=Paper= {{Paper |id=Vol-3899/paper11 |storemode=property |title=Hierarchical modeling of factors influencing the quality of interactive editions design |pdfUrl=https://ceur-ws.org/Vol-3899/paper11.pdf |volume=Vol-3899 |authors=Alona Kudriashova,Iryna Pikh,Vsevolod Senkivskyy,Irina Kalinina,Yurii Slipetskyi |dblpUrl=https://dblp.org/rec/conf/advait/KudriashovaPSKS24 }} ==Hierarchical modeling of factors influencing the quality of interactive editions design== https://ceur-ws.org/Vol-3899/paper11.pdf

Hierarchical modeling of factors influencing the quality
of interactive editions design⋆
Alona Kudriashova1,∗,†, Iryna Pikh1,†, Vsevolod Senkivskyy1,†, Irina Kalinina2,† and Yurii
Slipetskyi1,†
1 Lviv Polytechnic National University, Stepan Bandera Str., 12, Lviv, 79013, Ukraine
2 Petro Mohyla Black Sea National University, Desantnykiv Str., 68, Mykolaiv, 54000, Ukraine

Abstract
Reader demands for book products are constantly increasing. There is a growing popularity of interactive
editions. Therefore, building a model that prioritizes the influence of factors on the quality of interactive
edition design, based on their weighted coefficients, is a relevant scientific task, and the goal of this research.
A set of factors influencing the quality of the studied process has been formed, which is of great importance
for predicting the optimal algorithm for its progression and achieving the expected result. A semantic
network has been constructed, illustrating the relationships between factors, and serving as the basis for
determining their weighted values. A formalized representation of the relationships between factors has
been carried out using elements of predicate logic. The ranks and priority levels of the factors have been
determined by constructing hierarchical trees of direct and indirect influences and dependencies using the
ranking method. A multi-level structured model has been built, which reflects the place of each factor in
the overall hierarchy and illustrates the connections between them, as defined in the semantic network.
The weighting of the factors has been refined using the hierarchy analysis method, and an optimized model
for the priority influence of factors on the quality of interactive edition design has been developed. The
results, obtained through experimental research and mathematical modeling, can be used for managerial
decision-making regarding interactive edition design, allowing for improved printing production efficiency
and the quality of the finished book.

Keywords
interactive edition, design, factor, semantic network, ranking, priority, model, quality 1

1. Introduction
In recent years, book production technologies have undergone significant changes [1–3]. Innovative
products — interactive books — have appeared on the market [4–6]. An interactive book is an edition
that integrates traditional textual content with multimedia and digital elements, providing active
interaction between the reader and the material. Such an edition may include audio, video,
animations, hyperlinks, and other interactive components that enhance the perception of
information. An interactive book can be produced in both digital and printed formats, where printed
editions are supplemented by technological means such as QR codes or augmented reality
applications that activate supplementary content. This book format allows for deeper user immersion
into the content, enabling the creation of multi-layered narratives and interaction tailored to the
audience's needs.
The total computerization has not only increased the variability of publication and design
formation but has also fundamentally changed the methodology of these processes. An increasing

AdvAIT-2024: 1st International Workshop on Advanced Applied Information Technologies, December 5, 2024, Khmelnytskyi,
Ukraine - Zilina, Slovakia
∗ Corresponding author.
† These authors contributed equally.

