Программные продукты и системы, 2023, том 36, № 1

Научно-исследовательский институт

«Центрпрограммсистем»

Программные

продукты и системы

НАУЧНЫЙ ЖУРНАЛ

2023, том 36, № 1

(год издания тридцать шестой)

Главный редактор

Г.И. САВИН, академик РАН

SOFTWARE & SYSTEMS

Research journal

2023, vol. 36, no. 1

Editor-in-Chief 

G.I. SAVIN, Academician of the Russian Academy of Sciences

Research Institute CENTERPROGRAMSYSTEM

 ПРОГРАММНЫЕ ПРОДУКТЫ И СИСТЕМЫ
Научный журнал 

2023. Т. 36. № 1
DOI: 10.15827/0236-235X.141

Главный редактор 

Г.И. САВИН, академик РАН

Научные редакторы номера:

С.В. УЛЬЯНОВ, д.ф.-м.н., профессор

К.А. МАМРОСЕНКО, к.т.н., доцент

А.Н. СОТНИКОВ, д.ф.-м.н., профессор

Издатель НИИ «Центрпрограммсистем»

(г. Тверь, Россия)

Учредитель В.П. Куприянов

Журнал зарегистрирован в Роскомнадзоре 3 марта 2020 г.

Регистрационное свидетельство ПИ № ФС 77-77843

Подписные индексы в каталогах

Почты России ПП879

Урал-Пресс 70799

ISSN 0236-235X (печатн.)
ISSN 2311-2735 (онлайн)

РЕДАКЦИОННАЯ КОЛЛЕГИЯ

Семенов Н.А. – заместитель главного редактора, д.т.н., профессор Тверского государственного технического 
университета (г. Тверь, Россия)
Сотников А.Н. – заместитель главного редактора, д.ф.-м.н., профессор, заместитель директора 
Межведомственного суперкомпьютерного центра РАН (г. Москва, Россия)
Афанасьев А.П. – д.ф.-м.н., профессор Московского физико-технического института (технического университета), 
заведующий Центром распределенных вычислений Института проблем передачи информации РАН (г. Москва, Россия)
Баламетов А.Б. – д.т.н., профессор Азербайджанского научно-исследовательского и проектно-изыскательского института 
энергетики (г. Баку, Азербайджан)
Батыршин И.З. – д.т.н., профессор Мексиканского института нефти (г. Мехико, Мексика)
Борисов В.В. – д.т.н., профессор филиала Национального исследовательского университета «МЭИ» в г. Смоленске 
(г. Смоленск, Россия)
Голенков В.В. – д.т.н., профессор Белорусского государственного университета информатики и радиоэлектроники 
(г. Минск, Беларусь)
Елизаров А.М. – д.ф.-м.н., профессор Института математики и механики им. Н.И. Лобачевского Казанского федерального 
университета (г. Казань, Россия)
Еремеев А.П. – д.т.н., профессор Национального исследовательского университета «МЭИ» (г. Москва, Россия)
Кузнецов О.П. – д.т.н., профессор Института проблем управления РАН (г. Москва, Россия)
Курейчик В.М. – д.т.н., профессор Инженерно-технологической академии Южного федерального университета 
(г. Таганрог, Россия)
Лисецкий Ю.М. – д.т.н., генеральный директор «S&T Ukraine» (г. Киев, Украина)
Мамросенко К.А. – к.т.н., доцент Московского авиационного института (национального исследовательского университета), 
руководитель Центра визуализации и спутниковых информационных технологий НИИСИ РАН (г. Москва, Россия)
Мейер Б. – доктор наук, профессор, заведующий кафедрой Высшей политехнической школы – ETH (г. Цюрих, Швейцария)
Палюх Б.В. – д.т.н., профессор Тверского государственного технического университета (г. Тверь, Россия)
Серов В.С. – д.ф.-м.н., профессор Университета прикладных наук Оулу (г. Оулу, Финляндия)
Сулейманов Д.Ш. – академик АН Республики Татарстан, д.т.н., профессор Казанского государственного технического 
университета (г. Казань, Республика Татарстан, Россия)
Татарникова Т.М. – д.т.н., доцент, профессор Санкт-Петербургского государственного электротехнического университета 
«ЛЭТИ» им. В.И. Ульянова (Ленина) (г. Санкт-Петербург, Россия)
Ульянов С.В. – д.ф.-м.н., профессор, ведущий научный сотрудник Объединенного института ядерных исследований 
(г. Дубна, Россия)
Хорошевский В.Ф. – д.т.н., профессор Московского физико-технического института (технического университета) 
(г. Москва, Россия)
Шабанов Б.М. – д.т.н., чл.-корр. РАН, директор Межведомственного суперкомпьютерного центра РАН (г. Москва, Россия)
Язенин А.В. – д.ф.-м.н., профессор Тверского государственного университета (г. Тверь, Россия)

