=Paper=
{{Paper
|id=Vol-3899/paper10
|storemode=property
|title=Formation of an indicator of the information message reliability level by fuzzy logic toolkit
|pdfUrl=https://ceur-ws.org/Vol-3899/paper10.pdf
|volume=Vol-3899
|authors=Iryna Pikh,Vsevolod Senkivskyy,Alona Kudriashova,Lyubov Tupychak,Roman Andriiv
|dblpUrl=https://dblp.org/rec/conf/advait/PikhSKTA24
}}
==Formation of an indicator of the information message reliability level by fuzzy logic toolkit==
https://ceur-ws.org/Vol-3899/paper10.pdf
Formation of an indicator of the information message
reliability level by fuzzy logic toolkit⋆
Iryna Pikh1,†, Vsevolod Senkivskyy1,†, Alona Kudriashova1, ∗,†, Lyubov Tupychak1,†, and
Roman Andriiv1,†
1 Lviv Polytechnic National University, Stepan Bandera Str., 12, Lviv, 79013, Ukraine
Abstract
In the conditions of the growing information flow and the presence of a large amount of inaccurate or
questionable data, an important task is to identify the messages veracity. The proposed research is
devoted to the development of models and approaches for assessing the information messages reliability
level using fuzzy logic tools. Fuzzy logic-based prognostic assessing allows one to take into account the
data fuzziness and ambiguity, creating more flexible and adaptive models for analysis. Linguistic variables
are singled out and grouped by types and functional characteristics – generalized factors of influence on
the veracity of the message content, which serve as the basic information basis of the studied issues. A
universal term-set of values of linguistic variables and their corresponding linguistic terms containing a
descriptive identification of the importance level of the variable in the separation quanta of the values set
is designed. A model of logical inference is developed, which reflects the hierarchical dependency of the
information messages veracity degree on the values of linguistic terms of factors, and serves as a basis for
prognostic assessment of the news reliability level. The membership functions of the linguistic variables
at the separation points of the term-sets of values are calculated based on the results of the processing of
matrices of pairwise comparisons of the factors ranks, and their visual graphic representation is
performed. Knowledge matrices are constructed and the general form of fuzzy logic equations is designed
for linguistic variables that determine the integral indicator of the information messages reliability level.
Keywords
reliability level of a message, fuzzy logic, linguistic variable, membership function, knowledge matrix1
1. Introduction
In today's information space, the issue of the message’s reliability is becoming more and more
relevant. Today's world is in the conditions of an information revolution, when the amount of data
generated every day exceeds the capabilities of traditional analysis methods. With the technology
development, the emergence of new media and the increase in the speed of information
dissemination, users are increasingly faced with the need to verify its veracity. This problem is
especially acute in the era of social networks, where the lack of strict moderation and control over
authenticity can lead to the spread of fake news, manipulation, and facts distortion. In the
conditions of information oversaturation of modern society, the problem of information messages
reliability becomes extremely relevant.
It is advisable to focus the research of the information messages reliability level on the
development of methods, models and tools for prognostic assessment of the probability of the false
information appearance arising as a result of the news filtering and distorting, the appearance of
fake messages, manipulation of data accuracy, and the use of sources that had a good reputation. It
requires a comprehensive approach that integrates the efforts of various areas of computer science,
information technology, linguistics, sociology, and other sciences to create reliable methods of
AdvAIT-2024: 1st International Workshop on Advanced Applied Information Technologies, December 5, 2024, Khmelnytskyi,
Ukraine - Zilina, Slovakia
∗ Corresponding author.
†
These authors contributed equally.
iryna.v.pikh@lpnu.ua (I. Pikh); vsevolod.m.senkivskyi@lpnu.ua (V. Senkivskyy); alona.v.kudriashova@lpnu.ua (A.
Kudriashova); lyubov.l.tupychak@lpnu.ua (L. Tupychak); roman.andriiv@icloud.com (R. Andriiv)
0000-0002-9909-8444 (I. Pikh); 0000-0002-4510-540X (V. Senkivskyy); 0000-0002-0496-1381 (A. Kudriashova); 0000-
0002-0963-3360 (L. Tupychak); 0009-0001-2450-5439 (R. Andriiv)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
analysing the factors influencing the process of the information messages appearance for the
purpose of prognostic assessment of their reliability level.