alona.v.kudriashova@lpnu.ua (A. Kudriashova); iryna.v.pikh@lpnu.ua (I. Pikh); vsevolod.m.senkivskyi@lpnu.ua (V.
Senkivskyy); irina.kalinina@chmnu.edu.ua (I. Kalinina); yurii.b.slipetskyi@lpnu.ua (Yu. Slipetskyi)
0000-0002-0496-1381 (A. Kudriashova); 0000-0002-9909-8444 (I. Pikh); 0000-0002-4510-540X (V. Senkivskyy); 0000-
0001-8359-2045 (I. Kalinina); 0009-0003-6931-6767 (Yu. Slipetskyi)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
number of key issues in preparing publications for print are being solved through the automation of
prepress processes, the primary means of which are computer publishing systems [7].
The activities aimed at producing print products have a systematic nature. The primary signs of
systematicity in any activity are goal orientation and algorithmicity [8]. The primary goal of printing
enterprises is to produce high-quality printed products. In addition to the main goal, a hierarchy of
goals may be created, where intermediate and higher-level goals exist. In the editorial and publishing
process, intermediate goals may include the successful selection of the author's original work, the
correct determination of the type of edition, the choice of the design option for the edition, quality
editing, illustration, and font design, layout, and others, while higher-level goals may include the
formation and design of the edition, the production of a sample copy, successful distribution of the
edition, building a customer base, and more. The algorithmicity of activity lies in the sequential
execution of operations necessary to achieve these goals.
The systematic approach allows for rational and comprehensive solutions to the tasks at hand.
However, it should be noted that the execution of any tasks in the editorial and publishing process
is impossible without the intellectual, creative, and reproductive work of the professional publishing
team. In fact, a computer publishing system is a set of tools designed to meet the production needs
of editors, proofreaders, designers, and other specialists.
In contrast to the positive trends of automation and computerization of prepress processes, there
is also a trend of declining editorial and publishing culture in book design. This negative
phenomenon is associated with two main factors. The first is the increase in the number of titles of
printed editions and the reduction in the time allocated for their production. The fast pace of societal
activity demands more efficiency in the development and production of printed products. As a result,
the workload on publishing industry workers has increased. Due to the lack of an a priori quality
assurance algorithm, design elements of the edition often do not receive adequate attention.
Additionally, this problem has arisen due to a careless attitude toward prepress preparation.
Often, people who are proficient with the necessary software and hardware tools but do not
understand the basics of publishing and printing processes are allowed to participate in the book
creation process. This is the second factor that negatively affects editorial and publishing culture,
effectively destroying it. The formation and design of a publication have shifted from a creative,
intellectual process to an unsystematized execution of operations without adhering to necessary
standards and requirements. As a result, there is a high probability of producing book products that
fail to meet consumers' aesthetic and practical needs. Therefore, simply knowing how to use a
computer should not be a qualification for working on book creation. Below is the ontology [9–11]
of interactive edition design, which reflects the core concept of key factors and provides insight into
the multitasking and variability of the studied process (Fig. 1).

Figure 1: Ontology Graph of Interactive Book Edition Design.
To optimize publishing processes, maximum integration and harmonious functioning of the three
levels of computer publishing systems are required: hardware, software, and user. Inconsistent,
chaotic execution of operations and a lack of understanding of the connections between them result
in an inability to predict the final outcome, which undoubtedly negatively affects the quality of the
finished publication.
To ensure a high level of book quality and improve the efficiency of the publishing house as an
organizational system, it is necessary to ensure thoughtful, consistent, and orderly execution of
production procedures. This is possible by understanding the prioritization of key factors influencing
the quality of interactive book editions, particularly one of the key stages — design. Therefore,
determining the weighted values of the factors and constructing a model for the priority influence
on the quality of interactive edition design is a relevant scientific task, and its resolution will be the
goal of this research. Achieving this goal will promote the development of rational managerial
decisions during the design of the edition and provide direct executors with a solid theoretical and
practical foundation, serving as a guide not only for technical operations but also for the creative
component.

2. Literature review
An analysis of literary sources on this topic shows that the issue of forming the quality of interactive
editions is relevant and widely discussed. According to [12], the development and research of
interactive books fully align with the challenges of today, due to the continuous penetration of
advanced technologies into all spheres of human life. Attention is focused on comparing the level of
knowledge acquisition by students through working with traditional versus interactive editions. For
instance, when using a specific test sample of an interactive book, learning effectiveness reached
90,7%, product practicality was 91,8%, and attractiveness reached 94,2%. Based on the study [13], it
can also be concluded that student motivation increases due to the use of interactive books — 96,37%.
From the perspective of evaluating the quality of book products, an interesting study [14]
analyzed reader behavior at various stages of book consumption using the expectation confirmation
theory. It is stated that readers can send feedback not necessarily after full consumption but at any
point along this trajectory, even before consumption begins. The results show that a significant
number of consumers leave positive or negative feedback before they start reading or after
progressing to an early chapter of the book. The data confirm the correctness of the research vector
chosen for our study, demonstrating that the initial impression of a book’s quality is formed based
on design: the correct format selection, the suitability of font and illustration design to the type of
publication, professional layout, etc.
It is important to identify the factors that have a key influence on the quality of interactive
editions. In [15], a set of certain quality characteristics related to books and their usage is described.
It compares the relationship between mobility, formats, and the weight of books, which are
determined by their volume, and readers’ bodily practices from the early print period to today. It is
noted that the format and volume of the edition significantly influence the reader's interaction
experience with the book, as they determine the convenience of holding the book, the degree of book
opening, and the comfort of carrying it, for example, for reading on the way to work or study. In
[16], the high competition among designers to attract readers’ attention is rightly noted. It is
mentioned that, for successful design at the initial project stage, the correct choice of edition type,
which determines its further physical representation, is crucial. Typography is highlighted as a
separate factor, being a simple and effective means of visual communication, through which each
letter can convey a specific message. The selection of font design elements directly depends on the
type of publication being designed. Attention is focused on the importance of layout as the process
of organizing content that ensures readability and forms the hierarchy of the reader’s attention to
the elements of the book. Accordingly, proofreading the laid-out pages, i.e., copyediting, plays an
important role. [17] also highlights the importance of layout as one of the key processes in book
design, serving to create harmony, coherence among the elements of the publication, and
maintaining overall coordination between them. In [18, 19], research conducted in various fields of
visual communication is discussed. Visual communication creates the same feelings and emotions
among people, regardless of the language they speak. It is, therefore, a universal means of
communication since vision is the most important human sense. Information obtained through
vision is remembered more clearly than information received through other senses. Thus, many
studies are dedicated to improving the quality of image reproduction, such as [20–22].
This work expands on the authors' previous research concerning the identification of the best
alternative website design options based on linear aggregation of criteria and fuzzy preference
relations [23], the study of reader demand for books [24], and the development of quality models for
encyclopedias and reference books [25].
At the same time, the analysis of literary sources revealed a lack of studies focused on identifying
sets of factors to determine the weight of their influence on the design process of interactive editions.
Therefore, developing a model of prioritized factor influence on the quality of interactive book
design, based on methods of systems analysis, ranking, hierarchy analysis, graph theory, and
semantic networks, is a relevant scientific task.

