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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Mathematical Model and Approaches to Quantitative Analysis of Metadata of Scientific Articles⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Hryhorii Hnatiienko</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Vitaliy Snytyuk</string-name>
          <email>snytyuk@knu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliia Tmienova</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oleksii Ivanchenko</string-name>
          <email>ivanchenko.oleksii@knu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Yevhen Patkin</string-name>
          <email>yevhen.patkin@knu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Taras Shevchenko National University of Kyiv</institution>
          ,
          <addr-line>Volodymyrs'ka str. 64/13, Kyiv, 01601</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <fpage>103</fpage>
      <lpage>119</lpage>
      <abstract>
        <p>This article is devoted to the study of metadata of scientific articles. Quantitative analysis of this area of research contributes to the structuring of the scientific space. The mathematical model and some approaches to the quantitative analysis of metadata of scientific article are described. The structure of metadata is formalized. In particular, information about authors is structured and the tasks that arise when analyzing this metadata attribute are presented. The structure of the title of a scientific article, its functions, requirements for this attribute, problems of analyzing the titles of scientific articles are considered. The function of membership of the number of words in the title of the article is built. The abstract of a scientific article, its structure, functions of the abstract, requirements for this metadata attribute are investigated, and the problems of analyzing abstracts are presented. The requirements for the set of keywords are also analyzed and the membership function for the number of keywords in a scientific article is constructed. The problems and approaches to the description and analysis of keywords are presented.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;scientific research</kwd>
        <kwd>scientific space</kwd>
        <kwd>scientometric databases</kwd>
        <kwd>similarity measures</kwd>
        <kwd>metadata</kwd>
        <kwd>authors</kwd>
        <kwd>title</kwd>
        <kwd>abstract</kwd>
        <kwd>keywords 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Scientific activity in general, scientific research, and the vast majority of scientific results are
unpredictable, and thus the scientific space is a poorly structured area [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ]. This phenomenon has
been studied from different perspectives for many centuries [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ] , but this area of research remains
relevant today [
        <xref ref-type="bibr" rid="ref5 ref6">5, 6</xref>
        ] . The scientific results obtained in the field of research of scientific space [
        <xref ref-type="bibr" rid="ref7">7, 8</xref>
        ]
contribute to additional structuring of scientific space, its formalization and, thus, to obtaining new
knowledge about this important area of cognition.
      </p>
      <p>
        Scientific publications are one of the indicators of success in the competitive environment of the
academic community [
        <xref ref-type="bibr" rid="ref8 ref9">9, 10</xref>
        ]. The number and quality of scientific publications is an indicator of the
scientific level of both each individual scientist and the scientific institution as a whole. Therefore,
the study of the relationships associated with scientific publications is a relevant and promising area
of analysis [
        <xref ref-type="bibr" rid="ref10 ref11">11, 12</xref>
        ].
      </p>
      <p>It should be noted that a scientific publication is an electronic or paper publication that promotes
the publication of the results of theoretical or experimental research. Such scientific publications are
usually intended for professionals and for scientific work. They are the main source of formalized
authorship and one of the ways to establish scientific priority.</p>
      <p>0000-0002-0465-5018 (H. Hnatiienko); 0000-0002-9954-8767 (V. Snytyuk); 0000-0003-1088-9547 (N. Tmienova);
00000002-8526-8211 (Ivanchehko); 0009-0001-2538-1204 (Y. Patkin)</p>
      <p>A scientific article is a type of scientific publication that describes a study or a group of studies
related to a single topic and is written by scientific authors. A scientific article is one of the most
common ways to publish scientific results.</p>
      <p>
        In this article, we will focus primarily on defining the quality and structure of a scientific article.
Of course, these aspects are present in any formalized and published scientific article and, surely,
they are not the actual scientific result. However, indirectly, scientific results, their recording and
popularization largely depend on the correctness of the formal part of scientific publications [
        <xref ref-type="bibr" rid="ref12 ref13">13, 14</xref>
        ].