АССОЦИИРОВАННЫЕ ЧЛЕНЫ РЕДАКЦИИ

Национальный исследовательский университет «МЭИ», г. Москва, Россия
Технологический институт Южного федерального университета, г. Таганрог, Россия
Тверской государственный технический университет, г. Тверь, Россия

АДРЕС ИЗДАТЕЛЯ И РЕДАКЦИИ 
Россия, 170024, 
г. Тверь, просп. Николая Корыткова, д. 3а
Телефон (482-2) 39-91-49
Факс (482-2) 39-91-00
E-mail: red@cps.tver.ru
Сайт: www.swsys.ru

Дата выхода в свет 16.03.2023 г.

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Россия, 170100, г. Тверь, ул. Крылова, д. 26

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Год издания тридцать шестой

Формат 6084 1/8. Объем 184 стр.

Заказ № 13. Тираж 1000 экз. Цена 550,00 руб.

 SOFTWARE & SYSTEMS 
Research journal
2023, vol. 36, no. 1
DOI: 10.15827/0236-235X.141

Editor-in-chief 
G.I. SAVIN, Academician of RAS

Science editors of the issue:

S.V. Ulyanov, Dr.Sc. (Physics and Mathematics), Professor
K.A. Mamrosenko, Ph.D. (Engineering), Associate Professor
A.N. Sotnikov, Dr.Sc. (Physics and Mathematics), Professor

Publisher Research Institute 

CENTERPROGRAMSYSTEM (Tver, Russian Federation)

Founder V.P. Kupriyanov

The journal is registered with the Federal Service 

for Supervision of Communications, Information Technology 

and Mass Communications (Roskomnadzor)

March 3rd, 2020

Registration certificate ПИ № ФС 77-77843

ISSN 0236-235X (print)

ISSN 2311-2735 (online)

EDITORIAL BOARD

Semenov N.A. – Deputy Editor-in-Chief, Dr.Sc. (Engineering), Professor of the Tver State Technical University
(Tver, Russian Federation)
Sotnikov A.N. – Deputy Editor-in-Chief, Dr.Sc. (Physics and Mathematics), Professor, Deputy Director
of the Joint Supercomputer Center of the Russian Academy of Sciences (Moscow, Russian Federation)
Afanasiev A.P. – Dr.Sc. (Physics and Mathematics), Professor of the Moscow Institute of Physics and Technology, 
Head of Centre for Distributed Computing of Institute for Information Transmission Problems 
(Moscow, Russian Federation)
Balametov A.B. – Dr.Sc. (Engineering), Professor of the Azerbaijan Scientific-Research & Design-Prospecting Power 
Engineering Institute (Baku, Azerbaijan)
Batyrshin I.Z. – Dr.Sc. (Engineering), Professor of the Mexican Petroleum Institute (Mexico City, Mexico)
Borisov V.V. – Dr.Sc. (Engineering), Professor of the MPEI Branch in Smolensk (Smolensk, Russian Federation)
Golenkov V.V. – Dr.Sc. (Engineering), Professor of the Belarusian State University of Informatics and Radioelectronics 
(Minsk, Republic of Belarus)
Elizarov A.M. – Dr.Sc. (Physics and Mathematics), Professor of the N.I. Lobachevsky Institute of Mathematics 
and Mechanics of the Kazan Federal University (Kazan, Russian Federation)
Eremeev A.P. – Dr.Sc. (Engineering), Professor of the National Research University “Moscow Power Engineering 
Institute” (Moscow, Russian Federation)
Kuznetsov O.P. – Dr.Sc. (Engineering), Professor of the Institute of Control Sciences of the Russian Academy 
of Sciences (Moscow, Russian Federation)
Kureichik V.M. – Dr.Sc. (Engineering), Professor of the Academy of Engineering and Technology of the Southern
Federal University (Taganrog, Russian Federation)
Lisetsky Yu.M. – Dr.Sc. (Engineering), CEO of S&T Ukraine (Kiev, Ukraine)
Mamrosenko K.A. – Ph.D. (Engineering), Associate Professor of the Moscow Aviation Institute (National Research
University), Head of the Center of Visualization and Satellite Information Technologies SRISA RAS 
(Moscow, Russian Federation)
Meyer B. – Dr.Sc., Professor, Head of Department in the Swiss Federal Institute of Technology in Zurich, ETH 
(Zurich, Switzerland)
Palyukh B.V. – Dr.Sc. (Engineering), Professor of the Tver State Technical University (Tver, Russian Federation)
Serov V.S. – Dr.Sc. (Physics and Mathematics), Professor of the Oulu University of Applied Sciences (Oulu, Finland)
Suleimanov D.Sh. – Academician of TAS, Dr.Sc. (Engineering), Professor of the Kazan State Technical University
(Kazan, Republic of Tatarstan, Russian Federation)
Tatarnikova T.M. – Dr.Sc. (Engineering), Associate Professor, Professor of the St. Petersburg Electrotechnical 
University "LETI" (St. Petersburg, Russian Federation)
Ulyanov S.V. – Dr.Sc. (Physics and Mathematics), Professor of the Dubna International University for Nature, 
Society and Man (Dubna, Russian Federation)
Khoroshevsky V.F. – Dr.Sc. (Engineering), Professor of the Moscow Institute of Physics and Technology
(Moscow, Russian Federation)
Shabanov B.M. – Dr.Sc. (Engineering), Corresponding Member of the RAS, Director of the Joint Supercomputer Center
of the Russian Academy of Sciences (Moscow, Russian Federation)
Yazenin A.V. – Dr.Sc. (Physics and Mathematics), Professor of the Tver State University (Tver, Russian Federation)

