=Paper= {{Paper |id=Vol-2533/paper18 |storemode=property |title=The Use of Mathematical Tools to Determine the Importance of Multimedia Products Design Elements |pdfUrl=https://ceur-ws.org/Vol-2533/paper18.pdf |volume=Vol-2533 |authors=Oleksandr Tymchenko,Svitlana Vasiuta,Olha Sosnovska,Andriy Konyukhov,Marek Dudzik,Anna Romanska-Zapala |dblpUrl=https://dblp.org/rec/conf/dcsmart/TymchenkoVSKDR19 }} ==The Use of Mathematical Tools to Determine the Importance of Multimedia Products Design Elements== https://ceur-ws.org/Vol-2533/paper18.pdf

The Use of Mathematical Tools to Determine the
Importance of Multimedia Products Design Elements

Oleksandr Tymchenko1[0000-0003-2052-5165], Svitlana Vasiuta2[0000-0003-0079-9740],
Olha Sosnovska2[0000-0001-5413-2517], Andriy Konyukhov2[0000-0002-4643-9620],
Marek Dudzik3[0000-0002-2475-5489] and Anna Romanska-Zapala3[0000-0003-2303-4337]
1.
University of Warmia and Mazury, Olsztyn, Poland
o_tymch@ukr.net
2.
Ukrainian Academy of Printing, Lviv, Ukraine
lanapavliv@gmail.com, olhakh@gmail.com, konyukhow@gmail.com
3.
Cracow University of Technology, Cracow, Poland
mdudzik@pk.edu.pl, a.romanska@pk.edu.pl

Abstract. The development of digital technology has led to the creation of new
ways of transmitting information. These changes are particularly noticeable in
the field of education, namely the widespread introduction into the educational
process of multimedia products that promote learning in universities and
research institutions. Their attractive features significantly affect the interest of
students and better perception of the received information. This leads to the
constant modernization of information and functionalities used. That is why this
work presents a study of design elements that influence the creation of high-
quality multimedia products. Experts highlight the following main multimedia
product design elements: color palette, contrast, composition, background, font,
plasticity, and rhythm. We the use of the theory of graphs, mathematical
calculations are performed to rank the priority of the importance of the
described elements. As a result of mathematical calculations, we constructed a
hierarchical model of the importance of design elements that affect the quality
of the information in multimedia products. To optimize the obtained structured
multilevel model, we used the Saaty pairwise comparison method. The key
objective of this method is to investigate the presence and consistency of
pairwise comparisons of the weights of the elements and to obtain a numerical
estimate of the connection between them in the original graph. Finally,
suggestions are made for further research with the use of multimedia products.

Keywords:Multimedia Product, Graph Theory, Saaty Method, Pairwise
Comparison Method, Design Elements, Multilevel Model.

1. Introduction

The rapid development of computer technologies encourages developers to introduce
new models of cooperation and possibilities in the design of multimedia products. A

Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0)
2019 DCSMart Workshop.
striking example is the dynamics of publications on media products and their
widespread use in the learning process.
As noted in a study [1], in the so-called information society, the relations resulting
from the interaction of its technological bases with the consumer have changed the
perception of information in general. The Internet is considered as the multimedia
backbone and acts as the source of information. These changes put professors and
students in the new educational conditions and require teamwork to solve
technological challenges.
Today multimedia products face the task of addressing these challenges. These
products provide opportunities for both professors and students to rely on attractive
cognitive and effective resources for the development of the educational process. As a
result, the educational process became more interesting, and the use of multimedia
products increased students' motivation and creativity, which are considered to be two
key aspects of success.
However, it should be noted that the research that would be conducted to
determine how the elements of a multimedia product design affect one another and, in
general, how these elements affect a student's perception of information is rather
limited and is rare in literature. In our opinion, this indicates the feasibility and
relevance of these studies.

