=Paper=
{{Paper
|id=Vol-3101/Paper12
|storemode=property
|title=Forecasting the reader's demand level based on factors of interest in the book
|pdfUrl=https://ceur-ws.org/Vol-3101/Paper12.pdf
|volume=Vol-3101
|authors=Vsevolod Senkivskyy,Sergii Babichev,Iryna Pikh,Alona Kudriashova,Nataliia Senkivska,Iryna Kalynii
|dblpUrl=https://dblp.org/rec/conf/citrisk/SenkivskyyBPKSK21
}}
==Forecasting the reader's demand level based on factors of interest in the book==
https://ceur-ws.org/Vol-3101/Paper12.pdf
Forecasting the Reader's Demand Level Based on Factors of
Interest in the Book
Vsevolod Senkivskyy1, Sergii Babichev2,3, Iryna Pikh1,4, Alona Kudriashova1, Nataliia Sen-
kivska1,4 and Iryna Kalynii5
1Ukrainian Academy of Printing, 19, Pid Holoskom St., Lviv, 79020, Ukraine
2Jan Evangelista Purkyne University in Usti nad Labem, Ceske mladeze, 8, Usti nad Labem, 40096, Czech Republic
3Kherson State University, Universytetska st. 27, Kherson,73003, Ukraine
4Lviv Polytechnic National University, 12, Stepana Bandery St., Lviv, 79013, Ukraine
5Berezhany Agrotechnical Institute, 20, Academichna St., Berezhany, 47501, Ukraine
Abstract
The selection and description of a set of factors related to the study of the process of interest in the
book has been done, which became the initial precondition to assess the prognostic level of reader’s
demand. The growth of risks of the low reader’s demand level among young people is indicated. A for-
malized version of the relationships between the factors of demand for the book is represented using a
semantic network that provides a graphical and linguistic representation of reading intensity factors.
Using the methodology of hierarchy modelling, the levels of factors preferences are established and the
weight priorities of their influence on the studied process are calculated. An optimized variant of factors
ranking according to the importance of forming the intensity of the reader’s demand is obtained. Based
on the methods of fuzzy set theory, the membership functions of linguistic variables (factors of interest
in the book) are calculated, fuzzy knowledge bases are formed and fuzzy logical equations are derived,
which became the basis for prognostic assessment of the reader’s demand level.
Keywords 1
Factor, reader’s demand, risks of low demand for the book, fuzzy knowledge base, fuzzy logical equa-
tions, fuzzification, defuzzification.
1. Introduction
There is a book in front of us – a complex and ingenious work of the human spirit. It provides the
transfer and assimilation of knowledge, reproduces the life history of individuals and civilizations,
enables the communicative connection between different nationalities. While reading the book,
few people think about the difficult path of thought (ideas, considerations, views, life stories) be-
fore becoming a printed word in a usual format that ensures its dissemination, use and, conse-
quently, impact on human community.
CITRisk’2021: 2nd International Workshop on Computational & Information Technologies for Risk-Informed Systems, September
16–17, 2021, Kherson, Ukraine
EMAIL: senk.vm@gmail.com (V.Senkivskyy); sergii.babichev@ujep.cz (S.Babichev); pikhirena@gmail.com (I.Pikh); kudriasho-
vaaliona@gmail.com (A.Kudriashova); senkivskanata@gmail.com (N.Senkivska); iryna.kalynii@gmail.com (I.Kalynii)
ORCID: 0000-0002-4510-540X (V.Senkivskyy); 0000-0001-6797-1467 (S.Babichev); 0000-0002-9909-84444 (I.Pikh); 0000-0002-
0496-1381 (A.Kudriashova); 0000-0002-6096-2282 (N.Senkivska); 0000-0003-1296-6454 (I.Kalynii)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
A significant amount of research connected to the book relates to the processes and factors of
formation and prognostic assessment of the edition quality, taking into account the technological
stages of its production [1, 2]. Sociological and historical studies related to the book business, the
issue of book distribution also attract the attention of researchers [3, 4]. In contrast, the problem
of the demand for a book concerning the "life" of a book after it leaves the walls of a printing
house remains somewhat unexplored. The active age of a book depends on the spiritual needs of
its fans, which are determined by the reader's interest and many preconditions of an objective
nature.
The reader's demand for a book, like any other process of human activity, is characterized by
certain factors that affect its intensity. One of the important tasks will be the separation, description
and structured representation of the relationship between factors, reasonable ranking by levels of
importance, calculation of conditional weights and synthesis of structured, classified as multilevel,
display of the priority of factors on the book demand based on the obtained data. The formulation
and solution of problems of formalized assessment of the reader’s demand summarizes the study
of the process of interest in the book, which involves the formation of term-sets of values of lin-
guistic variables that identify the factors of interest in the book, the calculation of membership
functions of variables, the development of fuzzy knowledge bases of linguistic variables and the
derivation and solution of fuzzy logical equations, which has become the basis for prognostic as-
sessment of the reader’s demand level based on the methods of fuzzy logic.
The solution of such weakly formalized problems should be carried out on the basis of informational
approaches to systems analysis, which allow the use of universal tools of hierarchical systems theory,
modelling theory, fuzzy sets and fuzzy logic methods to achieve numerical characteristics of the stud-
ied process.