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. The main functions of scientific articles</title>
      <p>
        Scientific publications perform several functions [
        <xref ref-type="bibr" rid="ref14">15, 16</xref>
        ], which are interrelated and naturally
complement each other:
publishing the results of scientific article;
recording the completion of a certain stage of research in general;
confirmation of the fact of approbation or implementation of research results;
providing primary scientific information to the scientific community;
notification of the emergence of new scientific knowledge and securing its authorship;
transfer of new individual scientific results to the public domain;
serve as a source of data for scientometric databases;
contribute to raising the formal rating of a researcher;
provide an opportunity to adequately determine the winners of formal or informal
competitions in the educational and scientific environment;
evidence of the researcher's personal contribution to the development of a scientific problem
to determine his relative contribution to the work of the research team;
ensuring opportunities for transparency and quantitative, reliable reporting;
satisfy the interests of higher education institutions and academic institutions whose main
output is scientific results
help to establish the author's priority when comparing similar scientific articles, scientific
ideas, etc.
confirm the reliability of the main results and conclusions of the research article, its novelty
and scientific level.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Metadata structure for scientific articles</title>
      <p>
        Different researchers have some disagreements about which elements of scientific publications
should be considered metadata [
        <xref ref-type="bibr" rid="ref15 ref16">17, 18</xref>
        ]. In this article, we will consider such elements of scientific
publications as metadata and comprehensively study them:
information about the authors ( A) ;
title of the publication (T ) ;
keywords (W ) .
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The set of metadata of scientific articles can be represented as a tuple:
      </p>
      <p>A,T , B,W .
(1)</p>
      <p>The metadata of a scientific article is an important part of scientific research: they are symbiotic
in nature, and the importance of each of the above elements is unique in its own way. The absence
of any of the above metadata elements has a significant impact on the quality of a scientific
publication, and incorrect metadata design significantly affects the effectiveness of the entire
scientific publication.</p>
      <p>
        In general, metadata provides an opportunity for additional analysis of the scientific space and
helps to structure research papers, turning a poorly structured subject area into a structured one [
        <xref ref-type="bibr" rid="ref1 ref17">1,
19</xref>
        ].
      </p>
      <sec id="sec-3-1">
        <title>3.1. Problems of metadata analysis</title>
        <p>
          In many practical cases, there is a need to analyze all metadata components. And with regard to
the first three components of tuple (1), algorithms for comparing, determining preference relations,
their metricizing, calculating similarity measures of the components of tuple (1), etc. are often used
[
          <xref ref-type="bibr" rid="ref18">20</xref>
          ].
        </p>
        <p>
          These are just some of the common problems that are solved with the help of metadata or on the
basis of metadata-related information:
•
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•
•
•
•
making a decision on the official indexing of a scientific paper in a scientometric database
[
          <xref ref-type="bibr" rid="ref19">21</xref>
          ];
facilitating automated marketing of authors of well-described and properly formatted
research papers;
solving the problem of reviewing articles in scientific journals or appointing reviewers to
select materials for international conferences, symposia, etc.;
justified selection of scientists to evaluate projects submitted to research project
competitions, student research competitions, etc.;
determination of opponents and reviewers of one-time specialized academic councils when
awarding the measure of Doctor of Philosophy [
          <xref ref-type="bibr" rid="ref21 ref22">23, 24</xref>
          ]
in many other important activities and events that require formalization and justification of
the choice [
          <xref ref-type="bibr" rid="ref23 ref24">25, 26</xref>
          ].
        </p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Structure of information about authors</title>
      <p>Information about the authors ( A) is a metadata attribute and usually contains the following basic
characteristics ai  A, ai = (ai1,..., ai6), i  I , where</p>
      <p>I − a set of indexes of information about authors;
ai1 − the last name and first name or initials of the author or authors;
ai2 − academic measure, academic title, honorary title, etc.;
ai3 − data on the authors' affiliations: position and official name of the institution (enterprise,
organization) at the main place of work, city, country, e-mail address, home and mobile phone
numbers of the key author, etc.;
ai4 − ORCID identifiers;
ai5 − author profiles in scientometric databases;
ai6 − other information about the authors.</p>
      <sec id="sec-4-1">
        <title>4.1. Problems of analyzing information about authors</title>
        <p>
          When analyzing the characteristics of authors, a number of problems arise that should be
formalized and solved in order to structure the scientific space and solve other actual problems. Such
105
problems are solved, in particular, to improve the scientific space and develop open science trends
[
          <xref ref-type="bibr" rid="ref25 ref26">27, 28</xref>
          ]. In particular, the following problems can be solved:
•
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•
•
•
clustering of authors of scientific articles based on the analysis of their profiles in
scientometric databases;
identification of informal research groups based on the analysis of author profiles and other
indicators;
determining the level and number of indicators of mutual influence in informal research
groups;
determining the dynamics of authors' publications, their productivity, publication activity,
creativity, etc.;
detecting cases of popularity manipulation based on the analysis of author profiles.