2. Formal Problem Statement

The vast majority of all multimedia products consist of the same set of design
elements, which, depending on the scope, may differ in their "weight" and feature
feed.
One of the most important points in the multimedia product design is determining
which design element should take priority. Moreover, to which elements we need to
pay more attention to and highlight multimedia design. Given the above, to evaluate
the importance of the design elements of a multimedia product, we proposed to use a
mathematical tool called the graph theory. This theory is one of the modern direction
of mathematics, which is rapidly developing. To determine the optimality of decisions
in terms of multicriteria, as noted in the literature, a special place is taken by the
analytic hierarchy process by T. Saaty. This technique has qualitative advantages over
others, as it allows to evaluate higher levels based on the interaction of different levels
of the hierarchy.
The main problem that is determined in the framework of this study is solved by
the pairwise comparison and development of a certain importance priority ranking.

3. Literature Review

The work [2], among the other interesting studies in this area, concerns the studies of
cognitive component and multimedia learning from 2015 to 2019. We analyzed 94
articles in terms of types of cognitive component and its measurements, multimedia
learning principles, dependent and independent variables, cognitive processes, types
of multimedia learning environments, and demographic characteristics of research.
Most of the peer-reviewed multimedia cognitive studies have been conducted by
researchers from Europe, especially from Germany, then Asia, the USA, Australia,
and Africa. In this paper, it is noted that those studies are more dominated by
subjective than objective methods of measuring the cognitive component. The main
elements studied were design, material type, presentation format, and individual
differences. These studies have elaborated and identified a number of gaps in the
cognitive study of content related to multimedia learning.
The research [3] is considered as valuable work in this field. We analyzed 52
articles and 58 studies related to the study of cognitive processes in multimedia
learning with the help of certain variables using eye movement tracking technologies.
By using the eye movement tracking method, we came to the conclusion that there is
a certain link between cognitive processes and learning performance. Also, in work
based on the research, some inaccuracies were identified in existing conclusions
regarding multimedia learning design. The suggestions were made for further research
and practice.
In [4], [5] it is noted that the use of information technology in the educational
process is not new, and studies in this direction have been conducted by many
researchers. The use of multimedia products in this process is effective since it
involves different media with an interactive and informative connection with the
material. Their effectiveness lies in engagement and motivation, as well as reduction
of the mistakes in the learning process. It is also noted that the student sometimes
lacks sufficient cognitive awareness and skills in understanding the material
presented. Therefore, the pedagogical factor is an important moment in the
presentation of the material in a multimedia product. It serves to increase students'
cognitive awareness of what they know and what they need to learn from a particular
topic.
The usefulness of using multimedia products in the educational process is shown
in work [6]. In particular, multimedia products provide teachers with a great
opportunity to demonstrate and visualize their subject matter, as well as allow them to
prepare course material in a way that optimizes student learning skills. It also
describes the utility of using animation in multimedia products, which enables
students to become self-trained in subject learning. It gives the structure of animation
and advantages in its use. The issue of creating a virtual learning environment is also
considered important in work.
There are a number of other publications that discuss the multimedia features in
the educational process. For example, the study [7] shows the advantages of using
such multimedia elements in education as images, video, and multidimensionality.
And study [8], show that the use of gestures in combination with multimedia products
is useful for the education and student perception of the information provided.
Literary sources include works such as [9] concerning the review of networks and
their structure for multimedia transmission and development of a specialized software
product.
4. Materials and Methods

In order to highlight the main design elements and their weight in a multimedia
product, we conducted a survey that included students and professors as respondents.
Surveys results are the following important elements of the multimedia design:
- composition, this design element is responsible for the elements balance in
the multimedia product, which in turn allows the user to correctly define the
hierarchy of objects, the sequence of actions, and allows the developer to control
the user's view;
- the color palette, when the color is oversaturated in the multimedia product
design it is more difficult for the consumer to navigate in the product, and
accordingly, it is harder to gather the required information;
- contrast, this design element is responsible for the interaction of opposite
elements of the composition, it allows to distinguish differences and similarities,
to attract the attention of the consumer;
- background properties, the inconsistency of correct submission of
background parameters leads to compositional problems, often drawing
unnecessary attention, or the inability to read the text;
- font properties, this parameter strongly affects the readability of the text,
which is usually the main content in a multimedia product;
- plasticity and rhythm, these elements are used to achieve a certain purpose,
for example, to set the view direction or for continuity of attention, which in turn
will give the integrity, adjust the appearance, help in finding the necessary
materials.
The survey responses serve for further elaboration and ultimately clarification
what multimedia product design elements are important and which elements should
be given particular attention when using them.

