiveness of their approaches and the characteristics and quality of higher education should be improved.

2 Literature review

Chinese and foreign researchers conducted studies to evaluate private colleges and universities. Han [4] completed the application research on the efficiency assessment of universities by combining analytical hierarchy process (AHP) and data envelopment analysis (DEA) [4]. Wang (2011) carried out a performance evaluation of university teachers on the basis of fuzzy comprehensive evaluation [5]. Liu [7] evaluated the performance of universities on the basis of the slacks-based measure model [7]. Shi [2] analyzed the cost effectiveness of the evaluation method for institutions of higher education on the basis of the compound DEA model [2]. Zhang [14] established an evaluation model of teaching quality of university teachers on the basis of backpropagation neural network [14]. Yang [9] evaluated the collaborative innovation ability of school-enterprise cooperation [9]. Carlos León [3] assessed systemic importance with a fuzzy logic inference system [3].

Fuzzy comprehensive evaluation method is a comprehensive evaluation method based on the theory of fuzzy mathematics. The advantage of this method is that qualitative evaluation can be transformed into quantitative evaluation. It can solve fuzzy problems, which are difficult to quantify. This approach is widely used in risk assessment, safety assessment, and performance evaluation. Qi [15] established a fuzzy comprehensive evaluation and entropy weight decision making-based method to assess power network structure [15]. Gong [10] studied fuzzy comprehensive evaluation in control risk assessment based on AHP [10]. Afful-Dadzie [1] tracked the progress of African peer review mechanism using fuzzy comprehensive evaluation method [1]. Yang [6] adopted a qualitative comprehensive assessment method of system safety based on fuzzy AHP and fuzzy transform [6]. Zou [11] analyzed comprehensive flood risk assessment based on set pair analysis–variable fuzzy sets model and fuzzy AHP [11]. Fang [13] adopted AHP–fuzzy to establish a comprehensive evaluation model of venture investment and financing system [13]. Yang [8] studied the application of appraisal of special operation staff in coal enterprises [8]. Du [12] established the performance evaluation model of troop logistics construction on the basis of the fuzzy comprehensive evaluation method [12]. The literature review shows that a few studies employ fuzzy comprehensive evaluation method to study the level of college education. Limited works are based on the fuzzy comprehensive evaluation of college rankings. Thus, this paper adopted fuzzy comprehensive evaluation method based on fuzzy theory to construct the comprehensive Fuzzy evaluation model of the quality of private colleges and universities.

3 Establishing an index system

3.1 Composition of index system

In this paper, six indexes, namely, basic construction, library equipment, training quantity, culture quality, teachers, and construction of disciplines, are the primary evaluation indexes. The 13 indexes, namely, fixed assets investment, school area, library collection, value of teaching instruments and equipment, number of undergraduates, number of students, postgraduate rate, average employment rate of graduates in the past three years, award of subject competition, the total number of full-time teachers, senior professional title, the number of undergraduate majors, and the number of professional college entrance examinations, are secondary indexes, which are used to construct the evaluation system of private colleges and universities in Shandong Province. Hierarchical structure model is shown in Fig. 1.

3.2 Sources and processing of data

3.2.1 Sources of data

The data involved in this research were mainly obtained through the websites of the national education, science, and technology departments and other related departments, university websites, and other channels. Some errors occurred in the results because of restrictions in some conditions during the investigation.

3.2.2 Special data processing

This paper used the mean substitution method to deal with missing data. Mean substitution is the method of obtaining the average of the remaining data to replace abnormal or missing data.

The awards in subject competition and the different levels of awards given with various scores are presented in Table 1.