ASSOCIATED EDITORIAL BOARD MEMBERS

National Research University “Moscow Power Engineering Institute”, Moscow, Russian Federation
Technology Institute at Southern Federal University, Taganrog, Russian Federation
Tver State Technical University, Tver, Russian Federation

EDITORIAL BOARD AND PUBLISHER OFFICE ADDRESS 
Nikolay Korytkov Ave. 3а, Tver, 170024, Russian Federation
Phone: (482-2) 39-91-49  Fax: (482-2) 39-91-00
E-mail: red@cps.tver.ru

Website: www.swsys.ru

Release date 16.03.2023

Printed in printing-office “Faktor i K”

Krylova St. 26, Tver, 170100, Russian Federation

Published quarterly. 36th year of publication

Format 6084 1/8. Circulation 1000 copies

Prod. order № 13. Wordage 184 pages. Price 550,00 rub. 

Вниманию авторов

Журнал «Программные продукты и системы» публикует материалы научного и научно-практического 

характера по новым информационным технологиям, результаты академических и отраслевых исследований 
в области использования средств вычислительной техники. Практикуются выпуски тематических номеров 
по искусственному интеллекту, системам автоматизированного проектирования, по технологиям разработки 
программных средств и системам защиты, а также специализированные выпуски, посвященные научным 
исследованиям и разработкам отдельных вузов, НИИ, научных организаций. 

Журнал «Программные продукты и системы» внесен в Перечень ведущих рецензируемых научных журналов 
и изданий, в которых должны быть опубликованы основные научные результаты диссертаций на соискание 
ученых степеней кандидата и доктора наук.

Информация об опубликованных статьях по установленной форме регулярно предоставляется в систему 

РИНЦ, в CrossRef и в другие базы и электронные библиотеки.

Журнал «Программные продукты и системы» входит в бвзу данных RSCI, включен в ядро коллекции 

РИНЦ, размещенное на платформе Web of Science в виде базы данных RSCI.

Автор статьи отвечает за подбор, оригинальность и точность приводимого фактического материала. При 

перепечатке ссылка на журнал обязательна. Статьи публикуются бесплатно.

Условия публикации

К рассмотрению принимаются оригинальные материалы, отвечающие редакционным требованиям и со-

ответствующие тематике журнала. Группа научных специальностей: 

1.2. Компьютерные науки и информатика 
1.2.1. Искусственный интеллект и машинное обучение (физико-математические науки). 
1.2.2. Математическое моделирование, численные методы и комплексы программ (физико-математиче-

ские науки, технические науки)

2.3. Информационные технологии и телекоммуникации
2.3.1. Системный анализ, управление и обработка информации (технические науки, физико-математиче-

ские науки). 

2.3.3. Автоматизация и управление технологическими процессами и производствами (технические 

науки). 

2.3.5. Математическое и программное обеспечение вычислительных систем, комплексов и компьютер-

ных сетей (технические науки, физико-математические науки).

2.3.6. Методы и системы защиты информации (технические науки, физико-математические науки).
2.3.7. Компьютерное моделирование и автоматизация (технические науки, физико-математические 

науки).