        </p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Structure of the title of scientific article</title>
      <p>The title of a scientific article (T ) is a metadata attribute and, in turn, has a number of characteristics
that will be discussed below.</p>
      <sec id="sec-5-1">
        <title>5.1. Problems of metadata analysis</title>
        <p>It is known that in 70% of cases when readers first read a scientific paper, its title is the only factor
that focuses the attention of readers of scientific articles. It is believed that the probability that a user
will skip to the next paragraph of the article after the title if it does not attract his attention is reduced
by 10 times. So, the following heuristic can be derived from this.</p>
        <p>Heuristic H1. For every person who reads the entire article, there are hundreds of people who
read the title without looking at the article.</p>
        <p>The title is also the main search criterion in scientometric databases, i.e., we have such ranking
by a set of metadata attributes (1) in situations of determining the impact of metadata in studies with
an undirected search for information sources:</p>
        <p>T W</p>
        <p>B</p>
        <p>A .</p>
        <p>We will assume that  i T ,i  I = 1,..., n , where n − is the number of studied titles.</p>
        <p>
          All metadata attributes of a scientific article are important, but from the point of view of
qualitative preparation of the article for publication, from the point of view of its correct formatting,
from the point of view of its indexing in scientometric databases and the reliability of using the
scientific potential of the article for its dissemination in the scientific space, the most adequate is the
ranking of attributes of type (2) [
          <xref ref-type="bibr" rid="ref27 ref28">29, 30</xref>
          ]. After all, most bibliographic search engines, databases, or
journal websites rely heavily on the title of the article when implementing the search algorithm.
        </p>
        <p>Here are the criteria for a good title name:
f1 ( i ) − relevance of the article's concept to the subject matter of the publication;
f2 ( i ) − title reflects the subject of the study, not just the result;
f3 ( i ) − no "screaming" headlines in the style of the "yellow press" are used;
f4 ( i ) − no verbs are used;
f5 ( i ) − no vulgarities are used;
f6 ( i ) − the content of the article is described as accurately and discreetly as possible;
f7 ( i ) − the essence of the paper is concisely stated;
f8 ( i ) − matching the length of the title to the editorial requirements.
(2)</p>
        <p>It is believed that a successful title of a scientific article guarantees interest in this article on the
part of readers and the corresponding intensity of dissemination of the article in the scientific
community.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. Requirements for the title of a scientific article</title>
        <p>The title of a scientific article should clearly define the main purpose of the article, begin with the
name of the research object, and attract the attention of a potential reader. A properly formed title
of any scientific article  i T ,i  I , should meet at least several reasonable requirements. When
formulating a title, you should be guided by certain principles, including the following:
g1 ( i ) − adequacy of the article's content;
g2 ( i ) − specificity of the wording;
g3 ( i ) − informativeness of the wording (the measure of informativeness will be developed by
the authors in further research);</p>
        <p>g4 ( i ) − absence of such phrases as: "Research of the question", "Research problems", "Some
research questions", "Ways of solving", etc.;
g5 ( i ) − no abbreviations and acronyms other than commonly used ones;
g6 ( i ) − clarity, capacity and conciseness of the main idea of the article in the title;
g7 ( i ) − absence or minimization of keywords in the title of the article in order to increase the
number of indicators for indexing the article in scientometric databases;</p>
        <p>g8 ( i ) − correspondence between the title and purpose of the article, the main results and
conclusions (the measure of such correspondence will also be developed by the authors in further
research);
g9 ( i ) − absence of common phrases in the title name;
g10 ( i ) − observance of the correct word order: important words should always be listed in the
title in the first place.</p>
        <p>Following the principles of g1 ( i ) − g10 ( i ),i  I , the researchers believe that a good title of a
scientific article increases the number of readers of a scientific article, its scientometric indicators,
increases the popularity of the authors of a scientific article in the scientific space, etc.</p>
        <p>A good title for a scientific article should contain the following components:
 iR − outcome (in particular, principles, models, methods, classifications, information technology,
constructed clustering, etc.);
 iO − the object of research;
 iN − brief information about the scientific novelty, i.e., what distinguishes it from all other
scientific articles and highlights what has not been done before.</p>
        <p>That is, a good title of the article should be expressed by a formula:</p>
        <p> i = iR + iO + iN ,i  I ,</p>
        <p>Moreover, the "+" sign in formula (3) reflects the concatenation of the components of the title of
a scientific article.