4 Calculation of each index weight by using AHP method

4.1 Data preprocessing

4.1.1 Consistency of evaluation index types

In the general index system, the index set may have an excessively large index and a very small index, which are expected to be as large and small as possible, respectively. These aspects are known as quality factor and low quality factor. Sometimes, these factors are centered and interval indicators. Thus, these factors must be consistent with the type of evaluation index before being utilized in the evaluation. These factors can be unified as a large indicator. The consistent processing method is described as follows:

For the excessively small index, take the translation: $X_{i}^{'} = M_{i} - X_{i} (X_{i} > 0, i = 1, 2, \dots, 13)$ (1)

For the centered index, take the transformation: $X_{i}^{'} = {\begin{matrix} \frac{2 (X_{i} - m_{i})}{M_{i} - m_{i}}, m_{i} \leq X_{i} \leq \frac{1}{2} (M_{i} + m_{i}) \\ \frac{2 (M_{i} - X_{i})}{M_{i} - m_{i}}, \frac{1}{2} (M_{i} + m_{i}) \leq X_{i} \leq M_{i} \end{matrix}$

For the interval index, take the transformation: $X_{i}^{'} = {\begin{matrix} 1 - \frac{q_{1} - X_{i}}{max (q_{1} - m, M - q_{2})}, X_{i} < q_{1} \\ 1, X_{i} \in [q_{1}, q_{2}] \\ 1 - \frac{X_{i} - q_{2}}{max (q_{1} - m, M - q_{2})}, X_{i} > q_{2} \end{matrix}$

M_i and m_i are the maximum and minimum values of X_i, [q₁, q₂], respectively, which are the optimal stable interval of X_i.

The indicators involved in this article described the school running units. Thus, all the units that belong to the maximum index achieved the consistency of evaluation indicators.

4.1.2 Standardized treatment of evaluation index

The difference between the measurement units and the orders of magnitude of the evaluation indicators was impartial, which caused difficulties and problems in determining the comprehensive evaluation index. At this point, we adopted a common mathematical transformation, that is, the non-dimensional data, to eliminate the influence of the original standard data.

In this paper, the value of the 13 secondary indicators of the 23 samples was handled by range. The value of the 13 secondary indicators is $X_{ij} (j = 1, 2, \dots, 23, i = 1, 2, \dots, 13) .$

Thus $\begin{matrix} M_{i} & = & Max {X_{1 i}, X_{2 i}, \dots, X_{23, i}} \\ m_{i} & = & min {X_{1, i}, X_{2 i}, \dots X_{23, i}} \end{matrix}$

The new indicators were $X_{ij}^{'} = \frac{X_{ij} - m_{i}}{M_{i} - m_{i}} \in [0, 1]$ (2)

4.2 Using AHP method to determine the weight of the evaluation index

The level of the private colleges and universities is not the only classification level determined by a component. Thus, the effect of each component on the classification is not the same. To determine the weight of the effect of the indicators on the level of school operations, this paper employed the AHP method to calculate the weight of each index.

4.2.1 Establishing the hierarchy mode

4.2.1.1 Finding the judgment matrix

To determine the judgment matrix in AHP, the relative degree of each index was determined according to the result of the different factors. Hence, the following judgment matrix table was obtained see Table 2.

The judgment matrix is T. After the judgment matrix is obtained, the maximum feature vector is determined by calculating software. The weight vector of each effect evaluation index is obtained after normalizing the feature vector:

$\begin{matrix} W & = & (w_{i}) = (0.0917, 0.0611, 0.0750, 0.0723, \\ 0.0776, 0.0770, 0.0925, 0.0770, 0.0867, \\ 0.0693, 0.0623, 0.0840, 0.0735), \\ (i = 1, 2, \dots, 13) \end{matrix}$ (3)

4.3 Consistency check

Complete consistency cannot be achieved for each judgment matrix. Thus, the consistency and randomness of the judgment matrix must be tested. The test procedure is as follows:

First step: calculating TW.

Second step: calculating the largest eigenvalue of the matrix of computation: $λ_{max} = \frac{1}{13} \cdot \sum_{i = 1}^{13} (TW)_{i} / W_{i}$ (4)

Third step: calculating the consistency index of the judgment matrix: $CI = (λ_{max} - n) / n - 1, n = 1, 2, \dots, 13$ (5)

Fourth step: calculating the random consistency index: $RI = \frac{λ_{max}^{'} - n}{n - 1}, n = 1, 2, \dots, 13$ (6)

$λ_{max}^{'}$ is the average value of the maximum eigenvalue of the positive reciprocal matrix generated randomly. For the low-order matrix, the value of RI can be obtained from the average value of random index. However, the approximate method can be used in the judgment matrix of an order higher than 12.

