THE OPTIMIZATION PATH OF HIGHER
EDUCATION RESOURCE ALLOCATION IN
CHINA BASED ON FUZZY SET THEORY
Yuqi Zhao*
Academy of Music, Introduction of Henan University, Kaifeng, Henan, 475000,
China
vivizhaoqiqi@163.com
Reception: 26/11/2022 Acceptance: 13/01/2023 Publication: 07/03/2023
Suggested citation:
Z., Yuqi. (2023). The Optimization Path of Higher Education Resource
Allocation in China Based on Fuzzy Set Theory. 3C TIC. Cuadernos de
desarrollo aplicados a las TIC, 12(1), 308-328. https://doi.org/
10.17993/3ctic.2023.121.308-328
https://doi.org/10.17993/3ctic.2023.121.308-328
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed.42 | Iss.12 | N.1 January - March 2023
308
ABSTRACT
The use of fuzzy set theory to adjust the educational resource allocation model is the
optimal path to achieve the allocation of educational resources. The optimal path
realized by fuzzy set theory promotes the healthy development of education and
addresses the current important and urgent tasks in the field of higher education in
China. This study utilizes the basic theory of fuzzy sets and analyzes dynamic fuzzy
set theory, fuzzy relations and fuzzy matrices. The indexes of optimal allocation are
selected according to the classification of higher education resources, the fuzzy set
multi-objective planning model is designed, and finally, the combination of factors of
education production in colleges and universities is optimized. The experiment proves
that: the average allocation efficiency of excellent colleges and universities is 0.186,
and the average improvement is 35.41% after optimization. The average allocation
efficiency of ordinary colleges and universities is 0.174, which is improved by 22.12%
on average after optimization. It can be found that the resource allocation efficiency of
excellent colleges and universities is generally higher than that of ordinary colleges
and universities, and the role of excellent colleges and universities with more
abundant resources themselves is greater after the optimization of college resource
allocation. It indicates that by adjusting the quantity and structure of educational
resources according to the optimization path, the optimization of educational resource
allocation can be achieved. This verifies that: the emergence of optimal paths for
solving resource allocation realized by fuzzy set theory has greatly expanded the
application of fuzzy methods in the field of higher education and provided a new
theoretical tool for solving resource allocation.
KEYWORDS
Fuzzy set theory; optimization path; dynamic fuzzy set; resource allocation efficiency;
fuzzy matrix
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PAPER INDEX
ABSTRACT
KEYWORDS
1. INTRODUCTION
2. A PATH GENERATION MODEL FOR RESOURCE ALLOCATION
OPTIMIZATION BASED ON FUZZY SET THEORY
2.1. Fuzzy sets, fuzzy relations and fuzzy matrices
2.2. Classification of higher education resources
2.3. Resource allocation optimization modeling
2.3.1. Selection of capital indicators
2.3.2. Multi-objective planning model
2.3.3. Optimization of the combination of production factors in higher
education
2.3.4. A generative model of the optimized path
3. EXPERIMENTS AND ANALYSIS OF OPTIMAL PATHS UNDER THE FUZZY
SET THEORY
3.1. Faculty staffing resources
3.2. Resource utilization efficiency
3.3. Resource allocation efficiency
4. CONCLUSION
DATA AVAILABILITY
CONFLICT OF INTEREST
REFERENCES
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1. INTRODUCTION
Using fuzzy set theory to adjust the educational resource allocation model is the
optimal path to achieve the allocation of educational resources. The optimal allocation
of higher education resources in China refers to the integration and rational
arrangement of educational resources in the area to be determined according to the
principles of sustainability and resource sharing to achieve maximum benefits [1-4].