3. Material and methods
3.1. Determining the priority of factors
The creation of any interactive edition begins with conducting a thorough market analysis and
studying global trends to determine the relevance, expected demand, competitiveness of the product,
and the purchasing power of potential reader-buyers. In addition, as with any other stage, during
the design phase, it is crucial to meticulously follow all technological and aesthetic standards to avoid
releasing low-quality products. Therefore, there is a need to identify and analyze the factors affecting
the quality of the edition's design and to determine their priority.
The formalized representation of the relationships between the factors of interactive edition
design will involve the application of semantic networks and their description based on elements of
predicate logic. Structurally, a semantic network is a directed graph, where the set of nodes
corresponds to a set of factors, and the arcs represent the functional relationships between them.
The semantic network model creates a foundation for the further constructive description of the
subject area; it is visually clear and intuitive, as it is analogous to modern concepts of human
memory's physiological mechanisms [23].
Predicate logic is a part of mathematical logic, and its formal language is represented by terms
(any variables, constants, or functions) and the relationships between them—predicates (a logical
function that can take the value “true” or “false”). Here, we will provide some constructions of
predicate logic language that are used for the formal description of relationships between terms
through predicate formulas. The latter consist of simple (atomic) predicates and logical connections:
∧ — Logical “and”; ← — “if”; ∀ — Universal quantifier (for all); ∃ — Existential quantifier (there
exists at least one). In the context of the editorial and publishing process, we will refer to the terms
as factors, and the relationships between them will be illustrated by predicates. Thus, the use of
predicate logic in this work involves deriving all relationships between factors, taking into account
the structure of the semantic network.
In further research, it is advisable to consider the following definitions and statements [24].
Definition 1. Any technological process in printing production includes a set of factors that have
a decisive influence on the quality of its implementation, and, accordingly, on the quality of the
printed product.
Let 𝑅𝑅 = {𝑟𝑟1 , 𝑟𝑟2 , . . . , 𝑟𝑟𝑚𝑚 } — an arbitrary set of technological processes; 𝐷𝐷 =
�𝐷𝐷1 𝑚𝑚 , 𝐷𝐷2𝑚𝑚 , . . . , 𝐷𝐷𝑛𝑛𝑚𝑚 � — a set of factors influencing the quality of interactive edition design, where
nm — the number of factors m - the process. We will also consider that
n
=A ( Dk ) w ( D ), ( k 1, 2,..., m ) ,
= jk (1)
j =1

where: 𝐴𝐴(𝐷𝐷𝑘𝑘 ) — numerical indicator of the quality function m -the process; 𝑤𝑤�𝐷𝐷𝑗𝑗𝑗𝑗 � — numerical
weighted indicator of the contribution j - th technological process. Then the definition can be
presented as follows:

