=Paper=
{{Paper
|id=Vol-2422/paper20
|storemode=property
|title=Application of Fuzzy Logic Approach for the Determination of the Integral Index of the Implicit Impact of the Higher Education System on Regional Development
|pdfUrl=https://ceur-ws.org/Vol-2422/paper20.pdf
|volume=Vol-2422
|authors=Oksana Sotula,Viktoriya Denysenko
|dblpUrl=https://dblp.org/rec/conf/m3e2/SotulaD19
}}
==Application of Fuzzy Logic Approach for the Determination of the Integral Index of the Implicit Impact of the Higher Education System on Regional Development==
https://ceur-ws.org/Vol-2422/paper20.pdf
249
Application of Fuzzy Logic Approach for the
Determination of the Integral Index of the Implicit
Impact of the Higher Education System on Regional
Development
Oksana Sotula and Viktoriya Denysenko[0000-0002-1029-1871]
Bohdan Khmelnytsky National University of Cherkasy, 81, Shevchenko Blvd., Cherkasy,
18031, Ukraine
{ksuna5, vikaonline}@ukr.net
Abstract. In this paper the theoretical and methodological aspects of the
influence of the higher education system on the socio-economic development of
the regions of Ukraine are considered. On the basis of fuzzy logic approach, we
have calculated the integral index of the implicit impact (IIII = I4) of the higher
education system on regional development. Regions are grouped by this indicator
over time. The integral indicator allowed us to identify regions with the
corresponding I4 of the higher education system at the regional level and compare
them with other regions of Ukraine (identification of inter-regional imbalance).
The analysis shows that there is no strategy for embedding the university in the
local economy and society. It is impossible to state unequivocally that the most
developed regions have the greatest influence on the system of higher education,
and vice versa. An important continuation of the study should be an assessment
of the situation in each region of the country separately. Such analytics should
help develop differentiated directions for the development of regional higher
education systems.
Keywords: fuzzy logic approach, implicit impact, higher education system,
regional development, integral index, Mamdani inference.
1 Introduction
Over the past few decades, the evaluation of university contributions to the economic,
social, cultural and innovative development of society has been central to educational
policy issues. In higher education systems of economically developed countries, radical
transformations are taking place that are associated with the increasing importance of
universities for innovative development and economic growth. The two main objectives
of each university are education and science. However, there is a growing awareness
that universities are becoming enterprises with corresponding functions in the economy
and society, except for school and laboratory. They begin to position themselves as
engines of regional development. From the middle of the 20th century, the state policies
250
of developed countries are aimed at developing human capital, regional disparities of
which may undermine national security.
The issue of the role of higher education institutions in stimulating the development
of the regional economic system is being actively discussed in the scientific literature
today. Thus, the studies of P. H. Pellenbarg [1], A. Valero, and J.V. Reenen [2] are
devoted to the calculation of the quantitative contribution of universities to regional
development.
G. Huggins, P. Cook, D. Charles, P. Benneworth, G. Etzkowitz, D. Bock, etc. [3]
evaluate the contribution of universities to the innovative development of regions,
analyze how universities can produce not only new knowledge and technologies, but
also implement them in regional socio-economic and production systems [4].
Eliot, Levin and Mazil consider universities as generators of economic development
of the region at the expense of funds invested in education in the form of state financing,
tuition fees and living expenses for students from other regions, industrial orders [5].
The aforementioned approach expanded B. Bluestone [6] by adding to the criteria
for assessing the impact of higher education on the regional economy an assessment of
the level of qualifications of workers. According to this approach, universities train and
produce more skilled workers who have higher labor productivity, higher levels of
income and consumption, and therefore, provide higher tax deductions to the budget.
However, the methodology for assessing the integrated impact of the higher
education system on regional development is insufficiently developed.
Therefore, the aim of the article is to study the implicit impact of the higher education
system on the socio-economic development of the region. This will provide an
opportunity to develop practical mechanisms for ensuring balanced regional
development.
To achieve this goal, we use the following methods: theoretical generalization,
comparison and systematization (in the study of the nature and effects of the impact of
the higher education system on the development of regions). Abstract-logical method
(for theoretical generalization), the index method in context with the mathematical
apparatus of the theory of fuzzy sets (for determining the integral index of the implicit
impact of the higher education system on regional development), the graphical method
(for visualizing the relationship between input and output variables).
2 Results
The influence of the higher education system on the socio-economic development of
the region is increasingly becoming the center of research for domestic and foreign
scientists. Reality indicates a change in the socio-economic goals of the university.