2.3.8. Информатика и информационные процессы (технические науки).
Работа представляется в электронном виде в формате Word. Объем статьи вместе с иллюстрациями – не 

менее 10 000 знаков. Диаграммы, схемы, графики должны быть доступными для редактирования (Word, 
Visio, Excel). Заголовок должен быть информативным; сокращения, а также терминологию узкой тематики 
желательно в нем не использовать. Количество авторов на одну статью – не более 4, количество статей од-
ного автора в номере, включая соавторство, – не более 2. Список литературы, наличие которого обязательно, 
должен включать не менее 10 пунктов.

Необходимы также содержательная структурированная аннотация (не менее 250 слов), ключевые слова 

(7–10) и индекс УДК. Название статьи, аннотация и ключевые слова должны быть переведены на английский 
язык (машинный перевод недопустим), а фамилии авторов, названия и юридические адреса организаций 
(если нет официального перевода) – транслитерированы по стандарту BGN/PCGN. 

Вместе со статьей следует прислать экспертное заключение, лицензионное соглашение, а также сведения 

об авторах: фамилия, имя, отчество, название и юридический адрес организации, структурное подразделе-
ние, должность, ученые степень и звание (если есть), контактный телефон, электронный адрес. 

Порядок рецензирования

Все статьи, поступающие в редакцию (соответствующие тематике и оформленные согласно требованиям 

к публикации), подлежат двойному слепому рецензированию в течение месяца с момента поступления, ре-
цензия отправляется авторам. 

В редакции сформирован устоявшийся коллектив рецензентов, среди которых члены редколлегии жур-

нала, эксперты из числа крупных специалистов в области информатики и вычислительной техники ведущих 
вузов страны, а также ученые и специалисты НИИСИ РАН, МСЦ РАН (г. Москва) и НИИ «Центрпрограмм-
систем» (г. Тверь).

Редакция журнала «Программные продукты и системы» в своей работе руководствуется сводом правил 

Кодекса этики научных публикаций, разработанным и утвержденным Комитетом по этике научных публи-
каций (Committee on Publication Ethics – COPE).

Программные продукты и системы / Software & Systems
1 (36) 2023

5

Software & Systems
Received 15.06.22, Revised 19.10.22

DOI: 10.15827/0236-235X.141.005-013
2023, vol. 36, no. 1, pp. 005–013

An intelligent system for monitoring and analyzing 

competencies in the learning process

G. Kulikov 1, Dr.Sc. (Engineering), Professor, gennadyg_98@yahoo.com 
V. Antonov 1,2, Dr.Sc. (Engineering), Professor, antonov.v@bashkortostan.ru
L. Rodionova 1, Ph.D. (Engineering), Associate Professor, rodionovaKF@yandex.ru
A. Fakhrullina 1, Ph.D. (Engineering), Associate Professor, almirafax@mail.ru
L. Kromina 1, Ph.D. (Engineering), Associate Professor, luyda-kr@yandex.ru
E. Palchevsky 3, Lecturer, teelxp@inbox.ru 
T. Breikin 4, Ph.D. (Engineering), Associate Professor, t.breikin@shu.ac.uk

1 Ufa State Aviation Technical University, Ufa, 450000, Russian Federation
2 Ufa Law Institute of the Ministry of Internal Affairs, Ufa, 450103, Russian Federation
3 Financial University under the Government of the Russian Federation, 
Moscow, 125993, Russian Federation
4 Sheffield Hallam University, Sheffield, United Kingdom

Abstract. The article proposes an intelligent system (a software-analytical complex) based on an artificial 

neural network for managing the educational process based on data received from corporate business units. 
Modelling business process improvement involves using the Deming cycle. 

The paper presents a structure (model) of a software-analytical complex that makes it possible to identify 

and trace explicitly interconnected vertical and horizontal processes, which gives a formalized description of 
the system that meets the algorithm requirements. There is an ontological model of the program analytics com-
plex structure built; it is linked to a set of solutions using databases and knowledge bases; it is divided into 
classes of objects and categories with hierarchical relationships between them. In order to share this knowledge, 
a specific description of this data must be provided to the SAC. This description must be formal enough to be 
understood by another system and written in the same language. 

The novelty is in the consideration of a variant of solving the problem of integrating information systems 

associated with weakly structured subject-oriented information flows of an educational institution using the 
methods of set theory and category theory. The properties of relations between accounting objects are described
at a high abstraction level; it becomes possible to significantly expand the scope of the proposed method for 
constructing a software-analytical complex based on an ontological model for various subject areas, taking into 
account the multi-level consideration of the subject area itself, the same consideration of finite and infinite 
ranges of values. At the same time, the necessary abstraction level is automatically determined to ensure the 
structural and parametric integrity of the system being formed and the interpretation of the emerging problems 
of data analysis represented by semantic models.