(∃p ) ( ∀D ) A ( Dk ) ; r ∈ R; d ∈ D. (2)
Definition 2. The rank and priority of a factor are determined by its weight coefficient. Among
any set of factors, at least one priority factor can be identified.
Thus, for the set of 𝑊𝑊 = �𝑤𝑤1𝑚𝑚 , 𝑤𝑤2𝑚𝑚 , . . . , 𝑤𝑤𝑛𝑛𝑚𝑚 � the weights of the factors in the design of
interactive editions, provided that 𝐵𝐵(𝑤𝑤) = 𝑚𝑚𝑚𝑚𝑚𝑚�𝑤𝑤1𝑚𝑚 , 𝑤𝑤2𝑚𝑚 , . . . , 𝑤𝑤𝑛𝑛𝑚𝑚 �, we will have:
(∃𝑝𝑝)(∀𝑤𝑤)𝐵𝐵(𝑤𝑤); 𝑟𝑟 ∈ 𝑅𝑅; 𝑤𝑤 ∈ 𝑊𝑊. (3)
Statement 1. The existence of connections between factors is a prerequisite for their formal
representation in the form of a graph.
Statement 2. Taking into account and analyzing the influences and dependencies between factors
in the initial graphical model, constructed based on expert judgments, allows for determining the
initial ranks of the factors.
Statement 3. When comparing factors within the initial graph, the synthesized multi-level model
only shows the advantages among them.
Statement 4. The identification of final weight values, which determine the rank and degree of
influence of factors on the design of interactive editions, is possible through the creation and
processing of a pairwise comparison matrix and the calculation of the normalized components of the
principal eigenvector of the matrix.
Definition 3. The set of factors, ordered by descending their normalized weight values, does not
contain factors that are absolutely identical in their degree of influence on the quality of interactive
edition design.
Provided that С(𝑤𝑤) = 𝑤𝑤𝑗𝑗 > 𝑤𝑤𝑗𝑗+1 for (𝑗𝑗 = 1,2, . . . 𝑛𝑛 − 1) It would be fair to note:
(∀𝑤𝑤)𝐶𝐶(𝑤𝑤); 𝑤𝑤 ∈ 𝑊𝑊. (4)
According to Statements 1–4, the synthesis of a multi-level model of the influence of factors on
the quality of interactive edition design is carried out by identifying the factors characteristic of the
analyzed process, creating, analyzing, and processing the initial graphical model, in which
connections between factors have been established based on expert judgments.
The basis of the ranking method is numerical indicators related to the quantities of influences
and dependencies between factors and their corresponding weight coefficients. In this context, we
distinguish between direct actions, referred to as first-order influences, and indirect actions, referred
to as second-order influences. Dependencies will also be distinguished, establishing similar first and
second orders of importance for them.
To calculate the total weight values of direct and indirect influences of factors and their integral
dependence on other factors, we will introduce corresponding notations. Let 𝑞𝑞𝑖𝑖𝑖𝑖 — the number of
influences or dependencies for 𝑗𝑗 -th factor (𝑗𝑗 = 1, . . . , 𝑛𝑛); 𝑤𝑤𝑖𝑖 — weight 𝑖𝑖 -th type. We will distinguish
certain types of connections between factors, which will depend on the type of connection identified
by a numerical index value, namely: 𝑖𝑖 = 1 — first-order influences; i = 2 — second-order influences;
𝑖𝑖 = 3 — first-order dependencies; 𝑖𝑖 = 4 — second-order dependencies.
For calculations, we will establish certain conditional numerical values for the weight coefficients
concerning the types of interconnections. We will consider that for both types of influences, the
𝑤𝑤
weights will be positive, i. e. 𝑤𝑤1 > 0, 𝑤𝑤2 = 21 , while for dependencies, they will be negative, namely:
𝑤𝑤
𝑤𝑤3 < 0, 𝑤𝑤4 = 23. The integral weight values of the factors based on the sums of the weights of all
types of connections will be denoted as 𝐷𝐷𝑖𝑖𝑖𝑖 .
Ultimately, we will obtain the following formula for calculations:
4 n
Dij = ∑∑ qij wi , (5)
=i 1 =j 1

where n — is the conditional number of the factor in the technological process or its stage.
Since, according to the specified initial conditions, w3 < 0 and w4 < 0 , thus, respectively, 𝐷𝐷3𝑗𝑗 < 0
and 𝐷𝐷4𝑗𝑗 < 0. To bring the weight values of the factors “to the beginning of the coordinates”, meaning
to obtain positive values, it is necessary to shift the histogram of the integral graphical
representation of all types of connections upward based on the relationship:
= 4j ,( j
∆ j max D3 j + max D= 1, 2,..., n ) . (6)

Taking into account (5) and (6), the final formula for obtaining the total weight values of the
factors will be as follows:
4 7
=DFj ∑∑ ( q w + ∆ ).
=i 1 =j 1
ij i j (7)

The values DFj serve as the basis for ranking weights, i.e., establishing the levels of factors
influencing the quality of interactive edition design. Based on the results of the ranking, we
synthesize a graphical model according to the obtained weight values, reflecting the priority
influence of the factors on the process.