(3)</p>
      </sec>
      <sec id="sec-5-3">
        <title>5.3. The problem of analyzing the titles of scientific articles</title>
        <p>To formalize the research of the title of a scientific article, we can formulate and study different
types of problems that are formalized in different classes of mathematical models. In particular, the
following aspects of the title of a scientific article should be investigated:
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name structure;
the title corresponds to the content of the scientific article;
matching the length of the article title to a high value of the membership function that will
be built below;
the article and its title belong to the research areas declared by the authors according to the
classification of scientometric databases or other indicators;
the quality of the article's design in terms of external attributes, in particular, the
requirements for the title.</p>
        <p>In order to obtain high-quality results in solving these problems, it is necessary to choose the
appropriate areas of research.</p>
      </sec>
      <sec id="sec-5-4">
        <title>5.4. Length of the title of the scientific article</title>
        <p>Some values are inappropriate and incorrect to represent in a fixed form. By their construction
and function, they are interval. Limiting the intervals in such cases is violence against experts and
leads to deliberate a priori inaccuracy in expert assessments, i.e. deliberate conformism of experts.</p>
        <p>To determine the recommended number of words in the title of a scientific article, the authors of
this paper conducted a computational experiment. It should be emphasized that the sample is not
representative, but it largely indicates trends in the requirements of scientific editors of popular and
important scientific journals for recommendations on the length of article titles.</p>
        <p>The authors of this article have studied 55 websites that contain information on the rules for
formatting scientific articles. Based on the analysis of sites found by the Google search engine using
the queries "Number of words in the title of a scientific article", "Length of the title of a scientific
article", "Requirements for the title of a scientific article", Table 1 was compiled.</p>
        <p>It is obvious that the presentation of information in Table 1 is not only incomplete, but also
contains some "exotic" requirements for the number of words in the title. We will not exclude any
of the editors' suggestions from the generated data set and will introduce appropriate heuristics for
greater certainty.</p>
        <p>Heuristic H2. To fill in row 8 of Table 1, we assume that the lower bound of the recommended
word count is 5. For rows 9 and 10, the lower bound is 6, and for row 11, the lower bound is 7. For
lines 13 and 15, the lower bound is 3.</p>
        <p>Heuristic H3. For row 12 of Table 1, the upper bound is 13.</p>
        <p>Supplementing Table 1 with heuristic H2 and heuristic H3 and arranging the boundaries of the
intervals presented in the table in ascending order, we obtain Table 2.</p>
        <p>Note 1: The number of rows in Table 2 has decreased compared to the number of rows in Table 1
because after the introduction of the H2 heuristic and the H3 heuristic, the values of some rows
coincided and the corresponding rows were merged.</p>
        <p>To visualize the information in Table 2, let's plot the number of words in the title recommended
by editors and present it in Figure 1. The numbers in the cells on the orange background reflect the
frequency of use of the corresponding interval on websites based on queries to the Google search
engine.</p>
        <p>To build a membership function for the number of words in the title of a scientific article, we
applied the layering method using the data presented in Table 2. The results of the layering method
are approximated by a trapezoidal membership function. The results of this procedure are shown in
Figure 2. In this case, the maximum values of the membership function are in the interval with the
boundaries of 6-7 words in the title of the scientific article.</p>
        <p>The membership function of the indicator "Number of words in the title of a scientific article",
calculated as a trapezoid, is as follows:
 0,   1, 
 ( −1) / 5, 1   6, </p>
        <p>
Т ( ,1,6,7,15) =  1, 6   7 
(15 − ) / 8, 7   15,

 0,   15  .</p>
        <p>If the membership function is constructed based on the frequency of values, as shown in Figure
1, i.e., based on the number of sites represented in the last column of Table 2, the membership
function will look like Figure 3. In this case, the best approximation is the triangular membership
function. The membership function reaches its maximum value at point 7, which corresponds to the
number of words in the title of the scientific article.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Research of Abstract of the scientific article</title>
      <p>The Abstract is an important attribute of a scientific article and plays an important role in the
realization of the main functions of a scientific publication described in Section 2 of this article.