2. Problem Statement
The formalization of the input database of the studied subject area should be performed using
semantic networks [6, 7] and the method of hierarchy analysis [8] to establish the priority of the
influence on the described process of a set of the related factors (the first stage of the problem), as
well as fuzzy set theory means [9-11], which will provide a numerical expression of the reader’s
demand level, taking into account the term-set of values of linguistic variables (the second stage).
The application of these approaches will not only rank the factors of the reader’s interest in the
book, which in itself will improve the thematic planning of the publishing activity and the book
distribution processes, but also provide forecasting the reader’s demand level taking into account
possible combinations of values from a predetermined set.
The nodes of the semantic network will reflect the semantics of concepts, i.e. factors that in the
second stage of the study are presented in the form of abstract linguistic variables. The arcs repre-
sent functional (semantic) relationships or connections between them [1, 6]. The combination of
linguistics (semantics of linguistic variables) and mathematics (networks as a variant of the graph)
provides, on the one hand, the use of ordinary language to describe the knowledge base of the
studied process, and on the other hand, it allows the use of formal methods and fuzzy logic for the
research, the ultimate goal of which is the prognostic assessment of the reader’s demand level.
The model of the process of forecasting the reader’s demand intensity can be presented by a
set of appropriate steps, the implementation of which is shown in Fig. 1.
Development of a model of logical Formation of a term-set of values Designing a fuzzy knowledge
inference – a formalized display of of linguistic variables attributed base, constructing fuzzy logical
the process of forming the level of to subordinate levels of demand equations, assessment of subordi-
reader’s demand for a book and the for a book nate levels of demand
risk of its absence
Calculation of the numerical Analytical display and calcula- Construction of fuzzy logical
value of the integral indicator of tion of numerical values of equations of term-assessments
the level of reader’s demand for membership functions of subor- of the importance of subordinate
a book dinate levels of demand levels of demand for a book
Figure 1: Structural and functional model of the process of calculating the level of reader’s demand for
a book
The essential element and advantage of fuzzy logic is the possibility of fuzzification, i.e. the re-
placement of components of a certain set with the corresponding concepts of a fuzzy set. It is
known that its essence is to compare the term-set of values of the analysed factors corresponding
to the fuzzy format of variables – membership functions. Fuzzification provides a fairly high level
of conformity of the model to the real object and serves, as it will be shown later, as a basis for
further modelling of the prognostic assessment of the reader’s demand level.
In the works of the founder of fuzzy logic Zadeh [12, 13], the concept of a universal set D is
introduced as such, which applies to the whole problem area. Then the fuzzy subset M of the set
D is determined through the scale D and the membership function µ M ( d ) [2], i.e.:
=M {( µ ( d ) , d ) , d ∈ D} ,
M (1)
where ( 0 ≤ µ M ( d ) ≤ 1) .
The membership function establishes the degree to which each element of a fuzzy set belongs
to a universal set, i.e. M ∈ D . Under the condition of the discreteness and finiteness of the basic
scale (i.e. divided into quanta or intervals) the fuzzy set is:
n
=M (=
µ ( d ) / d , µ ( d ) / d ,..., µ ( d ) / d ) ∑ µ ( d ) / d ,
M 1 1 M 2 2 M n n M i i (2)
i =1
n
or simplified: M = ∑ µi / di . The record means "attachment" ФН µ M ( di ) to the element di .
i =1
Eventually the membership functions act as an identifier of the input values of linguistic variables
in a fuzzy format, i.e. the set of values of the variable d is matched to the membership function
µ (d ) .
3. Related Works
In the list of literary sources, much attention is paid to the study of factors that shape the habit of
reading throughout a person's life and the state of the book and newspaper and magazine market
related to it. Thus, the paper [5] justifies the need to study the reading audience, arguing that the
proper implementation of all technological procedures for the production of books, newspapers or
magazines without taking into account the information about the end reader can not fully ensure
the quality. In [14] it is about the influence of such factors as the purpose of reading, the level of
education, gender, income, access to the Internet, etc. on the choice of the carrier of book products:
e-books or printed on paper. It is also noted that e-books, despite their popularity, cannot replace
printed ones because they have unique characteristics. However, the emergence of e-books con-
tributes to the mass distribution and, consequently, the availability of books, on which the level of
reading depends. Studies [15, 16] confirm the existence of a relationship between the level of
reading and social status, cultural level, lifestyle. According to [17, 18], it is the family that instils
the habit of reading in a person in the early life stages, shaping him as a person. In [18] it is noted
that the profession and the level of education of parents significantly affect the interest in reading
in children. [19, 20] confirm the influence of living environment, place of study and family on
motivation to read. [21] presents a study of the level of reading and describes the results of a survey
in which most respondents noted one of the main factors being the influence of the family. In
contrast to the more definite influence of the above-mentioned factors, [16] deals with the obvious
relationship between the age of the reader and the level of his reading, and in [22] – between the
gender and the level of reading. It can be concluded that a person's socio-cultural environment,
personal characteristics and access to literature determine the level of reading to a greater extent
than the age or gender. The above considerations are taken into account in further research when
choosing a set of factors influencing the level of reading, their interdependencies and term-sets.
It should be noted that the analysed works do not give a clear idea of the priority of factors and
do not determine their impact on the level of a person’s reading in the quantitative area. The es-
sence of these publications is exclusively in the analytical and sociological description of the prob-
lem. That is why, in order to enable not only assessing, but also prognostic activity (and, as a
consequence, corrective one), it is expedient to establish clear relationships between factors, their
priorities and to carry out prognostic assessment of the reader’s demand level.