Known analysis methods often turn out to be insufficient to solve this task due to the
complexity and ambiguity of the data provided. Based on traditional logic, they are not always able
to adequately work with the information containing inaccuracies or uncertainties. In this
connection, there is a need to create effective tools that would prognostically assess the veracity
and reliability of information messages.
One of the effective ways of solving the stated problem and a promising approach for solving such
tasks is the use of fuzzy logic, which allows modelling processes with uncertainties and partial truths
and opens new perspectives in solving the problem of assessing the information messages reliability.
Thanks to the ability of fuzzy systems to process heterogeneous and imprecise data, it is possible to
create prognostic models that increase the accuracy and reliability of conclusions about the veracity
of this or that information.
In view of what has been said, it is considered expedient to use the toolkit of the multifactorial
analysis theory, modelling theory, and the fuzzy set theory in order to identify the linguistic factors
influencing the veracity of the news sites context, the processing of which by fuzzy logic toolkit
will enable the creation of a mathematical apparatus for fuzzy modelling, which reflects the direct
dependency of the information messages veracity degree on the values of the linguistic terms of
the factors, and will become the basis for the prognostic formation of the indicator of the news
reliability level.
2. Literature review
A significant increase in the amount of information in social networks has led to a new important
area of research, which is actively developing, related to the detection of the degree of information
messages veracity and reliability. This is confirmed by the analysis of literary sources on this topic,
which testifies to the growing interest of the scientific community and workers in the information
services area regarding the problem of establishing and ensuring the messages content veracity.
The fundamental work [1] describes the methodology of automated detection of fake news using
the method of probabilistic analysis of the main components to determine the characteristics that
may indicate the possibility of information falsification or unreliability. In the publication [2], the
detection of fake news and classification of unreliable information is carried out with the help of
extended text representation with recognition of multi-EDU structures. The work [3] recommends
implementing the process of detecting fake news campaigns using convolutional networks in the
form of graphs. The publication [4] is focused on identifying disinformation in social networks using
a framework capable of recognizing the information and classifying it by type: true text data; fake
data. In [5], an alternative approach to the manual verification of the facts objectivity is considered,
the essence of which is the use of machine learning algorithms to automate the process of detecting
fake news. At the same time, the necessity of obtaining a large set of training data and selecting
appropriate functions that can best detect deception is indicated. An interesting study [6] proposes a
fact-checking model that takes into account users' literacy and trust in the news in order to research
their behaviour in a social network environment prone to disinformation. Survey data collected from
social media users is analysed using structural equations. The publication [7] contains a methodology
for surveying teachers, students, and specialists in the media industry to find advanced practices for
training fact-checking and verification skills, since one of the primary requirements of the mass
media market is to master modern methods of verifying the facts veracity and establishing the
information messages reliability by future journalists. In work [8], it is noted that the use of various
methods of detecting fake news, in particular with the use of fuzzy logic and artificial intelligence,
consists in the development of mechanisms capable of performing an automated check of the content
authenticity provided in libraries. The developed model can be integrated into library digital data
processing systems, which, if necessary, will mark certain news content as potentially fake,
preventing the uncontrolled dissemination of untruth through libraries. The research [9] proposes an
innovative hybrid model based on fuzzy logic to improve the performance of fake news detection.
The model uses a combination of news articles and textual and numerical contextual information.
The model assessment results indicate that combining fuzzy logic with deep learning can improve
fake news detection and become a reliable tool to combat disinformation. In [10], the authors
assessed the methods based on the results of modelling for information about a sensitive area built on
fuzzy logic. Possible security vulnerabilities of an IoT environment insensitive to data transfer
conditions are explored. An algorithm is proposed that will guarantee detection and protection
methods aimed at protecting extremely sensitive areas, that is, where the attack probability is
maximum. The publication [11] substantiates the feasibility of using fuzzy logic, the technique of
fuzzy logic control and the corresponding functions of intelligent control systems, which can be used
as an alternative to traditional methods of process control. The benefits of using fuzzy components
by distributed systems are provided by high-level functions such as fusion and decision making. The
problem of methods selecting for increasing the solutions reliability is considered in the study [12].