According to the state of research on this metadata attribute, the Abstract (B) is more important than
the Author Information (A) and inferior to the Title (T) and Keywords (W), as reflected in the ranking
(2). This situation indicates, first of all, the need for further in-depth study of this metadata attribute
of a scientific article.</p>
      <sec id="sec-6-1">
        <title>6.1. Structure, functions, and requirements for abstract</title>
        <p>An important indicator of an abstract of a scientific article is its structure. In general, the structure
of an abstract should include:
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information about the main ideas and conclusions of the research;
a brief description of the main content of the article;
a list of the main issues covered in the article;
information about the purpose of the article and its scientific value;
subject of the research;
formulation of the problem;
ways to solve the problem;
the topic of a scientific article;
the purpose of the article;
description of methods, research methodology or methodological justification;
information indicating the relevance of the issue;
scientific novelty of the work and a description of its scientific significance;
a brief description of the experimental studies;
main results of the research;
the scope of the results;
description of the practical significance of the results and their practical value;
brief conclusions about the research work.</p>
        <p>The structure of an abstract may contain a different number of the above components in a
different order. However, the success of a research paper largely depends on the correct structure of
the abstract. An abstract includes the following attributes:
b1j − presents a description of the main topic;
b2j − reflects the problem discussed in the article;
b3j − focuses on the research object presented in the article;
b4j − summarizes the purpose of the research work;
b5j − presents and announces the main results of the work;
b6j − contains the scientific novelty of the study in comparison with other scientific works related
to the topic and purpose of the research;
b7j − gives the reader a complete picture of the content of the research paper
b8j − conveys information about the article, not just a summary of that information.
A well-prepared abstract should contain all these characteristics: bj = (b1j ,...,b8j ), j  J .
The abstract must additionally satisfy the following heuristic.</p>
        <p>Heuristic H4. An important characteristic of a well-designed scientific article is a certain
predefined level of similarity between the abstract (B) and the article content, title (T), and keywords
(W).</p>
        <p>At the same time, an important requirement for this metadata attribute is that the content of the
abstract should not coincide with the text of the main part of the article or the conclusions; the
purpose of the abstract is to attract the reader's attention.</p>
        <p>Heuristic H5. The abstract is read by at least 100 times more people than the scientific article itself.</p>
        <p>The requirements of different editorial boards for abstracts are varied and have significant
differences. The length of the abstract depends on the requirements of the editorial board, the field
of science, the direction of research, etc. In this case, it is impractical to build a membership function
for the length of the abstract. However, the information on the size of abstracts studied by the authors
of this paper is summarized in Table 3.</p>
        <p>Note 2: Some editorial boards, for example, for articles in the humanities, set a maximum length
limit for abstracts and keywords of 1800 characters. Other editorial boards set a range of 1800-2500
characters. Other quantitative values are also found among the requirements.</p>
      </sec>
      <sec id="sec-6-2">
        <title>6.2. Problems of abstract analysis</title>
        <p>
          As noted above, the abstract (B) as an attribute of the metadata of a scientific article is currently
the least formalized and its analysis can be largely automated in the future. For this purpose, the
following problems should be formulated and solved, in particular:
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•
•
•
defining tools for creating an abstract;
studying the similarity measure between the existing abstract of a published article and the
automatically generated one;
generating text abstracts using different approaches and determining the similarity measure
between the generated abstracts in order to identify the tools that best generate text abstracts
in the selected field of knowledge;
using abstracts to find reviewers for a journal or conference;
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•
determining whether the abstract reflects the content of the article in quantitative terms
calculating the quantitative correlation between the abstract and the title of the article;
calculation of quantitative correlation indicators between the abstract and the keywords of
the article;
formalizing the condition and determining whether the abstract meets the restrictions of the
editorial board;
determining the direction of the research and deciding the area in which the article need to
be included, in particular, building the appropriate membership function;
monitoring the existing similarity measures between texts based on abstracts and developing
new similarity measures, if necessary;
classification by abstracts of the materials submitted to the scientific event [
          <xref ref-type="bibr" rid="ref29">31</xref>
          ] of
publications in accordance with the declared areas (sections) of the scientific event.