The analysis of publications related to the above issues characterizes the lack of completeness
of scientific research related to the formation of components of the information database, focused
on the study of a poorly formalized social problem – the reader's demand for a book. In the vast
majority of cases, researchers focus on processing sociological and statistical data, which, despite
the relevance and demand as to the ways of intellectual development of society, does not provide
a final prognostic assessment of the level of reader’s interest in the book, which would operate in
a separate expert set of factors of demand for printed products.
The above considerations determine the application of non-traditional, in our opinion, infor-
mational approach in this area, the result of which will be, on the one hand, the ranking of factors
by importance and numerical weights based on the semantic network of relationships between
them, which will synthesize multilevel structural models of priority influence of factors on reader’s
demand; on the other hand, prognostic numerical assessment of the reader’s demand intensity us-
ing fuzzy set theory (fuzzy logic), including a hierarchical model of logical inference, membership
functions of linguistic variables, fuzzy knowledge base and fuzzy logical equations, calculation of
numerical value of generalized forecasting of interest in a book through the defuzzification of the
linguistic term "level of reader’s demand".
A separate problem today is a rather low reader’s demand level among young people, and the
risks of its increasing require separate research and coverage in scientific publications. This, how-
ever, does not detract from the general interest in the printed book.
4. Materials and Methods
According to the task, the research of the process of forecasting the intensity level of demand for
a book, is performed in two stages, focusing first on obtaining a multilevel model of factors, struc-
tured by the importance of influencing readers' preferences, which will be the initial information
component of determining and calculating a numerical indicator of the reader’s demand level.
4.1. Semantic network of the reader’s demand factors
For a formalized description and content filling of the subject area, a graphic representation is used
in the form of semantic networks, which will highlight significant aspects of knowledge about the
factors influencing the fundamental ability of forecasting the behaviour of readers as to the level
of their interest in a book [1, 2, 5].
Let the list of factors related to the process of assessing the demand for a book contain a mathe-
matical notation and its semantic interpretation. The nature of the factors relates more to the identity
of the reader, and to a lesser extent to a specific book, which can be seen from the following descrip-
tion: x1 – place of residence; x2 – level of education; x3 – profession (occupation); x4 – content,
subject of the book; x5 – availability (accessibility) of literature; x6 – family (role of the family);
x7 – reading traditions; x8 – social status. The semantic network of connections between the above
factors is shown in Fig. 2. The vertices of the network-graph identify the linguistic factors-arguments
of the set X = { x1 , x2 ,..., x8 } , the arcs are pairs of vertices ( xi , x j ), for which the connection (
i, j = 1 ÷ 8 ; i ≠ j ) is defined.
Place
х1
of residence
1-8 1-2
1-7 3-1
Social х8 Level of х2
2-8
status education
3-8 7-2
8-7 2-6 2-3
6-8
1-5
Reading х7 Profession х3
traditions 7-3
(occupation)
6-7 6-3
4-2
Family (role х6 4-7
5-7 5-2 Content, sub- х4
of the family)
ject of the book
Availability х5 5-4
of literature
Figure 2: Semantic network of factors of reader’s demand for a book
To obtain a model of the priority influence of factors on reader’s demand, the method of hierarchy
analysis has been used [8], the implementation of which involves: the construction of a pairwise
comparison matrix of factors using the scale of relative importance of objects; the calculation and
normalization of the values of the components of the main eigenvector of the matrix, which deter-
mine the weight advantages of the factors; the verification of the obtained results according to the
criteria of the maximum value of the eigenvector, normative values of the consistency index and
the consistency ratio; the establishment of levels of priority influence of factors on reader’s de-
mand.
4.2. Model of fuzzy logical inference
Let the level of reader‘s demand be the function Q = F ( x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 ) , the arguments
of which are the factors described above. Then the value of the function will determine the prog-
nostic integrated indicator of the reader’s demand level Q , which should be divided into partial
indicators, according to the semantic load: Q = FQ ( A, B, C ) .
The argument A determines the total indicator, which shows the level of influence of the socio-
cultural environment and contains the linguistic variables a1 – "place of residence" (belonging of
the settlement to a certain category by population), a2 – "family" (the role of the family ), a3 –
"reading traditions": A = FA ( a1 , a2 , a3 ) .
The argument B identifies the total indicator that accumulates the level of personal indicators
and includes the linguistic variables b1 – "level of education", b2 – "profession" (occupation), b3 –
"social status" (social class): B = FB ( b1 , b2 ) .
The argument C is related to the total indicator of the level of the book market and contains the
linguistic variables c1 –"content" (subject); c2 – "availability and accessibility of literature":
C = FC ( c1 , c2 ) .
The above structuring makes it possible to represent the process of forming an integrated indi-
cator of the reader’s demand level on the basis of the model of logical inference, taking into ac-
count the values of linguistic terms of factors.
Level of reader’s demand
Level
of socio-cultural Level of Level
environment personal indicators of book market
Figure 3: Multilevel model of fuzzy logical inference: the formation of an integrated indicator of
the reader’s demand level
The next step in this stage of the study will be the formation of a term-set of values of linguistic variables
that determine the reader’s demand level.