From its first generation (educational institution only), to the second generation
university (training and research), and the third generation university (integrated
educational, research and business environment).
Today we are talking about fourth-generation universities. Its exact characteristics
are still insufficiently investigated. The essential difference of such a university is the
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availability of a strategic approach to its own development and the ability to actively
influence the competitiveness of the regional environment [7].
We believe that the growth of influence on regional development can be expected
already from third-generation universities, because it is here that not only education and
research, but also the use of knowledge become important. As a result, the relationship
between production and universities is deepening, so there is the possibility of local use
of knowledge created in universities. This increases the competitiveness of enterprises
and, as a result, the region. In addition, the social environment of universities is
improving. A knowledge-based society is inevitably linked to the valuation of human
capital, since the competitiveness of an economy depends on the quantity and quality
of available human resources.
There are several classifications of areas and types of university influence on the
regional system. According to R. Florax, there are eight regional effects of university
activities in the demographic subsystem, economic subsystem, infrastructure, culture,
attractiveness of the region, education, social subsystem, political subsystem [1].
There are short-term and long-term impacts of universities on the region’s economy.
In the short term, there is an impact on the demand of local enterprises, the income and
expenses of local households, and the services and income of local governments. The
long-term impact on the university is the qualification of human capital, attracting
foreign capital and labor in the immediate vicinity of the university and the number of
enterprises based on university research. These factors can be considered as having a
secondary regional multiplicative effect, since they heighten the demand for local goods
and services [8].
Regional and local effects of the university can be observed in many areas outside
the economy. As a rule, three types of economic influence of universities are evaluated
in research: direct, indirect, and induced [9].
In our opinion, the most comprehensive by the nature of the impact of the
classification of the results of university activities should take into account the type of
impact on the regional subsystem (Table 1).
Table 1. Types of university influence on regional subsystems.
Types of university influence
Regional subsystems
Direct Indirect Induced Catalytic
Demographic ˅ ˅ ˅ ˅
Economic ˅ ˅ ˅ ˅
Infrastructure ˅ ˅ ˅ ˅
Culture ˅ ˅ ˅ ˅
Attractiveness ˅
Education ˅ ˅ ˅ ˅
Social ˅
Political ˅
It is clear that the selected areas are not isolated from each other but have different
effects. The most significant activity of the university affects the economic subsystem,
which is closely linked to the demographic changes, infrastructure, educational system
and image of the region.
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The economic impact of a higher educational establishment is defined as the
difference between the existing level of economic activity in the region and the level
that could have been if the institution did not exist [10].
However, the quantitative assessment of the impact of universities on the regional
subsystem is complicated by the presence of the implicit impact of the higher education
system on regional development.
Implicit mechanisms are based on mechanisms of different order. Its characteristics
are manifested in human activity in different ways. In psychology, it is associated with
the implicit personality theory, which allows you to form a holistic impression of
another person based on incomplete information about his personal characteristics.
Mathematicians and other representatives of the exact sciences are concentrating their
efforts in developing data search and recovery algorithms based on implicit factors that
influence various processes. In economics, the term “implicit” is associated mainly with
“intangible”, “immeasurable”, “elusive” factors that affect the economic activity of an
economic agent. Thus, implicit factors are implicit, hidden factors, production
resources, which in the course of economic activity do not find direct, official
reflection [11].
Implicit impact (the influence of implicit factors) is an implicit influence within the
economic system that can lead to a synergistic effect. This effect is that when the subject
achieves significant economic results, an area of unstable conditions arises. A minor
hidden influence of external forces can lead to diametrically opposite development
vectors: from the collapse of the system to a new, higher level of development. The
nature of implicitness lies in the presence of hidden (implicit) information that
circulates in the economic environment and requires decision-making after in-depth
analysis of data in order to obtain the most complete information. In our case,
implicitness is understood as the impossibility to take into account all aspects of the
impact under study, since in the process of analysis, hidden, implicit, unaccounted
information appears in the data-information-knowledge chain.
In our opinion, the urgent task is to construct an integral index of the implicit impact
(IIII = I4) of the higher education system on regional development and to group the
regions according to this indicator.