The priority allocation of educational resources is a condition and prerequisite for the
development of education; without sufficient and compliant educational resources, the
universalization of education and the improvement of educational standards cannot be
discussed [5-9]. The allocation of educational resources reflects the degree of
education adapting to social development in a certain period and also reflects the
level of efficiency and fairness of education. Entering the era of the knowledge
economy and talent competition, the development of colleges and universities affects
all aspects of social and economic life, and the construction of talent in colleges and
universities has been a problem that cannot be ignored in any country or region
[10-11]. Educational activities consist of four factors, which are the objectives of
educational activities, the basic principles or norms of educational activities, the
conditions of educational activities, and the means of educational activities [12-14]. In
summary, they can be divided into two categories: subjective factors and objective
factors. Subjective factors include the goals and norms of educational activities, which
are reflected in the meaning and value of educational activities [15-19]. Objective
factors include the objective conditions and means of educational activities, which are
the ways and means to achieve educational activities [20]. Higher education resource
allocation reflects this characteristic. On the one hand, resource allocation is a
subjective activity with strong purposefulness. On the other hand, it strictly depends
on certain objective methods and is carried out with the help of certain means [21-23].
This is an important path in the analysis of higher education resource allocation and is
of great significance for the study of the value theory of higher education resource
allocation [24].
Fuzzy set theory is generally used to express inexact evaluation data and
information in a fuzzy language in numerous decision problems with multiple attributes
and multiple dimensions. This is because when solving decision problems, the use of
fuzzy language can more accurately and efficiently reflect the information about the
decision maker's preferences for each attribute in the decision solution. The literature
[25] used fuzzy set theory to estimate the cognitive (or fuzzy) uncertainty that arises
due to limited data samples when measuring small field output factors. The literature
[26] conducted a questionnaire survey in which a total of 169 questionnaires were
sent to participants using Google Forms based on the results of the literature review
and interviews. The results of the linguistic fuzzy set approach identified three main
conditions that influence the wage level in the automotive industry in Mexico City,
including unskilled labor, the neoliberal economic model, and political and trade
reforms. On the other hand, organizational conditions were not considered relevant for
determining wage levels. Based on the findings, several recommendations were
made. The literature [27] explored all necessary and sufficient combinations of the
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presence or absence of outcomes in the fuzzy dataset. Necessary causal conditions
are those that produce an outcome, while sufficient combinations are those that
always lead to a given outcome. Many face images feature extraction and
dimensionality reduction algorithms, such as local graph embedding-based algorithms
or fuzzy set algorithms, have been proposed in the literature [28] for linear and
nonlinear data. However, the above algorithms are not very effective for face images
because they always suffer from overlaps (outliers) and sparse points in the database.
To solve these problems, a new effective dimensionality reduction method for face
recognition is proposed: sparse graph embedding fuzzy sets for image classification.
The purpose of this algorithm is to construct two new fuzzy Laplace scattering
matrices using local graph embedding and fuzzy k-nearest neighbors. Finally, the
optimal discriminative sparse projection matrix is obtained by adding elastic network
regression. Many problems have been solved in the above literature using the basic
theory of fuzzy sets with good results.
The construction of human resources education in colleges and universities has
become a problem that cannot be ignored in any country or region. To be able to use
resource allocation optimization to solve education construction problems, this study
uses the basic theory of fuzzy sets and analyzes dynamic fuzzy set theory, fuzzy
relations and fuzzy matrix. It elaborates to give specific higher education resource
classification, and selects indicators for optimal allocation of education resources in
Chinese universities according to education resource classification. And design the
fuzzy set multi-objective planning model according to the known allocation indexes,
and finally realize the combination optimization of higher education production factors
and determine the optimal path of higher education resources allocation based on
fuzzy set theory. Integrating fuzzy set theory into the construction of the optimal path
of resource allocation can not only provide a theoretical basis for solving the dynamic
fuzzy problem and create an important path for the value analysis of college teaching
evaluation but also lay the foundation for the value theory research of college teaching
evaluation.
2. A PATH GENERATION MODEL FOR RESOURCE
ALLOCATION OPTIMIZATION BASED ON FUZZY
SET THEORY
2.1. FUZZY SETS, FUZZY RELATIONS AND FUZZY MATRICES
Let a map be defined on the domain U of the argument:
(1)
Recorded as:
(2)
(
A,A
)
:
(
U,U
)
→[0,1] ×[←,→],
(
u,u
)
→
(
A
(
u
)
,A
(
u
))
(
A,A
)
=AorA
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Then call the fuzzy set on , or for short, and call
the subordination of the subordination function to .
