<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>N. Kanakaris I. Varlamis. Detection of fake news campaigns using graph
convolutional networks. International Journal of Information Management Data Insights</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1016/j.jjimei.2022.100104</article-id>
      <title-group>
        <article-title>Evaluation of methods for intellectual analysis of manipulative content in the information space⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Vsevolod Senkivskyy</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Iryna Pikh</string-name>
          <email>iryna.v.pikh@lpnu.ua</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alona Kudriashova</string-name>
          <email>alona.v.kudriashova@lpnu.ua</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Roman Andriiv</string-name>
          <email>roman.andriiv@icloud.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nazarii Senkivskyi</string-name>
          <email>nazarii.y.senkivskyi@lpnu.ua</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>0 Akademichna St.</institution>
          ,
          <addr-line>Berezhany, Ternopil region, Ukraine, 47501</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Lviv Polytechnic National University</institution>
          ,
          <addr-line>Stepan Bandera Str., 12, Lviv, 79013</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2019</year>
      </pub-date>
      <volume>2533</volume>
      <fpage>91</fpage>
      <lpage>103</lpage>
      <abstract>
        <p>The modern information space is characterized by a high level of manipulative content, which poses a serious threat and significantly affects public opinion, political processes and the level of trust in media resources. Determining the optimal methods for evaluating the veracity of information messages is an extremely urgent task that requires the use of intelligent data analysis and efficient means of counteraction. The attention is focused on the use of machine learning algorithms and artificial intelligence to detect manipulations in text, video and audio materials. Based on the developed expert survey methodology, logistic regression, decision trees and SVM (Support Vector Machine) are identified among the known methods of intelligent analysis of manipulative content. To determine the most efficient approach, a Pareto set of mutually non-dominated criteria is formed, which includes accuracy, execution speed, resource capacity and interpretability. A model of the priority influence of criteria on the message evaluation process is developed, which allows determining their weight coefficients as the basis for experimental calculations. In order to select the optimal method, the method of linear convolution of criteria is applied, which ensures the determination of the Pareto-optimal solution among the proposed alternatives. To implement this approach, alternative options are generated by varying the criteria and forming combinations of their efficiency degrees that correspond to the methods of evaluating the message probability. Based on the method of hierarchy analysis, a program calculation of normalized weights of criteria and utility functions for the corresponding alternatives is performed. The obtained final values of the combined functionalities of alternative options allow determining the optimal method for evaluating the probability of information messages. The results of the study demonstrate the dependency of the method selection on the requirements for accuracy and explainability of solutions. The obtained data can be used to develop automated systems for monitoring and analysing the information space, which will contribute to increasing the level of information security and efficient counteraction to manipulative content.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;manipulative content</kwd>
        <kwd>information message</kwd>
        <kwd>intelligence analysis</kwd>
        <kwd>machine learning</kwd>
        <kwd>information security</kwd>
        <kwd>method of linear convolution of criteria</kwd>
        <kwd>alternative option</kwd>
        <kwd>pairwise comparison matrix</kwd>
        <kwd>utility function</kwd>
        <kwd>Pareto-optimal method 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>In the context of growing information threats, there is a growing need to develop and improve
methods of intelligent analysis that allow for the efficient detection, identification and evaluation of
false content. The research in this area is aimed at developing algorithmic and analytical approaches
that provide the detection of signs of manipulation, analysis of information sources and
determination of its reliability level [1, 2]. The use of modern data analysis technologies, in particular
machine learning and artificial intelligence methods, increases the accuracy of information flow
evaluation and prevents the negative impact of destructive content on the society [3]. The
development of artificial intelligence, machine learning, linguistic analysis and neural networks
contributes to the improvement of methods for processing text and multimedia data [4, 5]. The
publication [6] analyzes the efficiency of artificial intelligence and machine learning methods in
cybersecurity, evaluating their ability to detect threats and anomalies. Various approaches, their
advantages, disadvantages and development prospects are considered. A feature of the issues studied
in this paper is the coverage of approaches in the work [7], which combine computational solutions
and propose strategies to combat disinformation, in particular, the use of machine learning-based
methods for automatic classification of disinformation. Machine learning methods use statistical