To construct the integral index, we used the index method in context with the
mathematical apparatus of the theory of fuzzy sets (fuzzy logic and Mamdani fuzzy
logical inference) [12], which allows to use of heterogeneous input variables, formalize
nonlinear dependencies, use natural language to describe the connection, and obtain
fuzzy models that are flexible for tuning and adaptation. The main stages of
constructing a Mamdani fuzzy logical inference are as follows:
1. determination of the main factors (parameters) of the system under consideration;
2. determination and formalization of linguistic variables (fuzzification);
3. the construction of a fuzzy knowledge base (fuzzy production rules);
4. implementation of a fuzzy inference;
5. reducing the fuzzy value of the output variable into a clear one using the center of
gravity method (defuzzification).
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Note that the index method of determining the integral index involves the following
steps:
1. the choice of indicators characterizing the phenomenon;
2. statistical analysis and standardization (normalization) of data;
3. the calculation of the partial indices (sub-indices);
4. determination of the resulting integral index on the basis of sub-indices;
5. analysis and interpretation of the result.
In our study, the main blocks (sub-indices) of the I4 of the higher education system in
the socio-economic development of the regions are economic, innovative, educational
and demographic (see Table 2).
Each of these partial indices will be determined using three indicators (stimulators).
According to the classical scheme, the aggregate index consists of partial indices and
is represented in the form of their weighted sum or product. The selection of indicators
for the evaluation of each of the blocks is based on the presented theoretical approaches,
but takes into account the features of the domestic system of higher education and the
factors associated with the characteristics of data collection.
It should be noted that the procedure for determining the weight coefficients of the
components of the general index is labor intensive, since it is necessary to take into
account considerable achievements in this sphere and cover a large number of
judgments, even often incomparable. But using the methods of the theory of fuzzy sets
allows us to avoid these difficulties in determining weight coefficients.
For calculations, only the normalized (standardized) values of the parameters
belonging to the segment [0, 1] are used. The process of normalization of indicators is
carried out according to the formula:
zi=(Xi–Xmin)/(Xmax–Xmin) – normalized values of the indicator in the i-th region.
The main idea of obtaining a resulting index is as follows.
1. Each sub-index is considered as the output variable in the Mamdani algorithm, and
the corresponding indicators that characterize this partial index are used as input
linguistic variables, moreover all input and output variables containing three terms:
L (low), M (medium), H (high).
2. The general index (I4) is considered as the output variable in the Mamdani algorithm,
and the sub-indices that characterize this general index (and found in the previous
step) are already used as input linguistic variables (Figure 1), moreover all the input
variables containing three terms: L (low), M (medium), H (high), and the output
variable – L (low), BM (below medium), M (medium), AM (above medium), H
(high).
The procedure for finding sub-indices and the overall integral indicator is conducted
for a specific year for all regions of Ukraine and their grouping is performed according
to this indicator. Each term corresponds to a fuzzy set, which is given by the
corresponding membership function. The specific form of membership functions is
determined on the basis of various additional assumptions about the properties of these
functions, taking into account the specificity of the existing uncertainty and the actual
254
situation, expert data, etc. For our fuzzy model of determining the integral index we use
the trapezoidal membership functions (Fig. 1). Formalized representations of input and
output variables are obtained by means of Matlab fuzzy logic toolbox [13].
Table 2. The list of indicators characterizing sub-indices.
Sub-
Economic contributi-
indi- Indicators (stimulators) Regional effect
on of the university
ces
Wages, purchase of equipment, go-
ods and services (direct). Income
Impact on the regional and expenditures of participants in
economy, budget reve- university supply chains (indirect).
Х1 – GRP per capita, UAH. nues, industrial struc- Income and employment are caused
ture, labor market, la- by the multiplicative effect of inco-
Economic (I1)
bor mobility me and expenditures of employees,
both of the university and its asso-
ciated companies (induced).
Impact on the level of Providing the labor market with
Х2 – GRP per worker of education, structure highly skilled labor, the growth of
working age, UAH. and quality of labor in labor productivity in the region (ca-
the region talytic).
Companies that are
Х3 – Small and medium bu- Income and employment in compa-
created by students
siness (SME) per 10 thou- nies that are formed thanks to the
(former) and university
sand population, units. university (catalytic).
staff
Х1 – Distribution of applica-
tions for inventions and uti- Income from research activities (di-
lity models addressed to na- rect).
tional applicants by region.
Jobs created by the functioning of
Innovative (I2)
Х2 – Regional gross value Selling knowledge in
the university (direct). Income and
added in the field of infor- the form of patents, re-
employment are caused by the mul-
mation and telecommunica- gional value added in
tiplicative effect of income and ex-
tions (IT companies) (UAH the field of information
penditures of employees in the IT
per capita). technology
sector (induced).