3.2. Optimization of the Multi-Level Model of Factors
The primary significance of optimization lies in improving the input data through the application of
an appropriate and reasonable set of measures. The optimization of the interactive edition design
model is carried out using the hierarchy analysis method, which involves solving a series of tasks
[24]:

• Construction of a pairwise comparison matrix of factors using a scale of relative
importance of the objects.

In this case, the order of the matrix is determined by the number of analyzed factors, with the
established weights of the factors ( d n , d m ) being compared pairwise based on expert evaluations for

( )
each row and column of the matrix A . We accept that A = aij . The matrix is constructed in the
form of a table and is inversely symmetric, meaning aij = 1 aij , and the elements of the main diagonal
are equal to one. To facilitate the expert's work, the scale of relative importance of objects according
to Saaty is used (Tab. 1).

Table 1
Scale of Relative Importance of Objects
Importance
Comparison Criteria Explanation for Choosing the Criterion
Rating
1 Objects are equivalent No advantage d n on d m
One object slightly dominates There is a basis for a weak advantage over
3
the other d n on d m
There is a basis for a significant advantage
5 One object dominates the other
over d n on d m
One object significantly There is a basis for a clear advantage over
7
dominates the other d n on d m
One object absolutely Absolute advantage d n on d m
9
dominates the other Is undisputable
2,4,6,8 Intermediate values Auxiliary comparative assessments

• Calculation of the components of the principal eigenvector of the pairwise comparison
matrix. The principal eigenvector 𝐷𝐷(𝑑𝑑1 , 𝑑𝑑2 , … , 𝑑𝑑𝑛𝑛 ) is defined as the geometric mean of the
elements of each row of the matrix:

Di = n ai1 ⋅ ai 2 ⋅ ain i = 1, n, (9)
where n — the number of factors.

• Normalization of the values of the components of the principal eigenvector of the pairwise
comparison matrix, which form the set of optimal weight values for the factors influencing
the quality of the process.

The normalized components of the vector Dn define the optimized numerical priorities of the
factors and establish the preliminary result of solving the task.

n 1, n
ai1 ⋅ ai 2 ⋅ ain i =
Din = n
(10)
∑ a ⋅a ⋅a
i =1
n
i1 i2 in

To facilitate the presentation of the weight values of the factors, we multiply the optimized
components of the vector Dn by an arbitrary coefficient k . The consistency of the weight values of
the factors is evaluated by multiplying the pairwise comparison matrix on the right by the vector
Dn . As a result of the calculation, we obtain the normalized vector Dn1 . The components of the
eigenvector Dn 2 of the pairwise comparison matrix are obtained by dividing the components of the
vector Dn1 by the corresponding components of the vector Dn .

• Verification of the optimization results based on the criterion of the maximum value of the
principal eigenvalue of the pairwise comparison matrix, normative values of the consistency
index, and the consistency ratio.

The maximum eigenvalue λmax of a positive, inversely symmetric matrix A is determined as the
arithmetic mean of the components of the vector Dn 2 . The evaluation of the obtained solution is
determined by the consistency index IU , which is calculated using the formula:

λmax − n
IU = (11)
n −1
The obtained values are compared with the reference values of the consistency index—the random
index DI . The results can be considered satisfactory if the calculated consistency index IU does
not exceed 10% of the reference value of the random index DI , chosen based on the number of
factors being analyzed.
Thus, to confirm the adequacy of the solution to the given task, the inequality IU < 0,1 × DI must
hold. Below is a table of random index values for matrices of different orders, where the order of the
matrix corresponds to the number of analyzed objects (factors) and is indicated in the first row, while
the reference consistency index value for each order is indicated in the second row.
Table 2
Random Index Values for Matrices of Different Orders

Number of objects 3 4 5 6 7 8 9 10 11 12 13 14

Reference value of
0,58 0,90 1,12 1,24 1,32 1,41 1,45 1,49 1,51 1,54 1,56 1,57
the index

Additionally, the results are evaluated using the consistency ratio, which is calculated by the
formula: DU = IU DI . The results of pairwise comparisons can be considered satisfactory if
DU ≤ 0,1 . This will indicate a sufficient level of process convergence and adequate consistency in
expert judgments regarding the pairwise comparisons of the factors, as reflected in the
corresponding matrix.

• Synthesis of the optimized model for the prioritized influence of factors on the quality of
interactive edition design.