approaches [8, 9] to identify patterns and anomalous deviations in large data sets, which allows
security analysts to timely detect potential threats, including previously unknown attacks. Deep
learning, as a subfield of machine learning, demonstrates high efficiency in increasing the accuracy
of recognizing malicious patterns due to multi-level information processing, which is especially
important for the analysis of complex cyber threats, including image recognition, traffic analysis,
and decryption of threatening messages.</p>
      <p>The efficiency evaluation of such methods can be based on the Pareto principle, which allows
selecting optimal solutions based on the criteria of accuracy, speed, and resource consumption. For
example, deep learning models [10, 11] demonstrate high accuracy, but require significant computing
resources, while classical machine learning methods are less expensive, but may be inferior in the
ability to recognize complex manipulative structures. The selection of a specific approach depends
on the characteristics of the information environment in which the analysis is carried out, as well as
on the needs for accuracy and speed of data processing [12].</p>
      <p>In view of the above, the goal of the study is to evaluate the efficiency of modern methods for
intelligent analysis of manipulative content by comparative analysis of their accuracy, speed,
resource capacity, and interpretability. Special attention is paid to the criteria for selecting the
optimal method, which allows increasing the efficiency of information security and minimizing the
negative impact of disinformation on the society.</p>
      <p>Strategies for evaluating methods of intelligent analysis of manipulative content based on
multicriteria optimization are proposed. This work analyzes modern methods of detecting manipulative
content, identifies key criteria for their evaluation, ranks alternatives using the method of linear
convolution of criteria and determines the optimal method. The results obtained can be used to
develop automated systems for monitoring the information space, which will help reduce the risks
of spreading disinformation and increase the level of information security.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Literature review</title>
      <p>Research and analysis of manipulative content in the information space covers a wide range of
methods and approaches aimed at identifying, assessing and neutralizing the impact of false
information. This includes improving fake detection algorithms, developing multi-criteria analysis
systems, and integrating modern machine learning technologies to improve the analysis accuracy.
The use of efficient methods is critical for protecting various areas of activity exposed to the risks of
disinformation and manipulation.</p>
      <p>Although most research focuses on detecting fake news [13] based on its content or using the
user interaction with news on social networks, there is a growing interest in proactive intervention
strategies to counter the spread of disinformation and its impact on society [14]. However, the
selection of the optimal method remains an open question, since the efficiency of algorithms
significantly depends on the characteristics of the input data, the context of their application, the
level of adaptability to new manipulative strategies, and the performance of computing resources.</p>
      <p>In the article [15], multimodal methods for detecting fake news based on semantic information
have achieved great success. However, these methods use only the deep features of multimodal
information, which leads to a large loss of real information at the surface level.</p>
      <p>For a well-grounded selection of the optimal method, a set of interrelated criteria is taken into
account by the authors. In this context, the use of multi-criteria analysis methods plays a special role,
such as the method of linear convolution of criteria, which allows evaluating alternative approaches
by key parameters. The formation of the Pareto set allows one to isolate mutually non-dominated
methods and determine the best option based on the calculation of utility functions.</p>
      <p>The study [16] presents a taxonomy of models, machine learning and deep learning functions,
used to detect fake news based on the content analysis. To solve this problem, machine learning
models are used that allow for automated identification of unreliable information. At the same time,
the work did not propose efficient methods for improving the accuracy of classification or optimizing
models, which leaves open the questions of their adaptation to new types of manipulative content
and increasing resistance to changes in the characteristics of fake news.</p>
      <p>The use of neural network technologies for detecting fake data is considered in the work [17].
The efficiency of the methods is assessed by comparative analysis of their strategies, approaches to
error estimation and the accuracy level on different data sets. Our goal is to help researchers in
determining relevant criteria and selecting the optimal method for solving specific tasks of intelligent
analysis of manipulative content.</p>
      <p>A detailed review of methods for generating and detecting deep fakes is presented in the study
[18]. Open challenges faced by detection systems are considered, and possible options for
overcoming them are proposed, in particular using deep learning. The main emphasis is placed on
the need to create efficient manipulative content detection systems that are able to adapt to new
challenges in the field of artificial intelligence. However, there are no experimental results and
practical evaluation of the proposed methods in real-world application scenarios. The work [19] is