Х3 – Organizations that car- Government funding, business inco-
ried out research and deve- me, income and employment in or-
lopment, per 10 thousand ganizations that carry out research
population, units. and development (catalytic).
Х1 – Economically active
Educational and demographic
population aged 15-70 ye- Providing the labor market with
ars, number of people by le- highly skilled labor, flexible supply
The impact on the le-
vel of education per 10 of student labor (induced).
vel, structure and qua-
thousand population.
lity of education in the
Provision of educational services
(I3)
region.
(direct).
Population growth,
Х2 – Number of institutions Income and expenditures of emp-
changing population
of higher education per 10 loyees of the university and related
structure and mobility.
thousand population. institutions (indirect).
Income and employment caused by
the multiplicative effect of income
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Sub-
Economic contributi-
indi- Indicators (stimulators) Regional effect
on of the university
ces
and expenditures of employees (in-
duced).
Expenditures for the purchase of go-
Х3 – Number of students, ods and services, tuition fees (di-
per 10 thousand population. rect).
Increase in labor force (induced).
Then the structural identification of the model is carried out with the help of forming
a fuzzy base of the production rules «IF-THEN» that reflect the connection of the
«input-output».
The set of fuzzy production rules for the given knowledge base has the form:
IF (І1=L) and (І2=L) and (І3=L) or … or (І1=L) and (І2=L) and (І3=M), THEN І=L;
IF ..., THEN …;
IF (І1=M) and (І2=H) and (І3=H) or … or (І1=H) and (І2=H) and (І3=L), THEN
І=AM.
A fuzzy logical inference is implemented, ranging from logical statements to fuzzy
logic equations. Such equations are derived from the knowledge base by replacing the
linguistic terms to the membership function, and the operations «and» and «or» to the
operation of finding the minimum () and the maximum () respectively, while the
weight of rule is taken into account by multiplying the fuzzy expression by the
corresponding value of weight:
b
j ( x1 ,..., xn ) w jp jp ( xi ),
p 1, k j i 1, n
where bj is the j-th term of output linguistic variable.
Fig. 1. Scheme of Mamdani fuzzy logical inference for the general integral index.
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The system of fuzzy logic equations has the form:
L ( I1 , I 2 , I 3 ) L ( I1 ) L ( I 2 ) L ( I 3 ) ... L ( I1 ) L ( I 2 ) M ( I 3 ) ;
. . .
AM
( I1 , I 2 , I 3 ) ( I1 ) ( I 2 ) ( I 3 ) ... H ( I1 ) H ( I 2 ) L ( I 3 ) .
M H H
~
The final fuzzy set І is obtained as the union of all trimmed fuzzy subsets for each
fuzzy rule:
5 1
I
b
min j ( I1 , I 2 , I 3 ), j ( I )
b
.
j 1 0 I
Next, the fuzzy result is defuzzified by the method of the center of gravity, after which
we obtain a clear value of the I4 at the regional level
1
I
y ( y)dy
I 01 .
I
( y)dy
0
Thus, on the basis of the indicated formulas and the methodology of fuzzy logic
inference, we can obtain the value of the integral index for each region in the dynamics.
To facilitate calculations, all phases of fuzzy simulation is performed by means of the
Matlab fuzzy logic toolbox. After adjusting the parameters of the membership functions
of the terms of input and output linguistic variables, the fuzzy knowledge base is filled.
A visual presentation of the procedure of the fuzzy logic inference of Mamdani type
and the defuzzification of the integral index is shown in Figure 2.
In the Figure 3 the visualization of the surfaces of the dependencies of the output
linguistic variable from the other two input variables is presented.
As a result of the assessment, we obtained three sub-indexes of the higher education
system: a contribution to the economic development of the region, a contribution to the
innovative development of the region, and a contribution to the educational and
demographic development of the region. The results of calculations for each of the sub-
indices are presented in Table 3.
As you can see, the value of sub-index ranges from 0 – the worst, to 1 – the best
value in the country. This allows us to represent all the regions of Ukraine in the order
of the degree of their development for each of the sub-indices. At the same time, the
place of the region in the uniform scale for Ukraine and the change in its potential is
important. This makes it possible to consider changes in the integral index in a regional
context and analyze the trends of each specific region.
The leaders in the sub-index of influence on economic development are Kiev,
Poltava, Dnipropetrovsk and Zaporizhzhia regions. The presence of large universities
in these regions explains the relatively high rates of income of universities.