        </p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>7. Researching a set of keywords for a scientific article</title>
      <p>To further study this metadata attribute of a scientific article, it is advisable to first introduce a
definition of this attribute.</p>
      <p>Definition. A keyword is a word or a stable phrase from the text of an article that carries a
semantic load in terms of information retrieval. The set of keywords should reflect the main content
of the scientific article out of context. In addition, keywords should be specific, relevant to the subject
area under study, meaningful, and unique.</p>
      <p>Keywords are intended for the efficient use of search engines and the systematization of articles
by topics. Keywords are used to index scientific articles in databases that abstract the material.</p>
      <p>Keywords can also be used to build a citation index. Let's formulate the basic requirements for
keywords:
wi1 − avoid general and ambiguous terms;
wi2 − avoid using abbreviations that are commonly used in the relevant field of research;
wi3 − keywords and words from the title should not repeat each other, since both of these elements
are simultaneously specified in databases.</p>
      <sec id="sec-7-1">
        <title>7.1. Research the recommended number of keywords</title>
        <p>Based on the analysis of 25 websites found by the Google search engine using the queries
"Number of keywords for a scientific article", "Keywords for a scientific article", "Requirements for
the number of keywords for a scientific article", Table 4 was compiled.</p>
        <p>Note 1: There are cases when editorial policy excludes keywords altogether.</p>
        <p>Remark 2: The ambiguity is, in particular, due to the fact that in some publications the phrase is
considered to be one keyword.</p>
        <p>For the sake of certainty, we will supplement the upper or lower bounds of intervals that are not
determined by the editorial boards by introducing appropriate heuristics.</p>
        <p>Heuristic H6. To fill in rows 7 and 10 of Table 4, we assume that the lower bound of the
recommended number of keywords is 2. For row 17, the lower bound is 4, and for row 22, the lower
bound is 6.</p>
        <p>Heuristic H7. For row 1 of Table 4, we set the upper bound to 6. For row 11, the upper bound is 9,
and for row 23, the upper bound is 13.</p>
        <p>Supplementing Table 4 with heuristic H6 and heuristic H7 and arranging the boundaries of the
intervals presented in the table in ascending order, we obtain Table 5.</p>
        <p>Note 3. The number of rows in Table 5 has decreased compared to the number of rows in Table 4
after the introduction of the H6 heuristic and the merging of rows with the same limit values.</p>
        <p>Based on Table 5, we use the layering method to build a membership function for the
recommended number of keywords in a scientific article. The constructed geometric figure is
approximated by a trapezoidal membership function, as shown in Figure 3.
The formula for the trapezoidal membership function shown in Figure 4 is as follows:
 0, w  1, 
 ( w −1) / 4, 1  w  5, </p>
        <p>
 
Т ( w,1,5,6,15) =  1, 5  w  6 
 
(15 − w) / 9, 6  w  15,
 0, w  15  .</p>
        <p>Let's also build a membership function taking into account the frequency of values, i.e., taking
into account the number of sites presented in the last column of Table 5. In this case, the membership
function will look like the one shown in Figure 4. The best approximation for the figure is a triangular
membership function. This membership function reaches its maximum value at point 6, which
corresponds to the number of keywords in the scientific article.