5. Experiment
Returning to the previous stage, a square inversely symmetric pairwise comparison matrix is con-
structed, taking into account the logic of connections in the semantic network, the order of which
is determined by a number of factors. The known scale of relative importance of objects is used to
establish the results of the expert comparison [2, 8].
Taking into consideration the above conditions, the elements of the matrix are represented in
Table 1. From the previous table it is clear that the elements of the main diagonal of the matrix
will be equal to one. The rest of the elements are obtained by comparing the factors of the first
information column with the factors similar to the purpose of the first additional line.
Table 1
Pairwise comparison matrix of factors of demand for a book
Factors x1 x2 x3 x4 x5 x6 x7 x8
x1 1 6 7 5 3 4 8 9
x2 1/6 1 2 1/3 1/5 1/5 5 6
x3 1/7 1/2 1 1/5 1/6 1/6 3 5
x4 1/5 3 5 1 1/4 1/3 5 7
x5 1/3 5 6 4 1 3 7 8
x6 1/4 5 6 3 1/3 1 7 8
x7 1/8 1/5 1/3 1/5 1/7 1/7 1 2
x8 1/9 1/6 1/5 1/7 1/8 1/8 1/2 1
To obtain the priority vector of the pairwise comparison matrix, the method described in [2, 8] is
used. First, the main eigenvector W ( w1 , w2 ,..., wn ) of the matrix is defined, the components of
which are obtained from the expression:
w=i
n a ⋅ a ⋅ ... ⋅ a
i1 i2 in i 1, n ,
= (3)
where n is a number of factors.
Normalized components of the vector Wnorm
n ai1 ⋅ ai 2 ⋅ ... ⋅ ain 1, n
i=
wi norm = n
(4)
∑ a ⋅ a ⋅ ... ⋅ a
i =1
n
i1 i2 in
determine the previous numerical priorities of the factors.
One of the determining criteria for the reliability of the constructed matrix is the maximum
eigenvalue λmax , which is used to calculate the subordinate criteria and is obtained as a result of
such actions. The normalized vector Wnorm1 is calculated by multiplying the matrix on the right by
the vector Wnorm . Dividing the components of the vector Wnorm1 into the corresponding components
of the vector Wnorm , the vector Wnorm 2 is obtained, whose components are correlated with the final
levels of factors. The maximum eigenvalue of a positive inversely symmetric matrix λmax is the
arithmetic mean of components of the vector Wnorm 2 .The assessment of the obtained solution is de-
termined by the consistency index IU , which is calculated by the formula:
IU =( λmax − n ) ( n − 1) . (5)
The value of the consistency index is compared with a random index WI , which is considered
a standard and depends on the number of objects. In this case, performing the inequality
IU < 0,1 × WI determines the appropriate level of results.
The continuation of experimental research on the use of fuzzy logic is to further identify lin-
guistic variables that correspond to the selected expert factors of demand for a book. Linguistic
variables are accompanied by mathematical notations presented in the model in Fig. 2, and the
additional semantic (linguistic) nature of the variable. A universal set of values and the corre-
sponding linguistic terms are introduced, defined by a fuzzy scale that express the qualitative prop-
erty of a variable. The elements of the universal set of values for variables, the limits of which are
indefinite, are denoted by conventional units. The representation of the above characteristics will
be presented in a table for convenience.
Table 2
Term-sets of values of linguistic variables
Universal
Varia- Linguistic nature Linguistic terms
set of values
ble of a variable (set L)
D
a1 Place of residence (be- (0–1500) Small, average, large, more significant,
longing of the settle- thousand the most significant
ment to a certain cate- people
gory by population)
a2 Family (role of the fam- (1–5) c.u. Low (poorly developed values), average
ily) (formed basic values), high (formed social
and spiritual values)
a3 Reading traditions (1–5) c.u. Weak, average, strong
b1 Level of education (1–5) c.u. Low (general secondary education: pre-
school, primary, basic, complete), below
secondary (vocational education), sec-
ondary (professional pre-higher educa-
tion), above secondary (higher education:
short, first, second cycle), high (high edu-
cation: third cycle, PhD)
b2 Profession (occupation) (1–5) c.u. Gnostic, transforming, research
b3 Social status (social (1–5) c.u. Lower, average, higher
class)
c1 Content (subject) (1–5) c.u. Reference and scientific editions, popular
science and educational editions, literary
and artistic editions
c2 Availability and accessi- (1–5) c.u. Custom editions, limited editions, mass
bility of literature distribution
The level of the reader’s demand formation is denoted by a linguistic term Q . In this case, the
universal set D is divided into parts (quanta). At the points of division, the linguistic variables
and ranks rq ( di ) which identify linguistic terms are specified. Therefore, the output database will
be the set D = {d1 , d 2 ,...d n } and ranks rq ( di ) that set the priority of linguistic terms in the ranges
di ( i = 1,..., n ) . Taking into account the above, the linguistic term "level of reader’s demand" Q
is presented in the form of some fuzzy set, the elements of which form a set of pairs [2, 9, 10]:
µ q ( d1 ) µ q ( d 2 ) µq ( d n )
Q= , ,..., , (6)
d1 d2 dn
where: Q ⊂ D ; µq ( di ) is a membership degree of the element di ∈ D to the set Q .
