Forecasting the Reader's Demand Level Based on Factors of Interest in the Book

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 formalized 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 equations
• fuzzification
• defuzzification

1. Introduction

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 linguistic 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 assessment 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 studied 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 represent 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 inference – a formalized display of the process of forming the level of reader’s demand for a book and the

risk of its absence

Calculation of the numerical value of the integral indicator of the level of reader’s demand for a book

Formation of a term-set of values of linguistic variables attributed to subordinate levels of demand

for a book Analytical display and calcula

tion of numerical values of membership functions of subordinate levels of demand

Designing a fuzzy knowledge base, constructing fuzzy logical equations, assessment of subordi

nate levels of demand Construction of fuzzy logical equations of term-assessments of the importance of subordinate levels of demand for a book The essential element and advantage of fuzzy logic is the possibility of fuzzification, i.e. the replacement 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 =M( {(µ d ) , d ) , d ∈ D} , (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:

M =d2 (µ M ( d1 ) / d1,µ M ( ) / d2 ,...,µ M ( dn ) / dn ) n ∑µ M ( di ) / di , (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 contributes 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 essence of these publications is exclusively in the analytical and sociological description of the problem. 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, informational 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 using 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, however, 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, structured 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 mathematical 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 description: 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.

1-8 х8

6-8 Social status 8-7 Reading traditions

х7 6-7 Family (role of the family) х6

Place of residence 1-7 х1 3-1

1-2 3-8 7-3 5-7 1-5 2-8

7-2 5-2 Availability of literature х5 2-6 4-7 6-3 5-4

Level of education х2 2-3 Profession (occupation)

х3 4-2 Content, subject of the book х4 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 determine 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 demand.

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 prognostic integrated indicator of the reader’s demand level Q , which should be divided into partial indicators, according to the semantic load: Q = F ( A, B, C ) .

Q

The argument A determines the total indicator, which shows the level of influence of the sociocultural 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 indicator of the reader’s demand level on the basis of the model of logical inference, taking into account the values of linguistic terms of factors.

Level of reader’s demand

Level

of socio-cultural environment

Level of

personal indicators

Level of book market

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 constructed, 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. (3) 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: wi = n ai1 ⋅ ai2 ⋅ ... ⋅ ain i = 1, n , where n is a number of factors.

Normalized components of the vector Wnorm

n ai1 ⋅ ai2 ⋅ ... ⋅ ain i =1, n wi norm = n (4) ∑ n ai1 ⋅ ai2 ⋅ ... ⋅ ain i=1 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 vectorWnorm2 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 Wnorm2 .The assessment of the obtained solution is determined by the consistency index IU , which is calculated by the formula:

IU =(λmax − n) ( n − 1) .

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 linguistic 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 corresponding linguistic terms are introduced, defined by a fuzzy scale that express the qualitative property 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.

Reading traditions

Level of education

Profession (occupation)

Social status (social class)

Content (subject)

Availability and accessibility of literature

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, d2 ,...dn} 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 ]: where: Q ⊂ D ; µ q (di ) is a membership degree of the element di ∈ D to the set Q .

Degrees or membership functions µ q ( di ) , are basic components of logical equations, the solution of which provides the numerical value of the membership function of the linguistic term Q . For membership functions, the rationing condition is satisfied: µ1 + µ 2 + ... + µ n =1 .

The distribution of membership degrees (functions) meets the following conditions: µ µ µ 1 = 2 = ... = n , (7) r1 r2 rn where: µi = µ q ( 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, d2 , d3 , d4 , 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: 1 rr12 rr13 rr14 rr15  A =  rr12 1 rr32 rr42 rr52  . (8) ... ... ... ... ...     rr15 rr52 rr53 rr54 1

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 assessment 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: 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-cultural 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). 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 ) µhigh ( A) =µmore significant (a1 ) ∧ µhigh (a2 ) ∧ µ strong (a3 ) ∨ µthe most significant (a1 ) ∧ µhigh (a2 ) ∧ µ strong (a3 )

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). 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). 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 )

Level of book market C

low average high µ average (C )

=reference µ and scientific editions (c1 ) ∧ µlimited editions (c2 ) ∨ ∨µ popular science and educational editions (c1 ) ∧ µlimited editions (c2 ) µ high (C ) =popular µ science and educational editions (c1 ) ∧ µ mass distribution (c2 ) ∨ ∨µliterary and artistic editions (c1 ) ∧ µ mass 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:

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 principles of the selected stages.