To obtain the weight values of the factors based on the multi-level model of factors, we assign
them a grading of conditional numerical values according to the level of factor dominance, starting
from the lowest. Let the weight of the lowest level be equal to 20 conditional units, and the weight
of each subsequent level increase by 20 conditional units relative to the previous factor. The obtained
numerical values of the factors are presented as components of the initial vector D0 , according to
their order in the matrix. Based on the obtained weight values represented by the vectors Dn and
D0 we construct a histogram and a comparative graph. After a detailed analysis and comparison of
the initial and normalized vectors, we synthesize the optimized model for the prioritized influence of
factors on the process. This model serves as the basis for designing alternative and calculating optimal
options for implementing the technological process, its stages, or individual operations, where the factors
are ranked by weight coefficients of importance, which is a logical and promising continuation of the
presented research.

4. Experiment, results and discussion
To ensure proper execution of the publication's design, where the quality of the result directly
influences the quality of the final product, it is necessary to identify and examine a set of interrelated
factors in this process, where the priority of each depends on the number of direct and indirect
influences and dependencies.
The initial formalized representation of the relationships between the factors forming the design
of an interactive edition, as mentioned above, will involve the application of semantic networks and
their description based on elements of predicate logic.
We will assume that D = { D1 , D2 , D3 , D4 , D5 , D6 , D7 } — the set of factors forming the design of an
interactive edition, where D1 — the type of edition; D2 — the volume of the edition; D3 — the format
of the edition; D4 — the layout of the pages; D5 — proofreading; D6 — font design of the edition;
D7 — illustrative and multimedia design of the edition.
We will form a semantic network of connections between the identified factors influencing the
quality of interactive edition design (Fig. 2).
Figure 2: Semantic Network of Factors Structuring the Edition.

Using predicate language constructions, the functional relationships between the factors of
interactive edition design will be presented as follows:
( ∀Di ) [ ∃ ( D1 , type of edition) ← regulates ( D1 , D2 ) ∧ defines technical and artistic
requirements ( D1 , D6 ) ∧ defines technical and artistic requirements ( D1 , D7 ) ];
( ∀Di ) [ ∃ ( D2 , volume of the edition) ← determines the scope of work ( D2 , D4 ) ∧ is regulated
( D2 , D1 ) ]; ( ∀Di ) [ ∃ ( D3 , format of the edition) ← defines the parameters ( D3 , D4 ) ∧ defines
technical requirements ( D3 , D6 ) ∧ defines technical and compositional requirements ( D3 , D7 ) ];
( ∀Di ) [ ∃ ( D4 , layout of the pages) ← foresees ( D4 , D5 ) ∧ implements the composition ( D4 , D6 )
∧ implements the composition ( D4 , D7 ) ∧ is determined by the scope of work ( D4 , D2 ) ∧
parameters are established ( D4 , D3 ) ]; ( ∀Di ) [ ∃ ( D5 , proofreading) ← is anticipated ( D5 , D4 ) ];
( ∀Di ) [ ∃ ( D6 , font design of the edition) ← technical and artistic requirements are taken into
account ( D6 , D1 ) ∧ technical requirements are taken into account ( D6 , D3 ) ∧ the composition is
realized ( D6 , D4 ) ∧ artistic requirements are stipulated ( D6 , D7 ) ];
( ∀Di ) [ ∃ ( D7 , illustrative design of the edition) ← stipulates artistic requirements ( D7 , D6 ) ∧
technical and artistic requirements are taken into account ( D7 , D1 ) ∧ technical and compositional
requirements are taken into account ( D7 , D3 ) ∧ the composition is implemented ( D7 , D4 ) ].
To establish the ranks of the factors in the design of interactive editions, we will use the factor
ranking method.
For the implementation of this method, we will construct hierarchical trees of connections with
other factors for each factor based on the developed semantic network (Fig. 2), taking into account
direct and indirect influences (Fig. 3) as well as direct and indirect dependencies (Fig. 4).
Based on the formulated statements and the introduced indicators, we will determine the total
weight values of the direct and indirect influences of the factors, as well as their integral dependence
on other factors. For calculations, we will accept the following conditional values for the weight
coefficients in conditional units: w1 = 10 , w2 = 5 , w3 = −10 , w4 = −5 . We will inpu0t the calculated
data using the formulas 2.1–2.8 into Table 3.
Figure 3: Graphs of Hierarchical Direct and Indirect Influences Between Factors of Interactive Edition
Design.

Figure 4: Graphs of Hierarchical Direct and Indirect Dependencies Between Factors of Interactive
Edition Design.