Note: Any number , can be fuzzy to
.So that we can
visualize the development trend of the state. If the teaching quality is good, it means
good or bad, good means good teaching quality but with a downward trend, and bad
means bad teaching quality and with an upward trend. The fuzzy theory can not only
represent the fuzzy degree of the data but also can visualize the trend of the fuzzy
data.
There can be more than one -set on the theoretical domain , and the whole of
the -set is as shown in Equation (3):
(3)
There is a one-to-one correspondence between fuzzy relations and fuzzy matrices,
and fuzzy matrices are an important tool for studying fuzzy relations. Let and
are both fuzzy data, then the relationship between and is
defined as follows:
If equation (4) holds, then is a type type relation from to
.
(4)
If equation (5) holds, then is the relation from to .
(5)
Let the -relationship from to. be a -matrix and expressed
as Equation (6).
(6)
2.2. CLASSIFICATION OF HIGHER EDUCATION RESOURCES
All the elements that can play an influence and role in the allocation of educational
resources in higher education can become educational resources, and their content
(
A,A
)
(
U,U
)
DFS
(
A
(
u
)
,A
(
u
))
(
A,A
)
a∈[0,1]
a
aDF(a,a), aDF a or a ,ma x(a,a)Δa,min(a,a)Δa
a
DF
U
DF
U
DF(U)
DF(U) =
{(
A,A
)
|
(
A,A
)
,
(
u,u
)
→[0,1] ×[←,→]
}
=
{
(A×(←,→))|(A×(←,→)),(u×(←,→))→[0,1] ×[←,→]
}
(
X,X
)
(
Y,Y
)
(
X,X
)
(
Y,Y
)
(
R,R
)
L
DF
(
X,X
)
(
Y,Y
)
(
R,R
)
∈DFL
(
X,X
)
×
(
Y,Y
)
(
R,R
)
DF
(
X,X
)
(
Y,Y
)
L
=
[(
0 , 0
)
,
(
1 , 1
)]
DF
(
X,X
)
(
Y,Y
)
DF
{(
Xn,Xn
)}
,
(
Y,Y
)
=
{(
y1,y1
)
,⋯,
(
yn,yn
)}
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composition is relatively complex and can be classified according to their different
qualities. As shown in Table 1.
Table 1. Classification of higher education resources
The higher education resources under different classification levels are detailed
below:
1.
Land and space resources: Land and space resources are the most traditional
resources and the most basic elements that enable education and teaching to take
place. It mainly includes natural resources such as suitable teaching land and
teaching space [29-30]. However, with the development of the times and the
advancement of network technology, its basic role has not changed but its
importance is weakening.
2.
Financial and material resources: The progress of all disciplines needs financial and
material support. Financial resources refer to the financial investment to support the
development of university education, including research funds and public funds.
Financial resources are characterized by the diversity of sources, continuity of
supply and professionalism of management. Physical resources refer to all material
elements that support the development of university education, including teaching
places, libraries, dormitory buildings, logistic facilities and so on. There are man-
made and natural physical resources, and this paper refers to physical resources in
a narrow sense.
3.
Equipment resources: This resource refers to the sum of various teaching
equipment that assists teaching and learning to be carried out effectively, with the
characteristics of the times, and the complete teaching equipment has begun to
play and will continue to play its important role in today's teaching. Equipment
resources mainly include advanced multimedia teaching facilities, abundant library
Classification
category Higher education resources
Own attribute
Land space resources
Financial resources
Equipment resources
Time resources
Human resources
Information resources
Existential form
Dominant resources
Recessive resources
Time node
Traditional resources
Real resources
Future resources
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materials and retrieval equipment, experimental equipment, etc. It provides more
possibilities for the development of big data teaching.
4.
Time resources: Time resources are a more important factor than space resources
because they control the trajectory of all human development, and time is also our
wealth. The improvement of an idea is an accumulative process, so time and
resources must play a very important role and are one of important factors for
educational development.
5.
Human resources: Broadly speaking, it refers to all the people involved in the
educational process to achieve the educational goals, including the implementers of
the goals and the goal bearers. For example, teachers, counselors, administrators
and all students in the university.
6.