Fifth step: calculating the random consistency ratio of the judgment matrix CR = CI/RI.

When CR < 0.1, the consistency of the judgment matrix can be accepted. By contrast, if CR > 0.1, then the judgment matrix would be corrected until consistency can be accepted. After testing the judgment matrix passes the consistency check.

5 Constructing fuzzy comprehensive evaluation model

5.1 Determining the factor sets and evaluation sets of the evaluation objects

On the basis of the national evaluation indicators and the collected data, the factor of the evaluation object was U: $U = {X_{1}, X_{2}, \dots, X_{13}}$

Unlike the ordinary fuzzy comprehensive evaluation method, this article studies the quality of 23 private universities, and data on the related factors have been collected. To determine the ranking of schools at the end of the evaluation, the evaluation set was established with 23 degrees. Each index that corresponds to the data of each university was assigned to 23 degrees by the proportion of the quantitative form. The evaluation set of the evaluation objectis V: $V = {V_{1}, V_{2}, \dots, V_{23}}$

5.2 Determining the fuzzy relation matrix

In accordance with the results of the questionnaire investigation and data collection, we conducted single factor fuzzy evaluation using Delphi method (the index data of each school is the expert scoring) and determined the fuzzy relation matrix R (U, V).

5.3 Multi-index comprehensive evaluation

Through the fuzzy comprehensive operator using matrix multiplication, a fuzzy comprehensive evaluation matrix B_i was obtained. $B_{i} = W_{i} \circ R_{i} = (b_{i 1}, b_{i 2}, \dots b_{in})$ (7)

In accordance with the first comprehensive evaluation results, second-level fuzzy comprehensive evaluation was carried out, and the evaluation matrix B was obtained:

$\begin{matrix} B & = & (\begin{matrix} B_{1} \\ B_{2} \\ ⋮ \\ B_{13} \end{matrix}) = W \circ R \\ = & (b_{1}, b_{2}, \dots b_{23}) \end{matrix}$ (8)

The following values were obtained by including the data to B: $\begin{matrix} B & = & (0.177, 0.033, 0.047, 0.038, 0.026, 0.037, \\ 0.042, 0.029, 0.028, 0.049, 0.020, 0.037, \\ 0.069, 0.076, 0.065, 0.068, 0.037, 0.060, \\ 0.041, 0.046, 0.037, 0.038, 0.044) \end{matrix}$

The data in B were sorted according to the principle of maximum membership. Thus, the ranking of the 23 private colleges and universities was obtained.

6 Evaluation result

By combining AHP and fuzzy comprehensive evaluation method, this paper established the evaluation index system of the quality of school operations and the evaluation model, and determined the ranking of 23 universities, as shown in Table 3.

Under the assumption that the collected data were true and reliable, the ranking was obtained by using AHP method and fuzzy comprehensive evaluation method. Some errors occurred between the true rank and the forecast ranking. The forecast ranking was only adopted as the research method but not represented as an official ranking.

7 Conclusion

The evaluation model of the school operation level of private colleges was established, and the corresponding rank was determined by using AHP and the innovative fuzzy comprehensive evaluation method. Results have a certain value in the development and application of fuzzy mathematics theory. In this paper, the constructed evaluation set was improved based on the traditional fuzzy comprehensive evaluation method. The larger dimension evaluation set was constructed based on the collected data, and the maximum membership principle was flexibly utilized to obtain the ranking of the 23 universities. The fuzzy comprehensive evaluation method is used in risk assessment, safety assessment, and evaluation index. However, in this paper, the fuzzy comprehensive evaluation method was used to evaluate the performance of private colleges. The evaluation model was established, and the corresponding ranking was given. Thus, this study can serve as a basis in establishing an evaluation system in the field of education and other industries in the future.

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