5. Experiments, Results and Discussions

In the conducted surveys, respondents identified a number of elements that provide a
convenient perception of information from multimedia products. The next task for the
respondents was to indicate which element is more important and how they are related,
that is, to indicate how the elements interact. For further work, we use graph theory
and construct a hierarchical model of the importance of design elements. By using
this method, we can rank the importance of the elements, and we can determine the
impact among them. The expediency of using this mathematical tool has been proved
in our previous similar studies [10 - 13].
To solve this problem, using the graph theory, we must assume that the elements
considered are a certain set В={b1, b2, …, bn}. From this set, we define the subset
В1  В of the most essential elements. To simplify the information presented and
further mathematical calculations, we supplement our mathematical notation with
certain mnemonic names, namely:
b1 – composition (COM);
b2 – color palette (CP);
b3 – background properties (BP);
b4 – plasticity (PL);
b5 – rhythm (R);
b6 – contrast (CONT);
b7 – font properties (FP).
A subset of the elements B1 and the interaction indicated by the respondents between
them are represented as an indicative graph (see Fig. 1).

b1
COM
b7 b2
FP CP

b6 b3
CONT BP

b5 b4
R PL

Fig.1. The graph of the relationship between the elements of influence in the multimedia
product design.

Taking into account the graphs theory and the graph above, we construct a binary
dependence matrix A for the set of vertices B with the following condition [14]:


 0, if the factor i does not depend on the factor j
а  1, if the factor i depends on the factor j
ij 
 (1)

For better display, we place the dependency matrix in Table 1 by adding an
information row and a column with mnemonic element names.

Table 1. The element dependency matrix.

COM CP BP PL R CONT FP
COM 0 0 0 0 0 0 0
CP 1 0 1 0 1 1 0
BP 1 0 0 0 0 1 1
PL 0 0 0 0 1 0 0
R 1 0 0 0 0 0 0
CONT 1 0 0 0 0 0 0
FP 1 0 0 1 1 0 0
Based on the graph and the obtained binary matrix A, we form the reachability
matrix by this rule (I+А), (where I – identity matrix), which is raised to a power n to
satisfy the condition:

 І  Аn 1 I  An  I  An 1
(2)

We are filling the reachability matrix (Table 2) with binary elements on rows
(from left to right) according to the following rule:


1, if we can reach the vertex i from the vertex j
d   0, in anothe case
ij 

(3)

Table 2. The reachability matrix.

COM CP BP PL R CONT FP
COM 1 0 0 0 0 0 0
CP 1 1 1 1 1 1 1
BP 1 0 1 1 1 1 1
PL 1 0 0 1 1 0 0
R 1 0 0 0 1 0 0
CONT 1 0 0 0 0 1 0
FP 1 0 0 1 1 0 1

The reachability matrix is necessary for dividing the set of vertices B into a subset
of levels. For this, all the vertices of our graph must be divided by the vertices of the
precursors and reached. The vertex bі is called reached from vertex bj, if there is a
path from bj to bі in the indicative graph. We denote this subset of the reached vertices
as R(bі). The vertex bj is called the precursor of the vertex bі, if it is possible to reach
bі from bj. We denote this subset of precursors vertices as А(bі). The intersection of
these subsets will be a subset
А(bі)=R(bі)  А(bі) (4)

The set of vertices A(bi)=R(bi)  A(bi), for which the condition of inaccessibility
from any of the vertices of the remaining set B is satisfied, will be defined as the level
of the hierarchy [10, 14].
Performing the sets of actions above enables us to determine the first level of the
element hierarchy and to form Table 3. In this table, a subset of R(bi) is formed from
the elements of the і-th row of the reachability matrix, if equal to one. The subset
formation А(bi) comes from the elements of the i-th column of the reachability matrix,
again, if it is equal to one. According to this theory, a subset R(bi)  А(bi) forms as a
logical intersection of element subsets R(bi) and А(bi).
Table 3. Defining the first level of the element hierarchy.