Information resources: Information resources are the collective term for all
information that has a positive impact on the achievement of educational purposes
and can be used. Educational information resources are characterized by the wide
range of sources, the timeliness of dissemination, and the comprehensiveness of
content.
7.
Explicit resources: Explicit resources are all the public and direct educational
processes conducted by education for college students. They undertake the main
task of systematic and formalized teaching, and the theoretical nature of the
information they contain cannot be replaced by other resources.
8.
Implicit resources: Implicit resources generally refer to all the resources that have
indirect educational effects on students in education. Generally speaking, we call all
resources other than "two courses" teaching in colleges and universities that can
have a positive effect on the improvement of students' thinking level as hidden
educational resources in colleges and universities.
9.
Traditional resources: Traditional resources refer to the rich human heritage that
has been accumulated in history and can be utilized by educational disciplines. Our
traditional culture is extremely rich and provides a constant source of cultural
support and inspiration for educational teaching.
10.
Realistic resources: Realistic resources are the general term for the resources that
are updated from the traditional resources in the context of the new era. Real
resources generally cover the healthy spiritual achievements formed in the process
of socialist modernization.
11.
Future resources: Future resources are the sum of all resources that will be
needed and used by the future society and can be predicted to be used in
education and teaching. With the acceleration of globalization, the exchange of
information is everywhere, and the earth has become a "village", which creates
conditions for the exchange of educational resources between countries of different
regions.
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2.3. RESOURCE ALLOCATION OPTIMIZATION MODELING
2.3.1. SELECTION OF CAPITAL INDICATORS
In this paper, we measure the efficiency of educational resources allocation in
colleges and universities according to the attributes of Chinese educational resources
in 2.2.1 and finally determine six indicators: teacher-student ratio (%), average
management-teacher ratio (%),
the total value of teaching instruments and
equipment assets (million yuan),
the average amount of special funds invested
(million yuan), the average area of practice platform room (m2) and
average
area of the educational base (m2). To quantify the allocation efficiency, the values of
the above indicators are used to calculate the resource utilization efficiency of
universities, and the calculation formula is shown in Equation (8):
(7)
where is the rating of and is
. Since the determination of
weights is subjectively influenced by individuals, this paper de-quantifies some
indicators and establishes a fuzzy set multi-objective planning model.
2.3.2. MULTI-OBJECTIVE PLANNING MODEL
According to the fuzzy set correlation theory in Section 2.1, suppose
denotes the vector of objective functions of nine
indicators of higher education resources, and
denotes the vector of constraint functions of each indicator. The problem of optimal
allocation of resources can be transformed into the following fuzzy set planning
model, as shown in Equation (9):
(8)
In the feasible domain as shown in Eq. (10):
(9)
where is the feasible domain of decision space and is the feasible domain of
target space.
2.3.3.
OPTIMIZATION OF THE COMBINATION OF PRODUCTION
FACTORS IN HIGHER EDUCATION
Higher education resources are influenced by multiple factors such as time,
geography and social structure, and the problem of their allocation is not a simple
linear distribution. Among the factors of production, quality is the life and ultimate
measure of higher education, and its ultimate goal is to maximize the benefits in terms
of student output, knowledge output and social output. Assuming that is the quantity
of educational output and is the different forms of the factors, then:
x1
x2
x3
x4
x5
x6
S=C1*A1+C2*A2+C3*A3+C4*A4+C5*A5+C6*A6
Ai
Ai
ci
(i= 1,2,⋯,6)
f(x)=(f1(x), f2(x), ⋯,f9(x))
g(x)=(g1(x), g2(x), ⋯,g9(x))
ma x ={(Z1=f1(x), Z2=f2(x), ⋯,Z9=f9(x))}
Z={z∈Rn|z1=f1(x), z2=f2(x), ⋯,z9=f9(x)}
Sm
Rn
z
x
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(10)
Where, , and denote the input-output ratio, the combination of different
educational factors and the quantity of educational output respectively. From the
above equation, it can be seen that when is larger, the combination of educational
production factors is more reasonable, so the combination with the largest input-
output ratio should be selected. However, at the same time, as the input increases,
the cost of education will also increase. Therefore, it is also necessary to consider the
cost issue.