257
Fig. 2. Procedure for the fuzzy logic inference of Mamdani type (Zaporizhzhia region, 2016) X
= [0.4; 0.1; 0.18].
The surface of the dependence of the output of the fuzzy system I on the input variables I1
and I2.
258
The surface of the dependence of the output of the fuzzy system I on the input variables I1
and I3.
The surface of the dependence of the output of the fuzzy system I on the input variables I2
and I3.
Fig. 3. Surfaces of the dependence of the output of the fuzzy system on the input variables.
On the second sub-index, besides Kiev, another region is leading – Kharkiv region.
Here are located large national universities, which constitute a significant part of the
regional innovation infrastructure.
The largest share of applications for inventions and utility models falls on the
«Science» and «Education» sectors. Moreover, the number of applications submitted
by educational institutions annually exceeds the number of applications submitted by
scientific organizations. In 2016, the applicants of the Ministry of Education and
259
Science of Ukraine submitted 2849 applications (this represents 37.9% of the total
number of applications filed).
Table 3. Calculated values of the sub-indices and the integral index of the regions of Ukraine
(2012/2016).
Sub-index І1 Sub-index І2 Sub-index І3 Integral index І
Region of the year of the year of the year of the year
2012 2016 2012 2016 2012 2016 2012 2016
Vinnytsia 0.08 0.20 0.09 0.10 0.08 0.09 0.07 0.15
Volyn 0.07 0.08 0.07 0.07 0.08 0.08 0.07 0.07
Dnipropetrovsk 0.49 0.48 0.29 0.22 0.49 0.49 0.50 0.50
Donetsk 0.45 0.09 0.23 0.08 0.50 0.13 0.50 0.08
Zhytomyr 0.07 0.08 0.08 0.07 0.08 0.08 0.07 0.07
Zakarpattia 0.07 0.08 0.08 0.07 0.08 0.08 0.07 0.07
Zaporizhzhia 0.29 0.40 0.09 0.10 0.18 0.18 0.29 0.29
Ivano-Frankivsk 0.08 0.08 0.08 0.08 0.08 0.08 0.07 0.07
Kiev 0.46 0.48 0.09 0.09 0.09 0.10 0.25 0.25
Kirovohrad 0.08 0.22 0.08 0.08 0.08 0.08 0.07 0.12
Luhansk 0.09 0.07 0.10 0.08 0.27 0.07 0.09 0.07
Lviv 0.08 0.28 0.15 0.17 0.39 0.47 0.13 0.41
Mykolaiv 0.08 0.12 0.09 0.08 0.08 0.08 0.07 0.09
Odessa 0.18 0.33 0.10 0.09 0.35 0.43 0.23 0.48
Poltava 0.44 0.50 0.08 0.08 0.09 0.08 0.21 0.25
Rivne 0.07 0.08 0.07 0.07 0.08 0.08 0.07 0.07
Sumy 0.08 0.08 0.07 0.07 0.08 0.08 0.07 0.07
Ternopil 0.07 0.08 0.07 0.07 0.08 0.08 0.07 0.07
Kharkiv 0.33 0.39 0.49 0.50 0.49 0.50 0.50 0.51
Kherson 0.08 0.09 0.08 0.08 0.08 0.08 0.07 0.08
Khmelnytskyi 0.07 0.08 0.07 0.07 0.08 0.08 0.07 0.07
Cherkasy 0.08 0.24 0.08 0.08 0.08 0.08 0.07 0.20
Chernivtsi 0.07 0.08 0.08 0.08 0.08 0.08 0.07 0.07
Chernihiv 0.08 0.09 0.07 0.07 0.08 0.08 0.07 0.07
city Kiev 0.95 0.95 0.95 0.95 0.95 0.95 0.94 0.94
The most active among the organizations of the Ministry of Education and Science
of Ukraine were institutions of higher education in the city of Kiev and the Kharkov
region: National University of Food Technologies (10.3% of the total number of
applications filed by applicants from this ministry) National Technical University of
Ukraine «Kiev Polytechnic Institute» (7.8%), National Aerospace University.
M.E. Zhukovsky Kharkiv Aviation Institute (4.3%), Kiev National University of
Technology and Design and Vinnitsa National Technical University ‒ 117 and 116
applications, respectively (4.1%), National Technical University Kharkiv Polytechnic
Institute ‒ 91 applications (3 2%), Odessa National Academy of Food Technologies –
83 applications (2.9%) [14].