devoted to the analysis of the problem of large language model radicalization. Semantic
vulnerabilities and the learning inadequacy based on human feedback are studied. At the same time,
the attention is focused mainly on theoretical aspects and does not contain practical
recommendations for the direct implementation of protective mechanisms.</p>
      <p>The work [20] is focused on the problem of manipulation by artificial intelligence and
recommends criteria for assessing the level of the system manipulability. The main attention is paid
to the analysis of algorithmic ethics and the need to create transparent decision-making systems that
are not susceptible to manipulation by users. However, there are no clear metrics or practical
methods for assessing the manipulability level.</p>
      <p>To solve this problem, improved approaches to fake news detection are proposed by the authors,
which combine traditional machine learning methods with the optimal selection of data
preprocessing. It is assumed to use the method of linear convolution of criteria to integrate various
performance indicators of models related to manipulative content. The proposed approach will
contribute to increasing the reliability of classification and the balance between accuracy and
computational efficiency. Summarizing, the research highlights a wide range of threats related to
manipulative content and artificial intelligence. This emphasizes the importance of a comprehensive
approach to countering such threats, which involves improving detection methods, applying
multicriteria analysis, and integrating modern machine learning technologies.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Material and methods</title>
      <sec id="sec-3-1">
        <title>3.1. Pareto principle and selection of a criteria set</title>
        <p>The Pareto principle, or 80/20 rule, is a fundamental approach to analysing efficiency and optimality
in various fields, including multi-criteria analysis and decision-making. It states that in many
processes, approximately 80% of the results are due to 20% of the factors. In the context of
optimization and efficiency analysis, this principle is used to identify the most important parameters
that have the greatest impact on the final result [21, 22].</p>
        <p>In multi-criteria analysis, the Pareto principle is applied through the concept of Pareto
optimality, which defines a set of solutions that cannot be improved on one criterion without
worsening another. This means that no solution in the Pareto set is dominant over another, and the
selection of a particular option depends on priorities or additional conditions set by the researcher
or the receiving party.</p>
        <p>The formation of a Pareto set of criteria involves analysing the set of possible solutions and
selecting those that are Pareto-efficient. If a solution is not inferior to others in any criterion and has
an advantage in at least one, it is considered Pareto-optimal and is included in the corresponding set.
In the case of a large number of criteria and a significant selection of solutions, evolutionary search
methods or stochastic approaches can be used.</p>
        <p>The criteria influencing the process of determining the optimal method for detecting
manipulative content are presented in Table 1.</p>
        <p>A feature of the Pareto set is its adaptability to a specific task: it allows one to identify compromise
solutions that take into account different aspects of the problem, and provides a basis for further
analysis and decision-making. Since none of the options is unambiguously the best according to all
criteria, the selection of the final solution is often made taking into account additional priorities or
weight factors that represent the significance of each criterion in a specific context.</p>
        <p>Figure 1 presents a diagram of the efficiency of the criteria assigned to the methods of detecting
manipulative content in the information space.</p>
        <p>Efficiency of methods
92%
90%
ira88%
e
itr86%
c
fo84%
t
cn82%
a
tro80%
Ipm78%
76%
74%</p>
        <p>Logistic regression</p>
        <p>SVM</p>
        <p>Decision Tree
Accuracy</p>
        <p>Speed</p>
        <p>Resource capacity</p>
        <p>Interpretability</p>
        <p>Thus, the use of the Pareto principle in multi-criteria intelligent analysis of manipulative content
allows for efficient resource allocation, finding optimal solutions, and minimizing trade-offs between
conflicting requirements. This is especially relevant in complex text message processing systems,
where it is necessary to obtain the interaction of many factors and their influence on the final result.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Formation of an expert group</title>
        <p>The use of expert reviews in the evaluation of methods for intellectual analysis of manipulative
content allows one to obtain a quantitative assessment of the importance degree of each of the
criteria that form a set of values of factors influencing the process quality [22]. In this case, the scale
rating method is used, which provides for obtaining quantitative assessments of the importance
degree of each of the factors belonging to a certain set, relative to the scale of their basic (reference)
values. In this case, the estimates of the relative importance of each factor are expressed in points on
a certain scale. The most commonly used is a 100-point scale, where the maximum possible
importance corresponds to a score of 100 points, and the minimum possible one is 0 (zero) points.</p>
        <p>When processing expert data, the survey results are summarized in a table, where   is the
relative importance of the parameter   from the point of view of the j -th expert, which is expressed
by the corresponding score or rank value (Table 2).