2.3.4. A GENERATIVE MODEL OF THE OPTIMIZED PATH
The objective function is obtained from the above analysis as:
(11)
(12)
Where: The following constraints should be
satisfied at the same time:
S.t. (13)
(14)
The above model is developed for each indicator of higher education in China.
Where, denotes the number of colleges and universities in regions, and other
indicators in regions are represented by annual totals . The different meanings of
these optimization indicators are represented in Table 2.
Table 2. Representative meanings of optimization path indicators based on fuzzy set theory
P
=
m
∑
j=1
Zj/
n
∑
i=1
X
i
P
X
Zj
P
m
a x R1=
n
∑
i=1
xf/
n
∑
i=1
yfm a x R2=
n
∑
i=1
yf/
n
∑
i=1
zfm a x R3=
n
∑
i=1
Df/
n
∑
i=1
yf
m
a x R4=
n
∑
i=1
Ef/
n
∑
i=1
yfm a x R5=
n
∑
i=1
Ff/
n
∑
i=1
xfm a x R6=
n
∑
i=1
xf
Xuv,Yuv,Duv,Euv,Fuv,Huv ≥0,∀uv
α
11 ≤
nj
∑
i=1
xij ≤α12 α21 ≤
nj
∑
i=1
yij ≤α22 α31 ≤
nj
∑
i=1
yij ≤α
32
α
41 ≤
nj
∑
i=1
yij ≤α42 α51 ≤
nj
∑
i=1
yij ≤α
52
nj
j
j
∑
Value of U Representative meaning
X Total number of students in school
Y Total number of annual management teachers
Z Total assets of teaching instruments and equipment
D Annual special fund input
E Annual floor area of practice platform
F Annual education base area
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3. EXPERIMENTS AND ANALYSIS OF OPTIMAL PATHS
UNDER THE FUZZY SET THEORY
Six excellent colleges and universities and six general local colleges and
universities in a province are used as research samples to integrate the optimization
objective functions and constraints of multi-objective higher education resource
allocation in China. The multi-objective planning model based on fuzzy set theory is
used to calculate the optimal path of the combination of higher education production
factors. When the configuration optimization model tends to be stable and the fitness
function tends to the minimum value, the six sets of optimal paths obtained at this time
are shown in Table 3. The optimal paths 1-3 indicate the highest efficiency of
educational resource utilization and allocation when the educational resources of
general colleges and universities are allocated in such a ratio. The optimal paths 4-6
indicate that when the educational resources of excellent colleges and universities are
allocated in this way, the educational resources are used and allocated with the
highest efficiency.
Table 3. Optimization path of higher education resource allocation in China based on fuzzy
set theory
To illustrate the positive utility of the optimization path in depth, further analysis is
conducted in three aspects: faculty staffing resources, resource utilization efficiency,
and resource allocation efficiency, respectively.
3.1. FACULTY STAFFING RESOURCES
To be able to use resource allocation optimization to solve the problem of equipping
resources for faculty in educational construction, the average number and structure of
faculty in educational resource allocation in 12 universities were analyzed according
Measurable index Optimal
path 1
Optimal
path 2
Optimal
path 3
Optimal
path 4
Optimal
path 5
Optimal
path 6
Teacher student ratio/% 1:220 1:215 1:213 1:201 1:198 1:189
Ratio of management teachers
per student/% 1:320 1:311 1:300 1:298 1:290 1:287
Total assets of teaching
instruments and equipment per
student/10000 yuan
0.0895 0.0845 0.0823 0.0811 0.0802 0.0800
Special fund input per student/
10000 yuan 0.0095 0.0091 0.0084 0.0082 0.0080 0.0071
Room area of practice platform
per student/m21.15203 1.15201 1.15198 1.15186 1.15166 1.1502
Area of education base per
student/m20.3860 0.3854 0.3823 0.3811 0.3802 0.3799
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to the classification of higher education resources using the resource allocation
optimization model of fuzzy set theory, and the following analysis results were
obtained:
1.