bi R(bi) А(bi) R(bi)  A(bi)
1 1 1, 2, 3, 4, 5, 6, 7 1
2 1, 2, 3, 4, 5, 6, 7 2 2 ←
3 1, 3, 4, 5, 6, 7 2, 3 3
4 1, 4, 5 2, 3, 4, 7 4
5 1, 5 2, 3, 4, 5, 7 5
6 1, 6 2, 3, 6 6
7 1, 4, 5, 7 2, 3, 7 7

From the obtained results of the construction of Table 3, we can state that equality
A(bi)=R(bi)  A(bi) holds for the element under number 2. This number corresponds
to the color palette used in the multimedia product. According to graph theory, this
element is considered to be the lowest ranking of importance. We remove the second
row and exclude from the table the value of 2. Similarly, how we determined the first
level of the element hierarchy, we obtain all the following levels (Tables 4-7):

Table 4. Defining the second level of the element hierarchy.

bi R(bi) А(bi) R(bi)  A(bi)
1 1 1, 3, 4, 5, 6, 7 1
3 1, 3, 4, 5, 6, 7 3 3 ←
4 1, 4, 5 3, 4, 7 4
5 1, 5 3, 4, 5, 7 5
6 1, 6 3, 6 6
7 1, 4, 5, 7 3, 7 7

Table 5. Defining the third level of the element hierarchy.

bi R(bi) А(bi) R(bi)  A(bi)
1 1 1, 4, 5, 6, 7 1
4 1, 4, 5 4, 7 4
5 1, 5 4, 5, 7 5
6 1, 6 6 6 ←
7 1, 4, 5, 7 7 7 ←

Table 6. Defining the fourth level of the element hierarchy.

bi R(bi) А(bi) R(bi)  A(bi)
1 1 1, 4, 5 1
4 1, 4, 5 4 4 ←
5 1, 5 4, 5 5
Table 7. Defining the fifth level of the element hierarchy.

bi R(bi) А(bi) R(bi)  A(bi)
1 1 1, 5 1
5 1, 5 5 5 ←

From the results of determining the hierarchy of importance of the multimedia
product design elements, we see that the highest level (level 6) corresponds to the
composition. According to the results obtained, we construct a hierarchical model of
the importance of the elements (see Fig. 2).

b2
1st level
CP

2nd level b3
BP
3rd level b7 b6
FP CONT
4th level b4
PL

5th level b5
R

6th level b1
COM

Fig.2. The hierarchical model of the element importance

The resulting hierarchical structured model simulates the priority of the
importance of the individual elements of multimedia product design. From the results
obtained, we can say that the composition is the most important element in the
multimedia product design. The aforementioned makes it possible to argue that it is a
key element in the construction, and it provides visual contact between the user and
the multimedia product. As we can see from the obtained model, the rhythm and
plasticity in the multimedia product design should also be considered as important
elements. These two elements make it possible to build the necessary hierarchy of the
representation of all components of a given product. At the lower level is a color
palette.
The next mathematical action is to solve the problem of optimizing the resulting
model. A special place for this is given to the method of analytic hierarchy by
T. Saaty. This method has certain advantages over others, as it allows to take full
account of all the criteria that have been put forward to determine the optimal
solution. The main task of using this method is the challenge of experts to determine
how much the use of one element outweighs the other [15]. In other words, we need
to give numerical weights to the elements of a product's multimedia design.
For the following mathematical calculations, we use the scale of relative
importance by Saaty [16, 17].
Using this scale, to determine the numerical weight of the design elements, we
create a matrix of pairwise comparisons B=(bij) that is equal to bij 1/ b ji (Table 8):

Table 8. The pairwise comparison matrix.