Keywords: additional professional education, competencies, Deming cycle, artificial neural network, for-

mal model, software analytical package. 

Knowledge in the modern world should not 

only correspond to the time, but also to constantly 
improve and accumulate for their effective applica-
tion in the future. In various spheres of their acti-
vity, enterprises record and replenish knowledge in 
the knowledge bases of intelligent information sys-
tems. However, according to modern conditions, 
the issues of intellectual management in the educa-
tional spheres require developing the implementa-
tion of new IT technologies; today there is no intel-
lectual approach to controlling and analysing re-
ceived competencies in the learning process both 
for a university and an enterprise.

It is important to note that nowadays the process 

of introducing information (including intellectual) 
technologies in the framework of education is at an 
advanced stage. For example, in a scientific stu-
dy [1], information technologies are considered as 
a teaching tool in a higher educational institution. 
In [2], it was revealed that information technologies 
in the higher education system increase the educa-
tion effectiveness. The problem of using infor-
mation and communication technologies in the 
educational process of a higher educational institu-
tion is considered in [3]. The work [4] considers in-
formation technologies in the context of their in-

Программные продукты и системы / Software & Systems
1 (36) 2023

6

tegration into the modern process of education in 
higher educational institutions and determines the 
prospects for their successful application in higher 
education. The research [5] aims to link infor-
mation and communication technologies (ICT) in
the processes of dissemination and use of 
knowledge in higher education institutions (HEIs). 
The study [6] analyzes the impact of information 
technologies on the education process in universi-
ties. The analysis of literary sources has revealed 
that the problem of intellectualization of infor-
mation technologies (including for the analysis of 
acquired competencies in training in the higher 
education system) is not considered explicitly.

Thus, the task of developing an intelligent sys-

tem (including a formal model) based on an artifi-
cial neural network for continuous analysis of ac-
quired competencies in the process of studying at a 
university becomes relevant.

The article is further structured as follows:
−
section 2 considers a model of continuous 

improvement of the additional professional educa-
tion processes;

−
section 3 considers the neural network node 

diagram of the software-analytical complex;

−
section 4 discusses the work results.

The model of continuous improvement 

of additional professional education processes

The main goal of the development and imple-

mentation of additional professional education
(APE) is to provide high-quality education for cor-
porate staff in a continuous production process. 
In turn, to ensure continuous adaptation and im-
provement of the educational process at all life cy-
cle (LC) stages of the APE, it is most expedient to 
use the model and the software analytical complex
(PAC) itself, to control and analyze the acquired 
competencies in the APE learning process both 
from the side of the educational institutions, and 
from the bodies controlling the learning process 
(departments and ministries of the Russian Fede-
ration) and interested enterprises.

Such model will make it possible to determine 

the information rules for the interaction of business 
processes, to identify objects in the HSS, to reflect 
the sequence of business processes and perfor-
mance benchmarks.

The formal model of continuous improvement of 

the APE business processes is presented in Figure 1.

In order to organize training in APE programs 

in the planning process (“plan”), regulatory bodies 

(
)
Ob

 
(
)
Ob
Н



GCr (V)

P

D
C

A

Plan

Do
Check

Act

Organisation

P

D
C

A

Plan

Do
Check

Act

University

P

D
C

A

Plan

Do
Check

Act

Supervising bodies, 

agencies

P

D
C

A

Plan

Do
Check

Act

SAC

Act
Plan

Do
Check

N
N
Y


=


(
)
(
)
Z N
Z N
N


=


(
)
(
)
(
)
Ob
Ob
Z N


= 


(
)
Y
Y
Ob


=


GCu (X)

GCra (L)
GCpak (U)

(
)
Ob
F



Fig. 1. The proposed formal model of continuous improvement of APE business processes

Программные продукты и системы / Software & Systems
1 (36) 2023

7

and departments in federal laws and regulations 
determine the basic requirements for the process of 
training students in APE and develop regulatory 
documents. There is a determined list of necessary 
software, equipment, laboratories, etc.; it is pre-
sented as a function Z(N) reflecting the regulatory 
documentation for organizing the educational pro-
cess (plans, work programs, practices, etc.). To 
eliminate disproportions in the labor market, re-
duce the employment time of qualified workers in 
the educational process and increase the level of 
professional preparedness of the population, a set 
of goals and objectives of learning processes is set 
N = {n1, ..., nd} (where d is the number of goals 
and objectives) including vocational retraining 
programs (RP).