where   is a number of experts evaluating the importance of factors xi .</p>
        <p>The values   and Ci can be expressed quantitatively in points or ranks. In the first case, the
value is called the average score (average value) of the criterion xi , in the second case it is the
average rank. Summing the numbers i, j in the rows with the subsequent division of the obtained
result by m gives the average ranking of the factors  1,  2, . . . ,   , which, in turn, serves as an
indicator of the generalized opinion about the importance of the factors (the smaller the sum in the
row j is, the more important role the factor i plays). The opposite picture occurs with respect to
the sums in the columns.</p>
        <p>Since the indicator of the generalized opinion Ci and the reference value essentially differ only in
their purpose, in the following, for the sake of simplicity of reasoning, one will consider the centre
of grouping of scale scores, considering that this concept covers the previous two.</p>
        <p>The method of searching the centre of grouping of expert data on the rating scale for any
distribution law uses the average, or weighted average score value. This approach (especially the use
of the weighted average value) allows to objectively determine the centre of grouping with a
sufficient degree of approximation [20]. However, with a large range of scale values, taking into
account all values without exception, as it will be shown below, can lead to a significant shift in the
centre of grouping.</p>
        <p>Suppose the centre of score grouping for a given distribution of experts by the values provided
by them is denoted by C . The following relation is valid:</p>
        <p>where: k is a number of experts in the group; h is a step for searching a grouping area; W is a
range of score values, to which the number of experts corresponds, is not less than θ k , at the step
(0 &lt;   &lt; 1).</p>
        <p>
          Suppose one has a scale with values i , where  = 0,1,2, . . . ,  . Then mi is a number of experts
who put the i -th value. If the group includes k experts, then ∑ =1   =  . In the first step of the
search (ℎ = 1) of the center of grouping, pairs of values are defined that satisfy the expression:
In this case, the following three logical options are possible:
no pair of values at this step satisfies the relation (
          <xref ref-type="bibr" rid="ref2">2</xref>
          ). Then the searching step of the grouping
area increases by one, that is, the "weighting" area expands, and the procedure is repeated;
there is exactly one area on the scale at this searching step that satisfies the relation (
          <xref ref-type="bibr" rid="ref3">3</xref>
          ). In
this case, the grouping area is identified and the centre of grouping is determined as the
weighted average of all values belonging to this area:
 =  ( , ℎ,  )
        </p>
        <p>,

 ∈ ℎ</p>
        <p>≥  
 =</p>
        <p>∑ ∈ ℎ  ⋅</p>
        <p>∑ ∈ ℎ  
 =</p>
        <p>∑ ∈  ⋅</p>
        <p>
          ∑ ∈  
(
          <xref ref-type="bibr" rid="ref2">2</xref>
          )
(
          <xref ref-type="bibr" rid="ref3">3</xref>
          )
(
          <xref ref-type="bibr" rid="ref4">4</xref>
          )
(
          <xref ref-type="bibr" rid="ref5">5</xref>
          )
there are several areas satisfying the relation (
          <xref ref-type="bibr" rid="ref4">4</xref>
          ). Then the grouping area is defined as follows:
the left boundary represents the smallest value for all values of the these areas, and the right
boundary represents their largest value, respectively. The grouping area is identified as the
weighted average of all values belonging to the grouping area:
1
8
2
6
3
7
4
3
5
4
6
7
7
4
8
5
9
1
10
2
11
2
12
1
where G is a set of all scale values belonging to the grouping area.
        </p>
        <p>Suppose the total set of criteria for evaluating the process efficiency is 8. Using expert evaluation,
a subset of four factors should be selected (Table 3). To solve the problem, a scale from 0 to 8 and the
number of experts corresponding to each scale value   = 50 are used.
number of experts for each area is calculated (Table 4).</p>
        <p>Suppose one takes  = 0,5, since the 50% comparison is the most common in the expert
evaluation method. For the total number of experts   = 50, the search step is set ℎ = 1 and the
Quantitative composition of experts in each area during the first step</p>
        <p>
          According to the last table, no area satisfies the relation (
          <xref ref-type="bibr" rid="ref2">2</xref>
          ) at a given step. Therefore, the
searching step is increased (ℎ = 2) and the expanded areas are calculated (Table 5).
        </p>
        <p>
          As it can be seen from the data presented, at this step there is also no area satisfying the relation
(
          <xref ref-type="bibr" rid="ref3">3</xref>
          ). Therefore, the searching step is increased again and the procedure is repeated until four optimal
influencing criteria are determined (Fig. 2).
        </p>
        <p>
          As it follows from the calculations, there is exactly one area that satisfies the relation (
          <xref ref-type="bibr" rid="ref4">4</xref>
          ), namely
area 1-8. It becomes the grouping area.