COM CP BP PL R CONT FP
COM 1 6 5 3 2 4 4
CP 1/6 1 1/2 1/4 1/5 1/3 1/3
BP 1/5 2 1 1/3 1/4 1/2 1/2
PL 1/3 4 3 1 1/2 2 2
R 1/2 5 4 2 1 3 3
CONT 1/4 3 2 1/2 1/3 1 2
FP 1/4 3 2 1/2 1/3 1/2 1

The pairwise comparison matrix enables pairwise comparisons of elements at a
certain level of the hierarchical structure in terms of their importance to the element at
the highest level of the hierarchy.
According to this method, experts give more weight to the elements that are more
significant by the results of the calculations, and accordingly, less weight is given to
elements with less importance. With the obtained hierarchical model (Fig. 2) and
using this method of experts, we give the following number of official registration
data, namely: COM (b1) – 60; CP (b2) – 10; BP (b3) – 20; PL (b4) – 40; R (b5) – 50;
CONT (b6) – 30; FP (b7) – 30.
The principal eigenvector, by this method, is calculated as the geometric mean in
the row of the resulting matrix and, in our case is equal to:

E0= (3,12; 0,333; 0,504; 1,345; 2,099; 0,905; 0,742).

The priority vector component can be calculated by the following equality:
n
En  Ei  Ei (5)
i 1

Accordingly, we obtain the following values of the normalized vector:

En = (0,344; 0,036; 0,055; 0,148; 0,231; 0,1; 0,082).

For a better representation of the components of this vector, we can multiply by a
factor k, for our case we can make it equal to 1000. Accordingly, we obtain:
En x k= (344; 36; 55; 148; 231; 100; 82).
To assess the consistency of expert judgment, we calculate max :

n
max   M j E j , (6)
j 1

n
where M j   zij – is the sum of the elements of the ith column of the matrix; Ej –
i 1
vector of priorities of the analyzed matrix. In our case, we obtain λmax = 7,18.
By the method described in the literature [12, 16], we can say that the value max
is the main characteristic, used to establish the consistency of expert judgment,
regarding pairwise comparisons of items in tasks with undetermined factors. The
result of the decision is determined by the consistency index, in our case, it is IU =
0,03. For the proper consistency of expert judgment, the following inequality must be
satisfied IU<0,1xWI. Where WI – the reference value of the consistency index, in our
case for 7 elements, it is 1.32. Substituting the data obtained into this inequality, we
can say that there is proper consistency (0,03< 0,1 х 1,32).
The weights of the design elements that are obtained as a result of using this
technique can be entered in Table 9.

Table 9. The factor weights.

b1 b2 b3 b4 b5 b6 b7
Е0 60 10 20 40 50 30 30
En 0,344 0,036 0,055 0,148 0,231 0,1 0,082
En x k 344 36 55 148 231 100 82

The obtained values of the components of the normalized vector are the optimized
weights of the considered elements of the multimedia product design used to build the
optimized model (see Fig. 3).

1st level 2nd level 3rd level 4th level 5th level 6th level 7th level

b2 b3 b6 b7 b4 b5 b1
CP BP CONT FP PL R COM

Fig.3. The optimized model of the hierarchy of importance of the multimedia product design
elements

Therefore, the obtained multilevel optimized model of the hierarchy importance of
the multimedia product design elements confirms that the most important element in
the design is the composition. The next priority is rhythm and plasticity, which are
also important. The less important design elements are the background and color
properties.

6. Conclusions

The proposed use of mathematical tools, namely graph theory made it possible to
evaluate and calculate the importance of multimedia product design elements that are
useful and highly regarded by students. As a result of the research, we constructed a
hierarchical multilevel model of the relative importance of the design elements. The
adequacy of the calculation is confirmed by the permissible consistency index. Based
on weight values, we constructed an optimized multilevel model of the importance
hierarchy of multimedia product design elements as a result of the expert survey. This
method of calculation can be used when the parameters of a certain process have
different numerical and qualitative characteristics, which does not allow to obtain an
adequate relation between them and influence them on the process itself.

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