Table 3
Calculated Data and Ranking of Factors in Interactive Edition Design
Factor
Rank of Level of
Number q1j q2j q3j q4j D1j D2j D3j D4j DFj
the Factor ri Priority
j
1 0 0 1 2 0 0 -10 -10 45 3 4
2 3 2 0 0 30 10 0 0 105 5 2
3 1 3 1 0 10 15 -10 0 80 4 3
4 3 4 0 0 30 20 0 0 115 6 1
5 3 1 2 0 30 5 -20 0 80 4 3
6 0 0 4 5 0 0 -40 -25 0 1 6
7 1 0 3 2 10 0 -30 -10 35 2 5

Using the ranking data, we will construct a multi-level structured model (Fig. 5) that reflects the
position of each factor in the overall hierarchy and illustrates the connections between them as
defined in the semantic network (Fig. 2).

Figure 5: Multi-Level Model of Factors Influencing the Quality of Interactive Edition Design.

Thus, the highest level of priority belongs to the factor “format of the edition”, which is logical,
as the subsequent choice of the technological process for producing the edition and the necessary
equipment, under ideal conditions, depends on the chosen format. It should also be noted that as a
result of the ranking, the factors “volume of the edition” and “layout” received the same level of
priority. Therefore, the information regarding the weight values of the factors influencing the quality
of interactive edition design should be clarified. To do this, we will use the method of multi-criteria
optimization.
We will construct a pairwise comparison matrix of the design factors of the edition using the
scale of relative importance of the objects (Tab. 1). For convenience, we will present the matrix in
tabular form (Tab. 4):

Table 4
Pairwise Comparison Matrix of the Factors Structuring the Edition
D1 D2 D3 D4 D5 D6 D7
D1 1 4 1/3 3 5 7 6
D2 1/4 1 1/5 1/2 3 5 4
D3 3 5 1 4 6 8 7
D4 1/3 2 1/4 1 3 5 4
D5 1/5 1/3 1/6 1/3 1 4 3
D6 1/7 1/5 1/8 1/5 1/4 1 1/3
D7 1/6 1/4 1/7 1/4 1/3 3 1

By calculating the pairwise comparison matrix of the factors, we obtain the principal eigenvector
of the pairwise comparison matrix (2.9) D , the normalized vector (2.10) Dn , the normalized vector
for evaluating the consistency of the weight values of the factors Dn1 and the components of the
eigenvector of the pairwise comparison matrix Dn 2 :
D = ( 0,641; 2,613;1,06; 4,12;1,388; 0, 248; 0,394 ) ;
Dn = ( 0,061; 0, 25; 0,101; 0,394; 0,133; 0,024; 0,038 ) ;
Dn1 = ( 0, 46;1,886; 0,762; 2,973;1,003; 0,181; 0, 287 ) ;
Dn 2 = ( 7,540; 7,544; 7,545; 7,546; 7,541; 7,542; 7,553) .
For the convenience of further comparison between the initial and normalized vectors, we will
multiply the latter by an arbitrary coefficient, let’s say k = 500 . Then the adapted normalized vector
will take the form:
Dn × k =( 30,5;125; 50,5;197; 66,5;12;19 ) .
We will check the optimization results according to the criterion of the maximum value of the
principal eigenvector of the pairwise comparison matrix, normative values of the consistency index,
and the consistency ratio. After performing the calculations, we obtain: λmax = 7,544 ; IU = 0,091 .
The inequality 0,091 < 0,1 × 1,32 is valid, confirming the adequacy of the solution to the task. Since
DU = 0,069 , also holds, the execution of the inequalit 0,069 ≤ 0,1 further confirms a sufficient level
of convergence in the process and the adequate consistency of the expert judgments.
We will assign weight values to the factors based on the multi-level model of factors influencing
the quality of interactive edition design (Fig. 5). We will obtain the following series of values:
D6 — 20, D7 — 40, D5 — 60, D4 — 80, D2 — 80, D1 — 100, D3 — 120. The obtained numerical
values will be presented as components of the initial vector, according to their order in the matrix
(Tab. 4): D1 — 100, D2 — 80, D3 — 120, D4 — 80, D5 — 60, D6 — 20, D7 — 40.
We will obtain the initial vector: D0 = (100; 80;120; 80; 60; 20; 40 ) . The values of the factors Dn
and D0 , as well as the adapted values Dn × k will be entered into comparative Table 5.

Table 5
Options for Weight Values of Factors in Interactive Edition Design
i 1 2 3 4 5 6 7
D0 100 80 120 80 60 20 40
Dn 0,25 0,101 0,394 0,133 0,061 0,024 0,038
Dn × k 125 50,5 197 66,5 30,5 12 19
350

Weight Values of Factors
300
250
200
150
100
50
0
1 2 3 4 5 6 7
Factor Numbers

Initial Vector Normalized Vector

Figure 6: Comparative diagram of the weight values of the output vector components ( D0 ) and
normalized ( Dn ) vectors.