        </p>
        <p>
          Using the relation (
          <xref ref-type="bibr" rid="ref5">5</xref>
          ), the value of the centre of grouping is calculated:
        </p>
        <p>1 × 8 + 2 × 6 + 3 × 7 + 4 × 3 + 5 × 4 + 6 × 7 + 7 × 4 + 8 × 5 183
C = = = 4
8 + 6 + 7 + 3 + 4 + 7 + 4 + 5 44
246
With a weighted average value of the entire scale  = 50 = 5.</p>
        <p>Thus, the method of generalizing scale scores during group examination ensures the formation
of the most reliable indicator of generalized opinion for any distribution of expert data – the centre
of grouping of scores, which, with a symmetric distribution of scores, coincides with the weighted
average value.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Method of linear convolution of criteria</title>
        <p>The multilevel models of the priority influence of technological indicators on the level of
performance of publishing and printing processes obtained in the work [24] serve as the basis for
making a decision on the importance of a particular factor and its “contribution” to the overall quality
of the resulting product. Using mathematical terminology, one has the necessary initial data on the
degree of the indicator influence on the process, but they are insufficient for their full practical
implementation. Knowledge is essential not only about the conditional importance of the
technological factor. It is necessary to study how much effort should be spent on each of the
indicators during their interaction to achieve proper process efficiency.</p>
        <p>The issues outlined in this paper concern the generation of alternative options based on methods
for processing text information messages and selecting the optimal solution in accordance with the
specified principle. This task belongs to the field of multi-criteria optimization, which involves
making a reasoned decision on selecting the most efficient method for evaluating the message
reliability.</p>
        <p>To solve this problem, it is necessary to determine a set of criteria, the composition and content
of which are formed on the basis of the Pareto principle [25]. The main idea of the approach is that
the criteria included in the set of Pareto-optimal solutions cannot be completely dominated by other
criteria. That is, there is no criterion that would surpass all the others in all indicators at the same
time. Within the framework of the study, based on expert evaluation, mutually non-dominated
criteria are selected that form the Pareto set, namely: accuracy, execution speed, resource capacity
and interpretability.</p>
        <p>According to the methods of decision theory [26, 27], multi-criteria optimization on a set of
alternatives</p>
        <p>in the presence of objective functions  ( ) =  1( ), . . . ,   ( )
constructing models of utility functions and determining their maximum value:   ( ) → 
1,  .</p>
        <p>The process of multi-criteria selection of the optimal alternative is based on the method of linear
convolution of criteria, which involves linear combination of partial target functionals f1,..., fm into
a single generalized functional:
the set of alternatives  is a finite set of elements  = { 1,  1, . . . ,   }that the decision-maker
the evaluation of alternatives is carried out by utility functions  , moreover   :  →
the decision-maker uses criteria ordered by their priority.
•
•
•
can list;
  = 1,  .</p>
        <p>A set of criteria  1,  2,  3,  4 is formed. The alternative options for the process are methods for
evaluating the probability of information messages, denoted by M1, M2, M3. For each option,

 ( ,  ) = ∑ =1     ( ) →</p>
        <p>;  ∈  ,
 ∈
where 
= {</p>
        <p>= ( 1, . . . ,   ) ;   &gt; 0; ∑ =1   = 1}.</p>
        <p>The above allows one to formalize the decision-making process by reducing a set of criteria to a
single target function, the value of which determines the optimal solution.</p>
        <p>Factor weights wi are identified with the numerical values of the corresponding utility functions.
To select an alternative, the theorem of the method of multi-criteria utility theory is used, the essence
of which is that if the criteria are independent in utility and preference, then there is a utility
function.</p>
        <p>( ) = ∑ =1     (  ),
which serves as a criterion for selecting the optimal option. At the same time  ( ) is a
multicriteria utility function (0 ≤  ( ) ≤ 1) for the alternative  ;   (  ) is a utility function of the  -th
criterion(0 ≤   (  ) ≤ 1); yi is a value of the alternative x by the criterion  ;   is a weight of the
i -th criterion, moreover 0 &lt;   &lt; 1, ∑ =1   = 1.
following basic assumptions [25]:</p>
        <p>
          In general, the process of multi-criteria alternative selection in decision-making is based on the
involves
 ∈
,  =
(
          <xref ref-type="bibr" rid="ref6">6</xref>
          )
(
          <xref ref-type="bibr" rid="ref7">7</xref>
          )
4
  =
        </p>
        <p>;  = 1,2,3
 =1</p>
        <p>Additional notations are introduced: wi is the initial weight of the  -th criterion, determined on
the basis of an expert evaluation of its influence on the priority of the selected methods;   are
expertly established percentage values of the importance of the  -th criterion during the formation
of the  -th alternative. It is important to note that the following condition must be met for each
criterion:
4</p>
        <p>= 100 ;  = 1,2,3
 =1</p>
        <p>The evaluation of alternatives by efficiency degrees   is represented in Table 6.
criterion ( = 1, . . . ,4). Finally, the multi-criteria evaluation of the utility of the  -th alternative:</p>
        <p>Considering the degrees of influence or efficiency of the criteria in different variants, that is,
when applied to each of the selected methods, matrices of pairwise comparisons are constructed
according to the method of hierarchy analysis. Processing these matrices allows one to obtain the
corresponding utility functions uij , namely:  1 –  11,  12,  13;  2 –  21,  22,  23;  3 –
 31,  32,  33;  4 –  41,  42,  43.</p>
        <p>An important addition to the previous considerations. It is obvious that the criteria of the Pareto
set form a new autonomous group, which requires the calculation of current weight values wi based
on the initial numerical priorities. The obtained values will be used for the final calculation of the
final target functions.</p>
        <p>
          The formal representation of the pairwise comparison matrix of the initial weights is presented
in Table 7.