Degrees or membership functions µq ( di ) , are basic components of logical equations, the so-
lution of which provides the numerical value of the membership function of the linguistic term Q
. For membership functions, the rationing condition is satisfied: µ1 + µ2 + ... + µn =
1.
The distribution of membership degrees (functions) meets the following conditions:
µ1 µ2 µn
= = ...= , (7)
r1 r2 rn
where: µi = µq ( di ) ; ri = rq ( di ) for all i = 1,..., n .
To graphically represent linguistic terms, the range of values of linguistic variables is divided
into four parts, resulting in five points ( d1 , d 2 , d3 , d 4 , d5 ) .
With known, or obtained on the basis of pairwise comparison matrices, ranks for each of the
linguistic terms, the membership functions µi are calculated as a result of processing the matrix:
r2 r3 r4 r5
1 r r1 r1 r1
1
r1 r3 r4 r5
1
r2 r2 r2 . (8)
A = r2
... ... ... ... ...
r1 r2 r3 r4 1
r5 r5 r5 r5
Obtaining the final result is to achieve the maximum value of the function, which characterizes
the level of reader’s demand at the maximum values of the membership functions of the assess-
ment terms of factors – linguistic variables.
Let one move on to an important component of fuzzy logic – the formation of a fuzzy
knowledge base, which according to the model of logical inference in Table 2 will look like:
IF (A = low) AND (A = average) AND (A = high)
AND (B = low) AND (B = average) AND (B = high)
AND (C = low) AND (C = average) AND (C = high),
THEN (Q = low) AND (Q = average) AND (Q = high).
On the basis of the formed conditions, a knowledge matrix is constructed:
Table 3
Knowledge matrix for linguistic variable Q
Level of socio-cultural Level of personal Level of Level of
environment A indicators B book market C reader’s demand Q
low low low
low
low average low
average average average
average
low high average
high average high
high
high high high
The knowledge matrices for the linguistic variable Q will correspond to fuzzy logical equations,
which will define the procedures for obtaining the values of membership functions for the set of
terms of the integral indicator of the level of reader’s demand. For the terms "low", "average",
"high", fuzzy logical equations are presented below:
µнизький ( Q ) = µlow ( A ) ∧ µlow ( B ) ∧ µlow ( C ) ∨ µlow ( A ) ∧ µaverage ( B ) ∧ µlow ( C )
µaverage ( Q )= µaverage ( A ) ∧ µaverage ( B ) ∧ µaverage ( C ) ∨ µlow ( A ) ∧ µhigh ( B ) ∧ µaverage ( C )
µhigh ( Q ) = µhigh ( A ) ∧ µaverage ( B ) ∧ µhigh ( C ) ∨ µhigh ( A ) ∧ µhigh ( B ) ∧ µhigh ( C )
Based on expert statements about the sets L ( a1 , a2 , a3 ) , L ( b1 , b2 , b3 ) , L ( c1 , c2 ) , fuzzy
knowledge bases, knowledge matrices and fuzzy logical equations for linguistic variables of the
level of reader’s demand are designed.
The generalized version of the logical statement for the linguistic variable "level of socio-cul-
tural environment" and the knowledge matrix (Table 4) will look like this:
IF ( a1 ) = (small, average, large, more significant, the most significant)
AND ( a2 ) = (low, average, high)
AND ( a3 ) = (weak, average, strong),
THEN ( A ) = (low, average, high).
Table 4
Knowledge matrix for linguistic variable A (level of socio-cultural environment)
Level of socio-cul-
Family Reading
Place of residence a1 tural
(role of the family) a2 traditions a3
environment A
small low weak
low
small average weak
average average average
average
large average average
more significant high strong
high
the most significant high strong
Fuzzy logical equations for the terms “low”, “average”, “high” are:
µlow ( A ) = µ small ( a1 ) ∧ µlow ( a2 ) ∧ µ weak ( a3 ) ∨ µ small ( a1 ) ∧ µaverage ( a2 ) ∧ µ weak ( a3 )
µaverage ( A ) = µaverage ( a1 ) ∧ µaverage ( a2 ) ∧ µaverage ( a3 ) ∨ µlarge ( a1 ) ∧ µaverage ( a2 ) ∧ µaverage ( a3 )
( A) µmore significant ( a1 ) ∧ µhigh ( a2 ) ∧ µstrong ( a3 ) ∨ µthe most significant ( a1 ) ∧ µhigh ( a2 ) ∧ µstrong ( a3 )
µhigh=
The logical statement for the linguistic variable "level of personal indicators" and the
knowledge matrix (Table 5) will be presented the following way:
IF ( b1 ) = (low, below average, average, above average, high)
AND ( b2 ) = (gnostic, transforming, research)
AND ( b3 ) = (weak, average, strong),
THEN ( B ) = (lower, average, higher).