In terms of the overall number of teaching and research staff on board and the
number of different titles, the total number of teaching and research staff has
steadily increased from 2017 to 2021, and the number of the four titles has tended
to stabilize. Among them, the number of associate professors tends to increase
slightly, the number of professors and lecturers remains unchanged, and the
number of assistant professors gradually decreases, as shown in Figure 1.
Figure 1. Statistics on the number of active teaching and research staff in the optimization
path
2.
The situation of student-teacher ratio shows a general downward trend. Due to the
adjustment of enrollment policy, it leads to the increase in the number of
undergraduate and master students in 2018-2019, while it returns to a stable state
in 2020, and the student-teacher ratio decreases to 20:1. The ratio of the total
number of graduate students to the total number of professors and associate
professors decreases to 15:1 from more than 20:1 in previous years. The ratio of
doctoral students to professors is higher than 20, which is caused by the expansion
of universities in the early stage on the one hand, and the lack of faculty on the
other hand The ratio of Ph. The specific situation is shown in Table 4.
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Table 4. Percentage of students and faculty under the optimized pathway (Unit:%)
3.
In terms of the title structure of the active faculty and researchers, the share of
professors remained unchanged from 2017 to early 2021, the share of associate
professors increased, while the share of lecturers and assistant professors
decreased. The details are shown in Table 5.
Table 5. Structure of teaching and research staff titles in the optimization path (unit:%)
4.
In terms of the academic structure of the teaching and research staff in post, as
shown in Figure 2, 67% of the total number of teaching and research staff have
doctoral degrees. Among them, 56% of the professors have Ph. D.s, 72% of the
associate professors and 80% of the lecturers. Since the current policy stipulates
that faculty and researchers who stay in the university must have a doctoral degree,
the academic structure at the beginning of 2021.
Student-
teacher
ratio
Ratio of students to the
number of professors,
associate professors
and lecturers
Ratio of graduate students
to the number of
professors and associate
professors
Ratio of the number
of doctoral students
to professors
2017 23 22 25 21
2018 23 22 20 23
2019 21 24 22 25
2020 20 23 25 21
2021 22 25 20 22
Professor Associate
Professor Lecturer Teaching
Assistants
2017 0.25 0.38 0.25 0.08
2018 0.27 0.38 0.26 0.07
2019 0.27 0.38 0.25 0.09
2020 0.27 0.45 0.26 0.07
2021 0.25 0.38 0.25 0.07
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Figure 2. Statistics on the educational structure of faculty and researchers in the optimization
path
5.
Looking at the age structure of the faculty and research staff with a reasonable
allocation of higher education resources in China, it is shown in Figure 3. 46% of
the faculty and research staff are less than 40 years old. Thirty-five percent of the
teaching and research staff are between 40 and 50 years old, and only 15% of
them are older than 50 years old, and they are mainly professors. Professors are all
older than 40 years old, and 50% of them are older than 50 years old. The age of
associate professors is mainly below 50 years old, among which 46% and 47% of
associate professors are above and below 40 years old respectively. Lecturers and
assistant professors are relatively younger, generally under 40 years old. In terms
of age structure, the age distribution is relatively reasonable.
Figure 3. Statistics on the age structure of faculty and researchers in the optimization path
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6.
The gender structure of in-service Chinese higher education researchers with
reasonable resource allocation is shown in Figure 4. Women account for 35%.
Among them, 21% of professors are female, 40% of both associate professors and
lecturers are female, and 33% of assistant professors are female.
Figure 4. Statistics on the gender structure of Faculty and Researchers in the optimization
path
3.2. RESOURCE UTILIZATION EFFICIENCY
Six excellent universities and six general local universities in a province were used
as the research samples, and the data of China's higher education resources from
2017-2021 were counted. To verify whether the resource allocation optimization path
generated by the fuzzy set multi-objective planning model improves the resource
utilization efficiency, optimal path 1 and optimal path 3 are used as examples for the
analysis of experimental results. According to the calculation of the resource utilization
efficiency of each university before and after the experiment, it is found that the
resource utilization efficiency of each university before and after the experiment has
improved, with an average increase of 18.25%, and the resource utilization efficiency
of each university tends to be in a balanced state. The experimental resource
utilization efficiency of excellent schools is shown in Figure 5(a), and the resource
utilization rate of ordinary colleges and universities is shown in Figure 5(b). The
resource utilization efficiency of excellent colleges and universities and general
colleges and universities are improved from 48.302 and 0.523 before optimization to
1.057 and 1.068, respectively, with an improvement rate of 32.3% and 52.4%. It can
be found that the resource utilization rate of ordinary colleges and universities is
generally higher than that of excellent colleges and universities, which indicates that
resource allocation optimization is more useful for ordinary colleges and universities
with scarce resources.