Effective factors that can significantly influence the achievement of decision-making goals in the
environment of fuzzy processes development are identified. The factors reproduced in the classical
form in natural language are singled out, which significantly increases the confidence in the
decisions made by determining the maximum and minimum values of the membership functions. The
effectiveness of the proposed solutions is assessed using the procedure of fuzzy inference and Zadeh-
Mamdani approach. The authors of [13] note that fake news has become a phenomenon that can be
considered a targeted disinformation policy used to spread false data or distorted messages. This
problem needs to be studied from both technical and social aspects, since the use of technical means
to disseminate information is aimed at people. In the publication [14], it is recommended to assess the
data reliability in the information space with the help of signs that do not require a certain level of
users’ qualification, which include the dubiousness of the presented facts, emotionality, tonality and
sensationalism of the content. The work [15] is focused on the criteria for monitoring the text data
reliability in the media environment, the essence of which involves the information balance, the
separation of facts from general considerations, the definition of accuracy, objectivity and
completeness of information messages.
As a result of the analysis of literary sources, it is noted that the methods of detecting the
credibility and veracity level of data disseminated by modern media sources, despite their originality
and novelty, do not fully use the fuzzy logic tools to determine the generalized indicator of the
information messages reliability level. At the same time, the need for a wider application of the fuzzy
set theory tools is confirmed in order to create effective mechanisms for assessing the information
reliability in the media space, thanks to which it becomes possible to examine information resources
for the presence of the influence of negative factors on them, identify information security problems
in a timely manner, recommend proven solutions for use on critical objects. It is worth emphasizing
that the research presented by these authors is aimed at the use of fuzzy logic components for
modelling processes that recommend a reasonable and effective preliminary analysis of the factors of
news formation through the use of original approaches and models of prognostic formation of the
indicator of the information messages reliability level.
Considering the above, it is believed that the subject area research in the direction of prognostic
assessment of the information messages reliability level is timely and relevant.
3. Material and methods
3.1. Model of logical inference
In the general interpretation, technological or production processes largely depend on the
established norms or characteristics that predictably determine the quality of their implementation.
The situation is more complicated with social processes, the factors of which often have little
formalized interpretation and a subjective, often unclear way of expression, which creates
problems for their research. Processes aimed at determining the information messages reliability
level can be attributed to them with a high probability degree. The above once again emphasizes
the need to use an adequate theoretical apparatus for the study of processes described by fuzzy or
descriptive (linguistic) characteristics, which ultimately proves in favour of the use of the fuzzy set
theory and its defining direction – fuzzy logic, the effectiveness of which is confirmed by a number
of publications [16-18].
The starting position defining the research concept, the essence of which is to determine the
degree or parts of the influence of factors related to the formation of an integral indicator of the
reliability level of information messages (IM) has the following interpretation [17].
{
Let D = {d1 , d 2 ,..., d m } be a generalized set of some information messages; M = x1m , x2m ,..., xnm }
be a number of factors influencing the reliability level of the m -th message, where nm is a number
of factors of the m -th message. Each of the messages can be characterized by a certain function
Am ( x ) , that determines the reliability level of its information content. Summarizing the initial
conditions formulated, it can be stated that:
n
( ) (k =
Am ( x ) ≡ ω x jk , 1, 2,..., m ) , (1)
j =1
where: Am ( x ) is a numerical indicator of the reliability level of the m -th message; ω x jk ( ) is a
numerical measure of the indicator of the reliability level introduced by the j -th factor in the k -th
message.
Then the preliminary statement is formulated as follows: among information messages there
will be at least one for all factors of which the condition (1) is fulfilled:
( ∃d ) ( ∀x ) Am ( x ) ; d ∈ D; x ∈ M . (2)
In the process of research, the statements formulated by the founder of the fuzzy set theory
Zadeh and developed and supplemented in works [17-19] are used.