Table 5
Knowledge matrix for linguistic variable B (level of personal indicators)
Level of Profession Social status Level of personal
education b1 (occupation) b2 (social class) b3 indicators B
low gnostic lower
low
below average gnostic lower
average gnostic average
average
average transforming average
above average transforming average
high
high research higher
Fuzzy logical equations for the terms “low”, “average”, “high” are:
µlow ( B ) =µlow ( b1 ) ∧ µ gnostic ( b2 ) ∧ µlower ( b3 ) ∨ µbelow average ( b1 ) ∧ µ gnostic ( b2 ) ∧ µlower ( b3 )
µaverage ( B ) = µaverage ( b1 ) ∧ µ gnostic ( b2 ) ∧ µaverage ( b3 ) ∨ µaverage ( b1 ) ∧ µtransforming ( b2 ) ∧ µaverage ( b3 )
µhigh=( B ) µabove average ( b1 ) ∧ µtransforming ( b2 ) ∧ µaverage ( b3 ) ∨ µhigh ( b1 ) ∧ µresearch ( b2 ) ∧ µhigher ( b3 )
The logical statement and the knowledge matrix (Table 6) for the linguistic variable "level of
book market " will look like this:
IF ( c1 ) = (reference and scientific editions, popular science and educational editions,
literary and artistic editions)
AND ( c2 ) = (custom editions, limited editions, mass distribution),
THEN ( C ) = (lower, average, higher).
Table 6
Knowledge matrix for linguistic variable C (level of book market)
Availability and accessibil- Level of
Content (subject) c1
ity of literature c2 book market C
reference and scientific editions custom editions
low
popular science and educational editions custom editions
reference and scientific editions limited editions
average
popular science and educational editions limited editions
popular science and educational editions mass distribution
high
literary and artistic editions mass distribution
Fuzzy logical equations for the terms “low”, “average”, “high” are:
µlow ( C ) µreference and scientific editions ( c1 ) ∧ µcustom editions ( c2 ) ∨
=
∨ µ popular science and educational editions ( c1 ) ∧ µcustom editions ( c2 )
µaverage
= ( C ) µreference and scientific editions ( c1 ) ∧ µlimited editions ( c2 ) ∨
∨ µ popular science and educational editions ( c1 ) ∧ µlimited editions ( c2 )
µhigh ( C ) µ popular science and educational editions ( c1 ) ∧ µmass distribution ( c2 ) ∨
=
∨ µliterary and artistic editions ( c1 ) ∧ µmass distribution ( c2 )
The general fuzzy set of the linguistic variable Q for the analysed membership functions in
relation to the fuzzy terms "low", "average", "high" and the corresponding values of the variable Q
will look like:
µ ( Q ) µaverage ( Q ) µhigh ( Q )
Q ( A, B, C ) = low , , ,
k1
k2 k3
where k1 , k2 , k3 are quantitative values of the variable Q in relation to the analysed terms.
6. Results
The calculation of numerical results can be performed according to the suggested and implemented
above structuring of the research process in accordance with the theoretical and experimental prin-
ciples of the selected stages.
As a result of processing the pairwise comparison matrix of factors and performing the calcu-
lations, a normalized vector is obtained:
Wnorm = (0,354; 0,062; 0,042; 0,102; 0,238; 0,160; 0,023; 0,016),
components of which are transformed into integers for convenience of perception by multipli-
cation by some scaling coefficient, for example, k = 1000 . One will get:
Wnorm × k = (354; 62; 42; 102; 238; 160; 23; 16).
To assess the consistency of the weight priorities of the factors, the elements of the pairwise
comparison matrix on the right are multiplied by the vector Wnorm . The vector is obtained:
Wnorm1 = (3,225; 0,541; 0,367; 0,914; 2,121; 1,405; 0,204; 0,145).
Next, by dividing the components of the vector Wnorm1 into the corresponding components of
the vector Wnorm , the components of the eigenvector Wnorm 2 .are found:
Wnorm 2 = (9,092; 8,691; 8,725; 8,930 8,897; 8,769; 8,670; 9,008).
The arithmetic mean of the components of the vector Wnorm 2 determines the maximum eigen-
value of the pairwise comparison matrix λmax = 8,85. The assessment of the obtained solution is
determined by the consistency index IU = 0,12 calculated by formula (5).
The adequacy of the solution of the problem is confirmed under the condition of inequality
IU < 0,1 × WI (where WI = 1, 41 is the standard value of the random index for eight objects). The
solution is acceptable because 0,12 < 0,1 × 1, 41 . Finally, the results are assessed by the consistency
ratio, the value WU = IU WI of which must satisfy the ratio WU ≤ 0,1 . For our variant
WU = 0,08 , which allows asserting the reliability of the results of pairwise comparisons according
to the above criteria.
As a result, the factors declared at the beginning of the study form the following levels of
influence priority on the process of the reader’s demand formation: x1 – place of residence; x5 –
availability (accessibility) of literature; x6 – family (role of the family); x4 – content, subject of
the book; x2 – level of education; x3 – profession (occupation); x7 – reading traditions; x8 –
social status. The interpretation of the priorities of the factors of interest in the book is quite close
(especially for the first two levels) to those obtained as a result of analytical and sociological sur-
veys [15, 20, 21], performed using fundamentally different methods, which indicates the reliability
of the first stage.
The study completes the calculation of the predicted numerical expression of the level of
reader’s demand using the mechanisms of fuzzy logic.