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(a) Resource utilization rate of excellent universities
(b) Resource utilization rate of general universities
Figure 5. Comparison of resource utilization of universities before and after the
implementation of the optimized path
3.3. RESOURCE ALLOCATION EFFICIENCY
To verify whether the optimized paths generated by the fuzzy set multi-objective
planning model improve the resource allocation efficiency, the overall resource
allocation efficiency of the original data and the optimized allocation solutions (optimal
path 1 and optimal path 3) of each university are calculated before and after
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optimization, respectively. The resource allocation efficiency of excellent universities is
shown in Figure 6(a), and the resource allocation efficiency of ordinary universities is
shown in Figure 6(b).
(a) Excellent university resource allocation efficiency
(b) Resource allocation efficiency of general universities
Figure 6. Comparison of resource allocation efficiency of universities before and after the
implementation of the optimized path
As can be seen from Figure 6, the difference in resource allocation efficiency
between excellent universities and ordinary universities before implementing the
optimized path is large, with a minimum value of 0.125 and the maximum value of
0.192. The average allocation efficiency of excellent universities after optimization is
0.186, with an average improvement of 35.41%. The average allocation efficiency of
ordinary colleges and universities is 0.174, with an average increase of 22.12%. It can
be found that the resource allocation efficiency of excellent colleges and universities is
generally higher than that of ordinary colleges and universities, and after the
optimization of college resource allocation, the role of excellent colleges and
universities with more abundant resources themselves is greater. It indicates that
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adjusting the quantity and structure of educational resources according to the
optimization path can achieve the optimization of educational resource allocation.
4. CONCLUSION
Using fuzzy set theory to adjust the education resource allocation mode is the
optimal path to achieve education resource allocation. This paper analyzes dynamic
fuzzy set theory, dynamic fuzzy relationship and dynamic fuzzy matrix according to
the basic theory of fuzzy sets. Combined with the classification of higher education
resources, indicators for the optimal allocation of educational resources in Chinese
universities are selected and a fuzzy set multi-objective planning model is designed.
Based on the combination optimization form of higher education production factors
and the fuzzy set multi-objective planning model, the fuzzy model for generating the
optimal path is structured. The research results obtained are as follows:
1. The content composition of educational resources is relatively complex and can be
classified according to their different qualities. First, according to the different
attributes of ideological and political education resources, they can be classified into
various kinds of resources with different attributes. Secondly, educational resources
are classified into explicit resources and implicit resources according to their
different forms of existence. Thirdly, according to the different times of their
existence, they can be divided into traditional, real and future resources.
2.
The average resources of excellent colleges and universities and the resource
utilization efficiency of general colleges and universities are improved from 48.302
and 0.523 before optimization to 1.057 and 1.068, respectively, with an
improvement rate of 32.3% and 52.4%. It can be found that the resource utilization
efficiency of ordinary colleges and universities is generally higher than that of
excellent colleges and universities, which indicates that resource allocation
optimization is more useful for ordinary colleges and universities with scarce
resources.
3. The average allocation efficiency of excellent colleges and universities is 0.186, and
the average improvement after optimization is 35.41%. The average allocation
efficiency of ordinary colleges and universities is 0.174, which is improved by
22.12% on average after optimization. It can be found that the resource allocation
optimization path generated by the adjustment of the multi-objective planning model
based on the fuzzy set theory makes the excellent colleges and universities with
more abundant resources get higher resource allocation efficiency.
DATA AVAILABILITY
The data used to support the findings of this study are available from the
corresponding author upon request.
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CONFLICT OF INTEREST
The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential conflict of
interest.
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