The leaders in the framework of I4 on the higher education system for regional
development are Kiev, Dnipropetrovsk, Lviv, Kharkiv and Odessa regions. These are
260
regions with large university centers. Here the number of universities is 45.8% of the
total in Ukraine (259 institutions out of 657).
The leaders in the contribution of higher educational institutions to the educational
and demographic development of the region are Kiev, Kharkiv, Odessa, Lviv and
Dnipropetrovsk regions.
According to the research of the CEDOS analytical center “Movement of applicants
between the regions of Ukraine” in 2017 and 2018, only Kharkov, Kiev, Odessa, Lviv
and Chernivtsi regions had a positive balance of arrival and departure. In other regions
there was an outflow of graduates [15].
The results of the sub-indices of the regions of Ukraine for 2012 and 2016 have been
summarized in the integral indicator of the implicit impact of the higher education
system on regional development (see Table 3). Based on the data in Table 3 we have
conducted a grouping of regions according to the I4 of the higher education system at
the regional level, the results of which are given in Table 4.
Table 4. Grouping of Ukrainian regions by I4, 2012/2016.
The boundaries The meaning
Year of the integral of the integral Distribution of regions by integral indicator
indicator indicator
Vinnytsia. Volyn. Zhytomyr. Zakarpattia. Ivano-
Frankivsk. Kirovohrad. Luhansk. Mykolaiv. Rivne.
[0;0.1) critically low
Sumy. Ternopil. Kherson. Khmelnytskyi.
Chernivtsi. Cherkasy. Chernihiv
[0.1;0.2) low Lviv
2012 below the
[0.2;0.4) Zaporizhzhia. Kiev. Odessa. Poltava
average
[0.4;0.6) average Dnipropetrovsk. Donetsk. Kharkiv
above the
[0.6;0.8) –
average
[0.8;1] tall city Kiev
Volyn. Donetsk. Zhytomyr. Zakarpattia. Ivano-
Frankivsk. Luhansk. Mykolaiv. Rivne. Sumy.
[0;0.1) critically low
Ternopil. Kherson. Khmelnytskyi. Chernivtsi.
Cherkasy. Chernihiv
[0.1;0.2) low Vinnytsia. Kirovohrad
2016 below the
[0.2;0.4) Zaporizhzhia. Kiev. Poltava. Cherkasy
average
[0.4;0.6) average Dnipropetrovsk. Lviv. Odessa. Kharkiv
above the
[0.6;0.8) –
average
[0.8;1] tall city Kiev
Most regions of Ukraine have integral indicator values that are critically low, low,
and below average. In addition, the belonging of regions to one or another group of
indicators practically did not change in 2016 compared to 2012. Growth rates are
observed in Vinnytsia (2.14), Kirovograd (1.71), Lviv (3.15), Nikolaev (1.29), Odessa
(2.09), Poltava (1.19), Kharkiv (1.02), Kherson (1.14), Cherkasy (2.86) regions. The
integral indicator decreased in Donetsk (0.16) and Luhansk (0.78) regions. But this is
261
due primarily to the unfavorable situation in the East of Ukraine and the neglect in the
statistical data of a part of the occupied territories. In the remaining regions, the integral
index remained almost unchanged. The current situation indicates that there is no
effective strategy of «embedding» universities in the local economy and society at both
the national and regional levels.
3 Conclusions
The analysis suggests that there is no direct link between the sub-indices and the level
of development of the regions. It is impossible to state unequivocally that the higher
education system has the greatest influence on the most developed regions, and vice
versa. The results obtained allow us to conclude that the degree of influence of the
higher education system on regional development is a complex characteristic.
The obtained integral indicator allows only to single out regions with one I4 of the
higher education system in comparison with others (identification of interregional
imbalance). Even high values of the indicator do not mean that regional universities
begin to play the role of centers of education and culture, or in general determine the
level of the region.
An important continuation of the study should be an assessment of the situation in
each region of the country separately. Such analytics will be able to provide
indispensable assistance in determining the differentiated directions for the
development of regional systems of higher education. Such systems should be focused
on maximally promoting the development of territories, taking into account their
specifics.
It is worth noting that the fuzzy model we have developed for determining the I4 can
be refined and adapted to new data. Some input variables may be entered new or
removed. One can extend the range of terms of linguistic variables etc. That is, the
constructed model is flexible in setting and changing parameters. It does not require
complex mathematical calculations (due to the use of Matlab).
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e%20the%20impact%20of%20a%20university%20on%20the%20regional%20economy.p
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