(
          <xref ref-type="bibr" rid="ref9">9</xref>
          )
        </p>
        <p>The sign " / " in the matrix elements means a comparison of the starting weight values of the
criteria.</p>
        <p>Processing the matrix will allow calculating the normalized weight values of the criteria, which
will become the initial data for generating alternative options and determining the optimal method
for evaluating the probability of text information messages.</p>
        <p>
          The final multi-criteria evaluations of the utility of alternatives for options M1, M2, M3, obtained
on the basis of the formula (
          <xref ref-type="bibr" rid="ref8">8</xref>
          ), are expressed by the relation (
          <xref ref-type="bibr" rid="ref10">10</xref>
          ):
 1 =  1 ⋅  11 +  2 ⋅  21 +  3 ⋅  31 +  4 ⋅  41;
 2 =  1 ⋅  12 +  2 ⋅  22 +  3 ⋅  32 +  4 ⋅  42; (
          <xref ref-type="bibr" rid="ref10">10</xref>
          )
 3 =  1 ⋅  13 +  2 ⋅  23 +  3 ⋅  33 +  4 ⋅  43.
        </p>
        <p>
          As noted earlier, the indicator of selecting the optimal method among alternative options for
evaluating the probability of messages is the option (method) for which the value of the utility
function of the combined partial target functions in the relation (
          <xref ref-type="bibr" rid="ref6">6</xref>
          ) reaches the maximum indicator.
        </p>
        <p>Since the experimental implementation of the above theoretical approaches requires the
information about the levels of the criteria preferences, a multi-level graphical model is designed
(Fig. 3), which visually reproduces the essence of the criteria and the priority of the influence on the
evaluation of text information messages. The preferences of the criteria in the model are reproduced
on the basis of the diagram (Fig. 1).</p>
        <p>To form the model, the essence of the criteria identified for the study are briefly summarized.
Thus, methods for text message processing are characterized by: accuracy, which determines the
ability of the method to correctly classify or analyse text data; interpretability, which reflects the
clarity and explainability of the results, which is critically important in areas where transparency of
decision-making is required; execution speed, which affects the performance of the system and
depends on the algorithmic complexity of the calculations; resource capacity, which determines
the amount of memory and computing power used, which is especially important when working
with large amounts of text data.</p>
        <p>Thus, an algorithm for generating and calculating alternative options is constructed, suitable for
studying the process of message evaluation using modern methods and functional criteria. The
essence of its theoretical foundations is based on mathematical calculations of modelling theory,
methods of hierarchy analysis and decision-making, and operations research theory.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Experiment, results and discussion</title>
      <p>As part of further research, the refined normalized weighted priorities of the model criteria are
calculated (Fig. 3), necessary for practical implementation (Table 6). To do this, using the scale of
K1
K2
K3
K4
relative importance of objects [27, 28], a pairwise comparison matrix of criteria is formed, taking into
account the levels of their preference in the priority model.</p>
      <p>Processing the matrix results in obtaining the initial numerical preferences of the criteria
expressed in conventional units, namely: K1 (accuracy) – 220 c.u.; K2 (interpretability) – 130 c.u.;
 3 (execution speed) – 80 c.u.;  4 (resource capacity) – 50 c.u. At the same time, normalized weight
values of the criteria are calculated:  1 = 0,46;  2 = 0,28;  3 = 0,16;  4 = 0,10</p>
      <p>As a result of processing the matrix, the following are obtained: the maximum eigenvalue of the
matrix   , the consistency index   = 0,01 and the consistency ratio  = 0,01.</p>
      <p>The calculation results correspond to the permissible limits of reliability, the essence of which is
as follows. The assessment of the obtained solution is determined by the consistency index, the value
of which is determined by the formula   = (  ()), where n is a number of objects. The
( −1)
consistency index value is compared with the reference values of the consistency indicator, the
socalled random index (WI ), which depends on the number of objects being compared. In this case,
the results are considered satisfactory if the index value does not exceed 10% of the reference value
 . Comparing the obtained value IU and the reference value  = 0,9 for four criteria, and
checking the inequality   &lt; 0,1 ×  , one obtains: 0, 01 &lt; 0,1× 0,9 . This confirms the reliability of
the obtained results. Additionally, the results are evaluated by the consistency ratio:  =   . One
obtains  = 0,01 . The results are considered satisfactory if  ≤ 0,1. Therefore, one has a
sufficient level of process convergence and proper consistency of expert judgments regarding
pairwise comparisons of criteria.</p>
      <p>Normalized weight coefficients will be applied when calculating the utility functions of the