The formula for the triangular membership function shown in Figure 5 is as follows:</p>
      </sec>
      <sec id="sec-7-2">
        <title>7.2. Problems and approaches to describing and analyzing keywords</title>
        <p>For the formalized description and analysis of keywords of scientific articles as an attribute of
tuple (1), we will introduce additional heuristics.</p>
        <p>Heuristic H8. The keywords sufficiently reflect the content and focus of the scientific article and
can be used to determine the similarity of research areas in other scientific papers.</p>
        <p>Heuristic H9. The similarity measure between the sets of keywords of any two scientific articles
sufficiently reflects the similarity of the content of these articles (for some areas of research and
decision-making situations).</p>
        <p>Heuristic H10. The study of the similarity of keyword sets can be used to identify clusters of
research groups and to identify the similarity of research interests of researchers.</p>
        <p>Keywords are used by search engines to index and rank scientific articles in search results and it
is an effective tool for increasing citations.</p>
        <p>An important characteristic of a set of keywords defined by the author or with the help of
software tools is its relevance, i.e. the level of correspondence between the specified set and the full
text of the scientific article that this set of words represents.</p>
        <p>The main criteria for determining the quality of keyword research are as follows:
1 (wi ) − accuracy in defining the topic of the research article and the essence of the article,
conference materials, etc.;
2 (wi ) − quality of the characterization of the field of scientific research;
3 (wi ) − the potential to help to group the information that researchers are looking for;
4 (wi ) − the ability to guide authors in finding the scientific material they need;
5 (wi ) − speeding up the process of searching and classifying information about the subject of
research;
6 (wi ) − giving a potential reader an idea of the article;
7 (wi ) − the number of keywords in the article.</p>
        <p>Heuristic H11. According to statistics, only every tenth user who reads the keywords then goes to
the text of the article.</p>
        <p>You should choose words that are frequently repeated in the main material, with the exception
of stop words, i.e. words that do not carry a semantic load. Stop words include particles, prepositions,
interjections, pronouns, introductions, etc.</p>
        <p>At the same time, next heuristic is fair.</p>
        <p>Heuristic H12. The importance and decision-making process for including words or phrases in a
set of keywords for a scientific article can be determined by other criteria than just frequency.</p>
      </sec>
    </sec>
    <sec id="sec-8">
      <title>8. Conclusions.</title>
      <p>This article discusses and studies various aspects of metadata of scientific articles. The problem
of formalizing metadata as an integral part of the scientific space is investigated. Thus, this area of
research is transformed from a poorly structured one into a structured one. In particular, the
elements of metadata are studied: information about authors, article title, abstract, keywords.
Membership functions were also constructed based on computational experiments conducted by the
authors.</p>
      <p>
        The research area proposed by the authors of this article has broad prospects for development
[
        <xref ref-type="bibr" rid="ref30 ref31">32, 33</xref>
        ]. Further work can explore the possibilities of manipulating metadata, approaches to the use
of natural language processing technologies to automate the processes of improving the quality of
metadata, and can develop algorithms for identifying and correcting errors in the design of a
scientific article and its structural elements, methods for automatically improving the quality of
scientific article design, determining the quality of metadata preparation in terms of its indexing, etc.
[
        <xref ref-type="bibr" rid="ref32">34</xref>
        ].
      </p>
      <p>Neural networks can also be used to identify potential situations of academic dishonesty, cases of
manipulation of authors' popularity, etc. Such results can be used to create expert groups in scientific
fields, identify reviewers for student research competitions, competitions of projects of the Ministry
of Education and Science, various tenders, competitions of infrastructure development projects,
identify the best urban transformation projects, form specialized scientific councils for the defense
of theses, appoint reviewers for articles in journals, conferences, etc.</p>
    </sec>
    <sec id="sec-9">
      <title>Declaration on Generative AI</title>
      <p>The authors have not employed any Generative AI tools.</p>
    </sec>
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