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Dynamical System Modeling and Stability Investigation�DSMSI-2025

May 08-10, 2025, Kyiv, Ukraine

ANALYSIS OF MATHEMATICAL METHODS FOR STRATEGIC MANAGEMENT IN HIGHER EDUCATION INSTITUTIONS

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Kateryna Merkulova, Iryna Lybak,

Shevchenko National University of Kyivliation�

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Introduction

One of the most important problems of society development is the development of education.

Strategic management is a determining factor for the effective operation, development of higher education institutions.

One of the key indicators of strategic management of higher education institutions is the provision of quality educational services.

Using fuzzy logic methods, which allow processing uncertain information and improving the quality of multi-criteria management decisions, it is possible to build a model for assessing the quality of educational services.

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Research methodology

Takagi-Sugeno fuzzy logic methods were used to construct a model for assessing the quality of educational services.

The advantage of fuzzy logic is that, with the same amount of input and output information, the central decision-making unit becomes easier for human perception, and the solution to the complex task of calculating precise actions is replaced by a simpler and more flexible strategy of adaptive adjustment, while maintaining the necessary accuracy of the result.

We chose the Takagi-Sugeno model, which operates with clear values, linguistic variables, and fuzzy sets.

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Experimental research and analysis

Linguistic terms and ranges of input and output variables of the fuzzy model

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Name of variable

Terms, range

MaterialSupport

Low

0-0,5

Medium

0,25-0,75

High

0,5-1

StaffQuality

Low

0-0,5

Medium

0,25-0,75

High

0,5-1

ProcessOrganization

Low

0-0,5

Medium

0,25-0,75

High

0,5-1

StudentMotivation

Low

0-0,5

Medium

0,25-0,75

High

0,5-1

Quality

Low

0-0,5

Medium

0,25-0,75

High

0,5-1

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Research methodology

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Experimental research and analysis

The next step was to build the Takagi-Sugeno fuzzy model in MATLAB:

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  • were added four input variables, which were normalized in the range [0, 1];
  • three linguistic variables (Low, Medium, High) were assigned to each variable using a triangular membership function;
  • the output variable was determined;
  • a rule base was formed (the maximum number of rules - 81 rules).

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Experimental research and analysis

Results of the assessment of the quality of educational services:

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Dynamical System Modeling and Stability Investigation, DSMSI-2025

№

MaterialSupport

x1)

StaffQuality

(x2)

ProcessOrganization (x3)

StudentMotivation (x4)

Коментар

Вихід

1

0.5

0.5

0.5

0.5

All average

0.5000

2

0

0

0

0

Minimum values

0.2000

3

1

1

1

1

Maximum values

0.9000

4

0.8

0.2

0.3

0.4

High material base, other - weak

0.2000

5

0.2

0.9

0.4

0.6

Low base, quality staff

0.2000

6

0.75

0.75

0.75

0.75

Above average

0.9000

7

0.25

0.25

0.25

0.25

Below average

0.2000

8

0.5

1

1

0

Extreme values (mixed)

0.2000

9

0.6

0.4

0.5

1

High motivation of students

0.2000

10

0.3

0.8

0.9

0.3

Good organization, low motivation

0.2000

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Experimental research and analysis

The next step was visualization, meaning plotting surface graphs to show the dependence of the model output on two input variables with the other two fixed.

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Experimental research and analysis

Also, we estimated the sensitivity for each of the parameters. As a result, we obtained the following sensitivity coefficients:

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  • MaterialSupport – 0.11667;
  • StaffQuality – 0.11667;
  • ProcessOrganization – 0.04375;
  • StudentMotivation – 0.05625.

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Conclusion

  • As a result of plotting the dependence of the input variables of staffing and motivation of applicants on the model result, it was found that it is important to have a balanced interaction between research and teaching staff and applicants.
  • The sensitivity assessment for each of the parameters was also conducted and it was found that the greatest impact on the quality of educational services is made by material and technical support and staffing. In turn, the organization of the educational process and the motivation of students have a more moderate impact.
  • In further research, it is planned to validate the model based on real data collected through a survey of students and academic staff, as well as on the data contained in the accreditation reports of educational programs.

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Thank you for your attention