At each stage of the described business process, 

the professional competencies Ф(Ob) of the 
learner Ob can be evaluated by the function 
F = {f1, …, fi} ϵ Q reflecting labor actions. Neces-
sary skills in the form of competencies of AVE 
programs from the state (professional standards, a 
reference book of professional competencies, etc.) 
can also be represented by a set of functions 
Ф(Ob)  F, where Q is a set of competencies that 
meet the requirements of the state and employers, 
i.e., a student’s reference model.

The generalized labor functions and actions of 

the student in the APE programs are achieved by 
the value of (Ob) at the “check” stage in the form 
of a final certification. At the final stage – “action”
(“act”), it becomes possible to analyze the fulfill-
ment of requirements both by regulatory authori-
ties and by employers; new and popular areas of 
APE programs are determined in accordance with 
the economy sectors and professional standards 
that ensure the competitiveness of the implemen-
tation of AVE programs.

At the execution stage (“do”), universities draw 

up curricula, regulations, and work programs for 
disciplines. During the educational process of APE 
programs, the object Ob learns new necessary 
knowledge and skills with new values of Ф(Ob) 
and is reflected in the form of a multilinear func-
tion of certain category objects f: Ф(Ob)  Z(N) →
→ Ф(Ob). Based on the multilinearity of the map-
ping and applying the First Isomorphism Theo-
rem [7], we come to the commutativity of the dia-
gram by the representable formula:

(
)
(
)

(
)
(
)
(
)

1

1
2

2

(
)
Ф

Ф (
)
Ф
.

)

: Ф

:

Ф
: Ф(

f
Ob
Z N
Ob

h
Ob
Ob

g
Ob
Z N
Ob



→


→



 



→


Accordingly, the composition of morphisms 

along any directed path depends only on the begin-
ning and end of the path; in our case, the Ob object 

can achieve the required value of new necessary 
knowledge and skills through different sequential 
chains, which opens up opportunities for optimiz-
ing the process itself. The universal object of this 
diagram is the tensor product of Ф(Ob) and Z(N). 
That is, we have the formula:

Ф(Ob) = Ф(Ob)  Z(N),
(1)

where the sign  is a tensor product.

According to our construction, all objects of the 

subject area under consideration are represented 
by their parameter values. To form various alter-
native chains, we can use the ordering of objects 
according to their similarity using the clustering 
method that represents objects as vectors. The nu-
merical parameters of such vectors are attributes of 
the corresponding objects and can be interpreted as 
a geometric location of an object in some space. 
Taking into account the fuzziness (or incomplete-
ness) of data on the properties of objects, we come 
to blurring of the boundaries of clusters and fuzzy 
clustering.

The choice of any alternative chain will be re-

duced to the option of choosing the components to 
be taken into account; the best trajectory of the 
educational process will be chosen according to a 
set of complex fuzzy criteria [8].

In HSS, it is necessary to use continuous infor-

mation support of the life cycle of processes. At 
the life cycle stages of the process under conside-
ration, it is possible to single out the following sub-
sets of criteria for assessing the quality of compe-
tencies from different points of view:

a) GCu(X) – from the university’s point of 

view;

b) GCr(V) – from the organization’s point of 

view;

c) GCra(L) – from the point of view of regula-

tory agencies and authorities;

d) GCpak(U) – from the PAK administrator’s

point of view.

Strengthening control on the part of the state is 

reflected in the requirements for students – the sub-
set L = {l1, …, lk}, as well as universities define 
the requirements in the form of a subset X = {x1,
…, xn}, which is used in the main criteria. All re-
quirements are analyzed and controlled in the sub-
set U = {u1, …, uj}, which allows making timely 
changes and adjustments to the learning process.

In turn, organizations determine the require-

ments for labor activities, the necessary skills and 
knowledge of employees, which can be formalized 
as a subset V = {v1, …, vm}.

There can be following restrictions:
−
on the one hand, the requirements for the 

level of necessary knowledge and skills trained 

Программные продукты и системы / Software & Systems
1 (36) 2023

8

from the professional standard by employers, 
which we will present in as a function

2
1
{
,...,
}
;
i
M
 = 



−
on the other hand, university’s requirements 

to the level of students in the programs of further 
vocational education, which can be represented as 
a function 

3
1
{ , ...,
}
,
i
H
h
h
M
=

where M is the set 

of requirements from the professional standard for 
a specialist, reflected in generalized functions.