After analyzing Fig. 6, we see that in order to synthesize the optimized model of the priority
influence of factors on the process of forming the design of an interactive publication, it is necessary
to use the components of the normalized vector. As a result of normalization, different weight values
were established for factors D2 and D4 .
When constructing the optimized model (Fig. 7), it will be possible to avoid the equal priority of
factors D2 and D4 , which was observed in the model obtained through the ranking of factors (Fig.
5).
Thus, the constructed model of factor priority influence reflects the importance of each factor for
the design of an interactive publication. This was made possible through the formation of a set of
factors using methods of expert evaluation, analysis, and synthesis. It was essential not only to
highlight the influencing factors but also to demonstrate the direct and indirect influences and
dependencies between them.
The visualization of the relationships between the analyzed factors was implemented using graph
theory and semantic networks. The semantic network model (Fig. 2) became the foundation for the
further constructive description of the subject area.
The formalized representation of the relationships between the factors influencing the quality of
interactive publication design was achieved using elements of predicate logic.
Thus, the use of predicate logic in this work involved the formalized presentation of all
relationships between factors, taking into account the structure of the semantic network.
Moreover, to establish the degree of influence of each factor on the quality of the analyzed
process, it was decided to use the method of factor ranking. To implement the method in the process
of publication design formation, based on the developed semantic network, hierarchical models of
relationships between factors were built (Fig. 3, 4). Based on the determined priority levels (factor
ranks) (Tab. 3), a multi-level model of factors influencing the quality of interactive publication design
was synthesized. According to expert judgments and calculations, the factor with the highest weight
is the “publication format”, while the lowest is “typographic design of the publication”.
In the course of the study, this model was optimized due to the presence of two factors with the
same priority level (Fig. 6). The optimization of the model was driven by the need to improve input
data and was carried out using the method of hierarchy analysis, which involves solving several
tasks: constructing a pairwise comparison matrix (Tab. 4); calculating the components and
normalizing the values of the main eigenvector (Expressions 9, 10); verifying optimization results
based on the criteria of the maximum value of the main eigenvector, normative values of the
consistency index, and the consistency ratio; synthesizing the optimized model of factor priority
influence on the quality of the analyzed process (Fig. 7).

Figure 7: Optimized Model of Factor Priority Influence on the Quality of Interactive Publication
Design.

The results of the study can be used in the planning and organization of work related to book
design. The obtained information serves as the basis for forming a strategy for creating interactive
book publications, which involves choosing optimal alternative options and provides an
understanding of the necessary labor costs and the importance of factors. The prospect of further
scientific research is associated with predictive evaluation of the quality of interactive publication
design based on fuzzy logic methods and tools.

5. Conclusions
1. Based on expert evaluation, the following factors influencing the quality of interactive book
design were identified: D1 — type of publication; D2 — volume of the publication; D3 — format of
the publication; D4 — page layout; D5 — proofreading; D6 — typography; D7 — Illustration and
multimedia design of the publication.
2. A semantic network has been constructed that reproduces the connections between the factors
influencing the quality of interactive book design. Using predicate logic, a formal representation of
the relationships between these factors has been created.
3. The ranks of factors have been established for the process of designing interactive
publications. Based on the developed semantic network, hierarchical trees of connections have been
constructed for each of the factors involved in this process, taking into account both direct and
indirect influences as well as direct and mediated dependencies.
4. Based on the ranking results, a synthesis of a graphical multi-level model of the factors
influencing the quality of interactive publication design has been carried out. It has been determined
that the factor D3 “publication format” holds the highest priority level, while the factor D6
“typographic design”.
5. Using the hierarchical analysis method, the optimization of the multi-level model of factors
influencing the quality of interactive publication design was carried out, due to the equal priority
obtained for the factors D2 “publication volume” and D4 “page layout” in the previous research
stage. As a result of the optimization, it was determined that the factor D4 “page layout” has a higher
priority than D2 “publication volume” and the weight values of other factors were clarified. The
optimization criteria include: the eigenvalues of the matrices λmax = 7,544 , the consistency index
IU = 0,091 , and the consistency ratio DU = 0,069 . These criteria fall within acceptable limits,
indicating the adequacy of the problem solution.
6. A model of priority influence of factors on the quality of interactive publication design has
been developed, which will serve as a theoretical and practical basis for making informed decisions
regarding the technological operations related to the formation of the design of interactive books.

Declaration on Generative AI
The authors have not employed any Generative AI tools.

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