As a result of processing the pairwise comparison matrix of factors and performing the calculations, 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 multiplication 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 Wnorm2 .are found:

Wnorm2 = (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 Wnorm2 determines the maximum eigenvalue 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 surveys [ 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 linguistic 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 ) = <small, average, large, more significant, the most significant>. For the terms "small", "average", "large", "more significant" and "the most significant" matrices will look like this: µ small ( d1 ) = 0,35 ; µ small ( d2 ) = 0, 25 ; µ small ( d3 ) = 0, 2 ; µ small ( d4 ) = 0,15 ; µ small ( d5 ) = 0, 05 . µ average ( d1 ) = 0,36 ; µ average ( d2 ) = 0, 28 ; µ average ( d3 ) = 0, 2 ; µ average ( d4 ) = 0,12 ; µ average ( d5 ) = 0, 04 . µlarge (d1 ) = 0,05 ; µlarge (d2 ) = 0,3 ; µlarge (d3 ) = 0, 45 ; µlarge (d4 ) = 0,15 ; µlarge (d5 ) = 0,05 . µmore significant (d1 ) = 0,047 ; µmore significant (d2 ) = 0,095 ; µmore significant (d3 ) = 0,19 ;

µmore significant (d4 ) = 0, 285 ; µmore significant (d5 ) = 0,38 . µthe most significant (d1 ) = 0,035 ; µthe most significant (d2 ) = 0,142 ; µthe most significant (d3 ) = 0, 214 ; µthe most significant (d4 ) = 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 =maxµе 1 (di ), (i =, 1, 2,3) where: е are the terms of the analyzed linguistic variable µеn (di ) = kе × µе (di ) .

Normalized values of membership functions of the linguistic variable "place of residence" are: µsmalln (d1 ) = 1; µsmalln (d2 ) = 0,714 ; µsmalln (d3 ) = 0,571; µsmalln (d4 ) = 0, 429 ; µsmalln (d5 ) = 0,143 . µaveragen (d1 ) = 1 ; µaveragen (d2 ) = 0,779 ; µaveragen (d3 ) = 0,556 ; µaveragen (d4 ) = 0,333 ; µaveragen (d5 ) = 0,111 . µlargen (d1 ) = 0,111 ; µlargen (d2 ) = 0,667 ; µlargen (d3 ) = 1; µlargen (d4 ) = 0,333 ; µlargen (d5 ) = 0,111. µmore significantn (d1 ) = 0,124 ; µmore significantn (d2 ) = 0, 25 ; µmore significantn (d3 ) = 0,5 ;

µmore significantn (d4 ) = 0,75 ; µmore significantn (d5 ) = 1. µthe most significantn (d1 ) = 0,109 ; µthe most significantn (d2 ) = 0, 442 ; µthe most significantn (d3 ) = 0,667 ; µthe most significantn (d4 ) = 0,888 ; µthe most significantn (d5 ) = 1 .

The terms of the linguistic variable "place of residence" are recorded in fuzzy sets according to the expression (6) with a visual graphical representation.

small settlement =  1 ; 0,714 ; 0,571; 0, 429 ; 0,143 thousand people;

50 250 500 1000 1500  average settlement =  1 ; 0,779 ; 0,556 ; 0,333 ; 0,111 thousand people;

50 250 500 1000 1500  large settlement = 0,51011; 02,65607 ; 5100 ; 01,030303 ; 01,510101 thousand people; more significant settlement = 0,51024 ; 02,5205 ; 500,50 ;100,7050 ;15100  thousand people; the most significant settlement = 0,51009 ; 02,45402 ; 05,60607 ; 01,080808 ;15100  thousand people 0,8 0,6 0,4 0,2 0 small Omitting similar calculations for the rest of the linguistic variables, one can move on to an important 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 normalised values of membership functions at the points of division of the universal set D is constructed.

µ average ( A) =0,556 ∧ 1 ∧ 1∨ 1 ∧ 1 ∧ 1 =1 µ high ( 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

µ average ( B) = 1 ∧ 0, 499 ∧ 1∨ 1 ∧ 1 ∧ 1 = 1 µ high ( B) =0,556 ∧ 1 ∧ 1∨ 0,555 ∧ 0,555 ∧ 0, 713 =0,556 µlow (C ) =0,555 ∧ 0, 625 ∨ 1 ∧ 0, 625 =0, 625

µ average (C ) =0,555 ∧ 1∨ 1 ∧ 1 =1 µ high (C ) =1∧ 0, 667 ∨ 0,555 ∧ 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

µ average (Q ) = 1 ∧ 1 ∧ 1 ∨ 0,571 ∧ 0,556 ∧ 1 = 1 µ high (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: Q = m  ∑ Q + (i − 1) i=1 

Q − Q 

µi (Q ) m − 1  

, m ∑ 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

Qforecast =0,571+ 1 + 0,555 =% 49,89

The results of the study allow for more sound planning of publishing and book trade organizations 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. (9)

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 consumption". 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 between 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. [18] G.Ozturk, S.Hill, G.Yates, Family context and five-year-old children’s attitudes toward literacy when they are learning to read, Reading Psychology, 2016, 37(3), pp. 487-509 [19] N.O.R.A.I.E.N.Mansor, Exploring perceptions on ESL students’ reading habits, Journal of

Business and Social Development, 2017, 5(2), pp. 19-24 [20] Q.Chen, Y.Kong, W.Gao, L.Mo, Effects of socioeconomic status, parent–child relationship, and learning motivation on reading ability, Frontiers in psychology, 2018, 9, 1297 p. [21] E.Herrmann, Note from the Editor, How do we choose what we read? TXT, 2016(1), URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4804024 [22] M.Becker, N.McElvany, The interplay of gender and social background: A longitudinal study of interaction effects in reading attitudes and behavior, British Journal of Educational Psychology, 2018, 88(4), pp. 529-549

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