The following formulas represent a system that 

allows achieving personal goals and objectives:

Φ(
)
,

Φ(
)
,

Φ(
)
.

Ob

Ob
H

Ob
F

 








(2)

The requirements of the professional standard 

that determine the experience gained can be repre-
sented as a function depending on the set of goals 
and objectives for implementing additional profes-
sional education Y(N). When the requirements 
change, a set Y(N) = Y(N)  Ф(Ob) is formed, for 
which Y(N)  Ф(Ob) is true. Based on these re-
quirements, a set of refined goals and objectives N'
can be formed, represented by the formula:

N' = N Y(N).
(3)

In view of the foregoing, the following formula 

can represent the formation of new regulatory do-
cuments:

Z(N) = Z(N)  N'.
(4)

Thus, a formal model has been developed for 

the continuous improvement of the business pro-
cesses of APE during the life cycle of systems, 
which makes it possible to form a single data re-
pository of the HSS.

An ontological model was built to form the 

PAC structure. The formal model of the PAK on-
tology is represented by an ordered triple of the 
following form [8]: PAK = M, R, U, where: M is 
the set of HSS modules; R is a set of relations be-
tween HSS modules; U is a set of functions per-
formed by HSS modules.

Many scientists mention the effectiveness of 

using the ontological approach when designing 
systems using artificial intelligence [8, 9]. Thus, 
the list of HSS modules can be represented as a fi-
nite set of the form M = {M1, …, Mn}. The ele-
ments of the set M are described by m features 
P = {p1, …, pm}. Thus, each element M has 
the form Мi= {pi1, pi2, …, pik}, where k is the num-
ber of instances of the j-th attribute p of the ele-
ment Мi.

The list of module functions can be represented 

as a finite set of the form U = {u1, u2, …, un}. The 
elements of the set U are described by a pair of the 

following form ui = {name, source}, where name 
is the module name, source is the set of module 
functions, I = 1, …, n.

Thus, based on the above, the ontology model 

has the following form: OPAK = {PAK, R, U}. Fi-
gure 2 shows a fragment of the ontology described 
by this structure. The ontology editor Protege 
using the OntoGraph plugin was chosen as a soft-
ware tool for creating an ontology.

The ontological model of the HAC structure is 

associated with a set of solutions using databases 
and knowledge and is divided into classes of ob-
jects and categories with a hierarchy relationship 
between them. To share this knowledge, it is ne-
cessary to provide a specific description of these 
data in the PAK. Such description must be suffi-
ciently formal for understanding by another sys-
tem and also written in the same language.

A scheme of a pak neural network node

Intelligent systems based on artificial neural 

networks currently allow solving various problems 
such as pattern recognition, forecasting, optimiza-
tion, control [10].

The development of a HSS for monitoring and 

analyzing the acquired competencies when learn-
ing under APE programs also provides for the 
presence of a neural network node, which is an ar-
tificial neuron scheme corresponding to a formal 
model of continuous improvement of business pro-
cesses based on the PDCA cycle. Thus, the neural 
network node scheme consists of the following 
sections: plan, do, check, act (Fig. 3).

Module_APK

APE_species_

module

Receiving_module_

at_DPO

Intelligence_aNa-

lyze_module

Educational_

prOgram_maNa-
gement_module

User_categories_

module

Module_of_general_

developmental_

programs

Module_of_retrain-

ing_programs

Module_of_advan-

ced_training_

programs

Reporting_module

Attendance_module

Listener_registries_

module

Registry_module

Grade_module

Document_genera-

tion_module

Fig. 2. Ontological model of the PAC structure

Программные продукты и системы / Software & Systems
1 (36) 2023

9

In the “plan” section, the input signal is the value 

corresponding to the trainee's competencies – Ф(Ob).

The weight, in turn, is a vector of three ele-

ments:

−
many requirements for the level of trainees 

on the part of employers – ;

−
a set of goals and objectives of the learning 

process – N;

−
a set of requirements for the competencies 

of trainees from the state (professional standards, 
a reference book of professional competencies, 
etc.) – F.