At the beginning, fuzzy sets for the terms of linguistic variables are formed according to the
characteristics given in Table 2. Pairwise comparison matrices W are constructed for the linguis-
tic variable "place of residence" (belonging of a settlement to a certain category by population)
with a universal set of values D ( a1 ) = [50; 250;500;1000;1500] thousand people and the term-set
of values L ( a1 ) = . For the terms
"small", "average", "large", "more significant" and "the most significant" matrices will look like
this:
1 5 4 3 1 1 7 5 3 1
7 7 7 7 9 9 9 9
7 1 4 3 1 9 1 5 3 1
5 5 5 5 7 7 7 7
Wsmall (a1 ) = 7 5 3 1 W ( a ) = 9 7 1 3 1
1 average 1
5
4 4 4 4 5 5 5
7 5 4 9 7 5
3 1 1 3 1 1
3 3 3 3 3 3
7 5 4 3 1 9 7 5 3 1
1 6 9 3 1 1 2 4 6 8
1
6 1 9 3 1 12 1 4 2 6 2 8 2
6 6 6
Wlarge (a1 ) = 1 6 1 3 1 Wmore significant (a1 ) = 1 4 2 4 1 6 4 8 4
9 9 9 9
1 6 9 1 1 1 2 4 1 8
3 3 3 3 6 6 6 6
1 6 9 3 1 1 2 4 6 1
8 8 8 8
1 4 6 8 9
1
4 1 6 4 8 4 9 4
1 4 1 8 9
Wthe most significant (a1 ) = 6 6 6 6
1 4 6 1 9
8 8 8 8
1 4 6 8 1
9 9 9 9
After calculating the matrices, the values of the membership functions are obtained for the
terms "small", "average", "large", "more significant" and "the most significant":
µ small ( d1 ) = 0,35 ; µ small ( d 2 ) = 0, 25 ; µ small ( d3 ) = 0, 2 ; µ small ( d 4 ) = 0,15 ; µ small ( d5 ) = 0,05 .
µaverage ( d1 ) = 0,36 ; µaverage ( d 2 ) = 0, 28 ; µaverage ( d3 ) = 0, 2 ; µaverage ( d 4 ) = 0,12 ;
µaverage ( d5 ) = 0,04 .
µlarge ( d1 ) = 0,05 ; µlarge ( d 2 ) = 0,3 ; µlarge ( d3 ) = 0, 45 ; µlarge ( d 4 ) = 0,15 ; µlarge ( d5 ) = 0,05 .
µmore significant ( d1 ) = 0,047 ; µmore significant ( d 2 ) = 0,095 ; µmore significant ( d3 ) = 0,19 ;
µmore significant ( d 4 ) = 0, 285 ; µmore significant ( d5 ) = 0,38 .
µthe most significant ( d1 ) = 0,035 ; µthe most significant ( d 2 ) = 0,142 ; µthe most significant ( d3 ) = 0, 214 ;
µthe most significant ( d 4 ) = 0, 285 ; µthe most significant ( d5 ) = 0,321 .
The values of membership functions are normalized with respect to one and the normalization
coefficients are determined for linguistic terms:
= kе 1= max µе ( d i ) , ( i 1, 2,3) ,
where: е are the terms of the analyzed linguistic variable µеn ( di =
) kе × µ е ( d i ) .
Normalized values of membership functions of the linguistic variable "place of residence" are:
µ small ( d1 ) = 1 ; µ small ( d 2 ) = 0,714 ; µ small ( d3 ) = 0,571 ; µ small ( d 4 ) = 0, 429 ; µ small ( d5 ) = 0,143 .
n n n n n
µaverage ( d1 ) = 1 ; µaverage ( d 2 ) = 0,779 ; µaverage ( d3 ) = 0,556 ; µaverage ( d 4 ) = 0,333 ;
n n n n
µaverage ( d5 ) = 0,111 .
n
µlarge ( d1 ) = 0,111 ; µlarge ( d 2 ) = 0,667 ; µlarge ( d3 ) = 1 ; µlarge ( d 4 ) = 0,333 ; µlarge ( d5 ) = 0,111 .
n n n n n
µmore significant ( d1 ) = 0,124 ; µmore significant ( d 2 ) = 0, 25 ; µmore significant ( d3 ) = 0,5 ;
n n n
µmore significant ( d 4 ) = 0,75 ; µmore significant ( d5 ) = 1 .
n n
µthe most significant ( d1 ) = 0,109 ; µthe most significant ( d 2 ) = 0, 442 ; µthe most significant ( d3 ) = 0,667 ;
n n n
µthe most significant ( d 4 ) = 0,888 ; µthe most significant ( d5 ) = 1 .
n n
The terms of the linguistic variable "place of residence" are recorded in fuzzy sets according to
the expression (6) with a visual graphical representation.
1 0,714 0,571 0, 429 0,143
small settlement = ; ; ; ; thousand people;
50 250 500 1000 1500
1 0,779 0,556 0,333 0,111
average settlement = ; ; ; ; thousand people;
50 250 500 1000 1500
0,111 0,667 1 0,333 0,111
large settlement = ; ; ; ; thousand people;
50 250 500 1000 1500
0,124 0, 25 0,5 0,75 1
more significant settlement = ; ; ; ; thousand people;
50 250 500 1000 1500
0,109 0, 442 0,667 0,888 1
the most significant settlement = ; ; ; ; thousand people
50 250 500 1000 1500
1,2
1 small
0,8 average
0,6
large
0,4
more significant
0,2
0 the most significant
50 250 500 1000 1500
Figure 4: Membership functions of the linguistic variable "place of residence" (belonging of a
settlement to a certain category by population)
Omitting similar calculations for the rest of the linguistic variables, one can move on to an im-
portant component of fuzzy logic – the process of defuzzification, which will provide reasonable
receiving of the predicted numerical value of the reader’s demand level.