criteria used in alternative approaches to message evaluation.</p>
      <p>Additionally, possible groups of combinations of the efficiency shares of the criteria in alternative
options are presented (Table 9), expressed in percentages [25,29].</p>
      <p>Based on the data obtained, a basic table for the method of linear convolution of criteria is formed
(Table 10).</p>
      <sec id="sec-4-1">
        <title>The resulting data are obtained: λmax</title>
        <p>=3,03; IU
=0,01; WU
=0,03. The utility functions of the
criterion K2 “Interpretability” in alternative options are expressed by the following values:  21 =
0,576;  22 = 0,341;  23 = 0,081.</p>
        <p>The criterion K3 “Execution speed” will form a similar matrix (Table 13).
20
50
20
20
М2
2
1
7
М2
2
1
1/5
М3
1/4
1/7
1
М3
6
5
1
K1
М1</p>
        <p>The matrix for the criterion K2 “Interpretability” looks like this (Table 12).</p>
      </sec>
      <sec id="sec-4-2">
        <title>As a result of processing the matrix, it is obtained: λmax</title>
        <p>=3,00; IU
=0,00; WU
=0,00. The utility
of the criterion "Resource capacity" is expressed by the following values:  41 = 0,6;  42 = 0,2;  43 =
0,2.</p>
        <p>
          Calculation indicators, in particular the maximum values of priority vectors λmax , consistency
indices IU and consistency ratio WU , meet the established requirements presented above.
Substituting the weight coefficients and the values of the utility functions of the criteria into the relation
(
          <xref ref-type="bibr" rid="ref10">10</xref>
          ), the final values of the combined functionalities of the alternative options are obtained (
          <xref ref-type="bibr" rid="ref11">11</xref>
          ).
 1 = 0.46 ⋅ 0.186 + 0.28 ⋅ 0.576 + 0.16 ⋅ 0.093 + 0.1 ⋅ 0.6;
 2 = 0.46 ⋅ 0.097 + 0.28 ⋅ 0.341 + 0.16 ⋅ 0.626 + 0.1 ⋅ 0.2; (
          <xref ref-type="bibr" rid="ref11">11</xref>
          )
 3 = 0.46 ⋅ 0.715 + 0.28 ⋅ 0.081 + 0.16 ⋅ 0.279 + 0.1 ⋅ 0.2.
        </p>
        <p>Finally, one gets: 1 = 0.322;  2 = 0.260;  3 = 0.416.</p>
        <p>Among the selected alternative methods for evaluating the probability of information messages,
the third option, i. e. the method M3 – SVM (support vector machine) is considered the most efficient,
since it is characterized by the maximum value of the combined functional  3. The theoretical
justification of this option indicates its ability to provide a high level of reliability of the obtained
score. Important parameters that determine the method efficiency are its ability to accurately
evaluate the veracity of messages and efficiently distribute computational resources. It is the
combination of such criteria as "accuracy" and "resource capacity" that makes this option the best
among other alternatives.</p>
        <p>The functional model of the algorithm of the probable software solution is shown in Fig. 4.</p>
        <p>This model will take into account a multifactor analysis of the characteristics of input data and
adaptively select the most effective approach depending on the context. It also ensures integration
with machine learning systems to enhance the accuracy of assessment and reduce the rate of
falsepositive results. For this purpose, machine learning algorithms such as classification methods,
regression, and neural networks are utilized, allowing the detection of hidden patterns in large data
sets. Additionally, the model can apply reinforcement learning techniques to dynamically adjust
evaluation criteria based on changing conditions in the information environment.</p>
        <p>Thus, based on the results of the conducted study, the most effective method for assessing the
credibility of messages is the Support Vector Machine (SVM). This method is based on finding a
hyperplane that maximally separates different data classes in the feature space, making it optimal
for binary classification tasks, such as distinguishing reliable information from disinformation or
manipulative content. However, the application of SVM for message credibility assessment also has
certain limitations. One of the key challenges is the complexity of interpreting the results, as SVM
does not provide clear explanations regarding which specific text features influenced the
classification. Additionally, this method is sensitive to imbalanced datasets, where one category of
messages significantly outweighs the other, which can distort classification results.</p>
        <p>It should be emphasized that the final selection of the optimal option within the method of linear
convolution of criteria can be improved by developing an appropriate software application, which
will allow automating the process of calculating the values of combined functionals for various
alternative methods and will provide the ability to take into account a wide range of options for
combinations of criteria efficiency degrees.</p>
        <p>The application of machine learning methods in this process is extremely important, as they
enable the analysis of large volumes of data, the identification of hidden dependencies between
criteria, and the automatic adjustment of weight coefficients to improve assessment accuracy.