Forming regulatory documentation for 

organizing the educational process

(
)
Ob
Ф

yes

N

(
)
F
N,
,


H

(
)
F
Ob
Ф


( )
N
Z

(
)
( )
N
Z
Ob
Ф


( )
Ob
Ф

(
)
F
,


(
)


 Ob
Ф

(
)
F
Ob
Ф



End-user categories

Managers

top executives

Managers

middle management

Practical
workers
Analysts 
Guest (external 

users)

( )
(
)
Ob
Ф
N
Y
=


Y
N
N


=


yes
no

(
)
F
N,
,


(
)
Ob
Ф

(
)
Ob
Ф

SAC

Block for 

remembering the 

states of the 

received 

experience
(
)
N
Y 

Архив (ХД)

Semantic layer

Operational data 
presentation unit
Intelligent Analyzer
Presentation unit

Information about the 

experience gained by K-users
Data showcases

( )
N
Y

plan

do, 

check
act

Fig. 3. A scheme of a neural network node (corresponding to the formal model of continuous improvement

of business processes based on the PDCA cycle)

Программные продукты и системы / Software & Systems
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10

In the first block of the “plan” section adder, 

the trainee’s competencies are compared with the 
state requirements for the considered competen-
cies of trainees.

If student's competencies exceed the state re-

quirements, then the weight vector is adjusted in 
the PAK in the section of the set of goals and ob-
jectives, which can be achieved, for example, by 
raising the level of qualifications, etc. If the re-
quirements of the state exceed student’s compe-
tence, then there will be a transition to the second 
block of the adder. Here, the vector of the three 
elements described above is the input, and the 
weight, in turn, is university's requirements for 
the level of students in the APE programs.

In the second block of the adder, regulatory 

documentation for organizing the educational pro-
cess (plans, work programs, practices, etc.) is 
formed based on a set of goals and objectives –
Z(N).

The “do, check” section on the presented 

scheme of a neural network node involves the im-
plementation of a learning process (training ses-
sions are held according to a training schedule, in-
cluding at the enterprise’s material and technical 
base). In this case, the input is also a value corre-
sponding to student’s competencies – Ф(Ob), the 
weight is represented by the documentation for or-
ganizing an educational process – Z(N). The adder 
block of the “do, check” section is aimed at replen-
ishing competencies with new values.

The “act” section receives competencies as in-

put supplemented with new values – Ф(Ob), the 
weight is a vector of two elements:

1) requirements for the level of trainees from 

the part of employers – ;

2) requirements for the competencies of train-

ees from the state (professional standards, a refe-
rence book of professional competencies, etc.) – F.

The adder of the “act” section is aimed at iden-

tifying the compliance of competencies sup-
plemented with new values – Ф(Ob) with the re-
quirements for the level of trainees from the em-
ployers – , as well as the requirements for the 
competencies of trainees from the state – F.

In the case when the competencies replenished 

with new values – Ф(Ob) exceed the requirements 
for the level of trainees from the employers – ; 
as well as the requirements for the competencies of 
trainees from the state – F, in the PAC, the weight 
vector is adjusted in the section of the set of goals 
and objectives associated with the refinement of 
goals, which, similarly to the plan section, can be 
achieved, for example, by raising the level of qua-
lifications, etc.

If the requirements for the level of trainees on 

the part of employers are ; as well as the require-
ments for the competencies of trainees from the 
state – F are not achieved, then the learning 
process should be started from the beginning.
However, it is necessary to adjust the values of the 
weight vector of the plan section aimed at lowering 
the requirements for learning outcomes.

The result of the final certification, which is the 

output from the adder, section “act”, is entered into 
the block for storing the states of the experience 
gained Y'(N).

Based on the above and the studies [11–13], the 

sets of objects of each section (Fig. 3) form cate-
gories with the vector relations between them that
are defined by “adjacent” functors. This allows us 
to apply the same conclusions to each of the above 
sections and to consider any of them in detail and 
use the most important property of adjoint func-
tors – their continuity.

The full functioning of the neural network node

is due to paying special attention to such a property 
of the neural network as the ability to learn based 
on data coming from the external environ-
ment [14–16]. Currently, neural networks are 
taught by the following methods: supervised and 
unsupervised. The choice of a method depends on 
the training conditions of a neural network [17].

The presented diagram of a neural network 

node involves using a supervised learning algo-
rithm when a training data set is an input, on the 
basis of which the neural network identifies de-
pendencies and correctly responds to an incoming 
test data set.

Thus, the knowledge received from a teacher 

will be transferred to the network in full. After 
completing the training, a teacher can be turned off 
and the neural network will go into autonomous 
operation.

It should be noted that the presented abstract 

model of a neural network node can also be applied 
to automate other business processes in the field of 
education.

Conclusion

We propose the concept and architecture of 

building a PAC, a researched subject-oriented area 
in the field of education.

It is shown that it is expedient to use the deve-

loped models in implementing HSS in order to per-
form operational adjustments to the learning process.

The constructed neural network node provides 

an opportunity to implement a formal model of 
continuous improvement of business processes 
based on the PDCA cycle. The result of the work