The implementation of the process is performed by analogy with the option described above,
taking into account the linguistic variable "place of residence". Preliminarily, a table with the nor-
malised values of membership functions at the points of division of the universal set D is con-
structed.
Table 7
Membership functions of the term-set (place of residence – by population)
di , thousand people 50 250 500 1000 1500
µ small ( di ) 1 0,714 0,571 0,429 0,143
µaverage ( di ) 1 0,779 0,556 0,333 0,111
µlarge ( di ) 0,111 0,667 1 0,333 0,111
µmore significant ( di ) 0,124 0,25 0,5 0,75 1
µthe most significant ( di ) 0,109 0,442 0,667 0,888 1
Tables for other linguistic variables are formed similarly to the above.
The values of membership functions for the terms "low", "average", "high" are substituted into
fuzzy logical equations for linguistic variables A, B, C.
µlow (=
A ) 0,571 ∧ 0,625 ∧ 0,665 ∨ 0,571 ∧ 1 ∧ 0,665
= 0,571
µaverage (=
A ) 0,556 ∧ 1 ∧ 1 ∨ 1 ∧ 1=
∧1 1
µhigh ( A ) =
0,5 ∧ 0,555 ∧ 0,556 ∨ 0,667 ∧ 0,555 ∧ 0,556 =
0,555
µlow ( B ) = 0, 428 ∧ 0, 499 ∧ 0, 428 ∨ 0,625 ∧ 0, 499 ∧ 0, 428 = 0, 428
µaverage ( B ) = 1 ∧ 0, 499 ∧ 1 ∨ 1 ∧ 1 ∧ 1 = 1
µhigh (=
B ) 0,556 ∧ 1 ∧ 1 ∨ 0,555 ∧ 0,555 ∧ 0,713
= 0,556
µlow (=
C ) 0,555 ∧ 0,625 ∨ 1 ∧ 0,625
= 0,625
µaverage (=
C ) 0,555 ∧ 1 ∨ 1=
∧1 1
µhigh ( C ) =
1 ∧ 0,667 ∨ 0,555 ∧ 0,667 =0,667
For the highest level Q, the membership functions will receive the following numerical values:
µlow (=
Q ) 0,571 ∧ 0, 428 ∧ 0,625 ∨ 0,571 ∧ 1 ∧ 0,625
= 0,571
µaverage ( Q ) = 1 ∧ 1 ∧ 1 ∨ 0,571 ∧ 0,556 ∧ 1 = 1
µhigh (=
Q ) 0,555 ∧ 1 ∧ 0,667 ∨ 0,555 ∧ 0,556 ∧ 0,667 = 0,555
Based on the obtained data, the defuzzification of the fuzzy set is performed by the formula:
m Q −Q
∑ Q + ( i − 1) µi ( Q )
i =1
m − 1
Q= m
, (9)
∑ µi ( Q )
i =1
where: Q and Q – are the maximum and the minimum values of the quality indicator; m – is a
number of fuzzy terms. The conditional limits for the variable Q are: Q = 1% , Q = 100% . The
calculations are performed at three points of division: 1%, 50%, 100%. As a result of calculation,
the numerical value of an integral indicator of the reader’s demand level is obtained:
1 ⋅ 0,571 + 50 ⋅ 1 + 100 ⋅ 0,555
= Q forecast = 49,89 %
0,571 + 1 + 0,555
The results of the study allow for more sound planning of publishing and book trade organiza-
tions due to the possibility of taking into account the priorities of factors of interest in books and
final forecasting of reader’s demand – the important components, the assessment of the importance
of which is obtained on the basis of the application of methods of system analysis and fuzzy sets,
taking into account the expert output data.
7. Conclusions
The analysis of the literary sources concerning the subject of the recommended paper is carried
out. Despite the considerable interest in the issues raised in the work, the amount of research on
the theoretical orientation of the processes of the reader’s demand formation is clearly insufficient
taking into account the dominance of modern media space with electronic products of "light con-
sumption". In view of the above, it is considered appropriate to use methodologies of information
orientation, significant developments of which in other areas of human activity in the form of
theoretically balanced and successfully applied models, methods, software, which form the basis
of modern information technology, would lead to significant progress in the interest in the book
and the intensification of the reader’s demand.
It is clear that the attraction to the book can be considered a subjective category of human
nature, at the same time it is very important as to its social nature and the enormous impact on the
intellectual level of society. It is characterized by the presence of certain factors that affect its
intensity. Therefore, an important task is to identify, describe and structure the relationship be-
tween the factors, their ranking substantiated by levels of importance in relation to the impact on
the book demand. The adequacy of this stage of the study is confirmed by the acceptable values
of the criteria of the methods used. An important stage in the study of the process of interest in a
book is the formulation and solution of problems of formalized assessment of the reader’s demand,
which involves the formation of term-sets of values of linguistic variables that identify factors of
interest in a book, the calculation of membership functions of variables, designing fuzzy
knowledge bases and deriving and solving fuzzy logical equations. This has become the basis of
the defuzzification process, the implementation of which provides a prognostic assessment of the
reader’s demand level.
Based on the obtained results, it is logical to state that the numerical value of the integrated
indicator of the reader's demand level is inversely proportional to the risk of low demand for a
book.
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