Furthermore, the use of machine learning will facilitate the model's adaptation to changing
conditions and enhance its ability to self-learn, ensuring a more flexible and reliable approach to
selecting the optimal evaluation method. A promising direction for future research is the refinement
of the proposed approach through the integration of advanced artificial intelligence methods and
hybrid algorithms that combine classical statistical models with neural network technologies. This
will improve the system’s adaptability to dynamic changes in the information environment, increase
its resistance to manipulative influences, and provide a more accurate and well-founded assessment
of message credibility in real-time.</p>
        <p>In conclusion, it is worth emphasizing that the research is based on the concept of the relationship
between the selection of the optimal method for evaluating the probability of information messages
and the combination of efficiency shares of the applied criteria. This approach makes it possible to
identify patterns that affect the accuracy and validity of the intellectual analysis of manipulative
content in the information space. The recommended algorithmic decision to the automated solution
of the problem provides an increase in the level of the evaluation objectivity, reducing the influence
of subjective factors. In addition, the proposed solution provides the possibility of flexible parameter
settings, which allows adapting the system to the specific conditions and requirements of a specific
research task, contributing to increasing its efficiency and practical value.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusions</title>
      <p>The results of the study confirm the relevance of the problem of evaluating methods of intellectual
analysis and detecting manipulative content in the information space. Determining the most efficient
method is a key task for ensuring the information security and countering disinformation. Given the
constantly growing threats in the information environment, combating manipulation and
disinformation requires not only the improvement of technical analysis methods but also the
development of strategies. This includes educational programs, increasing media literacy among the
population, and active collaboration between government institutions and scientific organizations,
which will enable effective resistance to manipulative content and ensure sustainable information
security.</p>
      <p>The study proposes an approach based on the formation of a Pareto set of mutually
nondominated criteria, which allows one to objectively evaluate the efficiency of machine learning
methods, in particular logistic regression, decision trees and the support vector method (SVM). The
generation of alternatives is carried out by identifying options determined by the selected methods
taking into account expertly established efficiency degrees of key criteria, such as accuracy,
execution speed, resource capacity and interpretability.</p>
      <p>The application of the method of hierarchies analysis to the developed model of the priority
influence of criteria on the process of analysis, evaluation and detection of manipulative content
provides the calculation of the utility functions of the criteria for each of the methods. As a result,
combined functionalities of alternative options are formed, which act as the main optimization
criterion. The use of multi-criteria analysis methods, in particular the method of linear convolution
of criteria, provides a balanced approach to selecting the optimal method for evaluating the
probability of information messages, contributing to increasing the accuracy and validity of decisions
made.</p>
      <p>The results of the study indicate that the selection of the optimal method largely depends on the
specific requirements for the evaluation system. In particular, in cases where accuracy is the priority
criterion, it is advisable to use the support vector method (SVM), while to ensure high data processing
speed it is more expedient to use decision trees. Logistic regression, in turn, provides a balance
between accuracy and interpretability, which makes it an efficient tool for analysing text messages.</p>
      <p>In view of the prospects for further development, the approach proposed in the study makes it
possible to adapt the evaluation system to the changing conditions of the information environment,
integrate additional analysis criteria and use modern machine learning algorithms to automate the
content evaluation process. The results obtained can be used to develop automated information space
monitoring systems, which will contribute to the timely detection of manipulative content and
increase the level of information security.</p>
      <p>The proposed approaches can be integrated into software solutions for intelligent analysis and
evaluation of the level of manipulative content in the information space, which is especially relevant
in the context of the growing information influence on the public opinion and political processes.
Further research should be directed at expanding the approaches by using the latest methods, in
particular deep learning and hybrid models, which can potentially provide significantly higher
efficiency in detecting manipulative content.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>The authors have not employed any Generative AI tools.</p>
    </sec>
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