The basic information unit of the fuzzy set theory is considered a linguistic variable (LV), which,
unlike a mathematical variable, is described by words of ordinary language. The set of possible values
of a linguistic variable forms a term-set, the elements of which are terms. An important characteristic
of LV is the membership function (MF), formed on the basis of the term-set of values and linguistic
terms (LT), characteristic for the factors of a random information process. A term-set or universal set
contains numerical or conventional (in the absence of numerical) characteristics of the established
boundaries of linguistic variables, linguistic terms describe discrete states of LV at certain separation
points of the existence domain, or the basic scale of values of linguistic variables, using verbal
qualitative formulations [20].
A set of factors (linguistic variables) that have an impact on the information messages reliability
is considered the initial information base of the proposed research. The analysis of literary sources
has made it possible to identify a number of factors related to the process of forming the indicator
of the news reliability level. According to the results of the expert survey, a number of the most
significant among them are singled out namely: fact checking, availability of multiple publications,
the author’s professionalism, the author’s objectivity, the information source, informativeness of
the message context, presence of refutation and criticism, social trust. As a result, the linguistic
variable identifying the integral indicator of the information messages reliability level is presented
in the form of a function:
D = FD ( B, T , L ) , (3)
the arguments of which are linguistic variables of the second level B, T , L
B is focused on factors of organizational orientation; the linguistic variable
T defines a function-procedure, the arguments of which are LVs relating to the author and the
context of the message; the linguistic variable L characterizes the part of the indicator of IM
reliability, which is assessed by the attitude (loyalty) of users in relation to the received news.
The essence of linguistic variables of the second level is represented by formalized expressions
describing their functional dependency on the LVs of the third level of the hierarchy.
B = FB ( b1 , b2 , b3 ) , (4)
where: b1 is LV “information source”; b2 is LV “fact checking”; b3 is LV “multiple publication”
(verification through multi-post search).
T = FT ( t1 , t2 , t3 ) , (5)
where: t1 is LV “author’s professionalism”; t2 is LV “author’s objectivity”; t3 is LV “context
informativeness”.
L = FL ( l1 , l2 ) , (6)
where: l1 is LV “refutation and criticism”; l2 is LV “social trust”.
Based on the completed structuring by functional groups and levels of the factors importance in
the process of forming an indicator of the information messages reliability level, a graphic model of
logical inference is designed (Figure 1), which represents a multi-level hierarchy of connections
between the components of the initial database and defines an algorithm for calculating the values
of the membership functions of linguistic variables taking into account linguistic terms.
Figure 1: Model of logical inference – formation of an indicator of the information message
reliability level.
The multi-level model conveys the logic of the algorithm for the formation of the IM reliability
indicator according to the "bottom-up" principle, taking into account the partial indicators of the
message reliability obtained at each level of the hierarchy. The parts of influence of the third-level
LV are determined through the universal term-set of values and linguistic terms of variables.
3.2. Term-set of values and membership functions of linguistic variables
The research model of the textbook adaptation process and the above structuring of the initial
database determine the transition to the following tasks, the essence of which is the formation of a
universal base or term-set of values and functions of linguistic variables. It should be noted that a
term-set represents the real (most often numerical), or conditional, in their absence, boundaries of
action or influence on the process by a specific linguistic variable. Linguistic terms provide the
information in a descriptive form about the importance of LV, attributed to the separation points of
the universal set U . For the convenience of representing the specified actions, Table 1 is designed,
which represents a mathematical symbol of a linguistic variable, its descriptive essence, a universal
set of LV values, and a special set of linguistic terms grouped into three-dimensional scales to
reproduce the qualitative states of linguistic variables in the quanta of the set U .
Table 1
Term-sets of values of linguistic variables
Universal base of
Linguistic description of a Linguistic terms
Variable values
variable (set H )
(term-set U )
Information source Low, medium, high
b1 (1-5) c. u.
(reliability)
b2 Fact checking (1-5) c. u. Infrequent, frequent, constant
Multiple publication Small, medium, big
b3 (1-5) c. u.
(number)
t1 Author’s professionalism (1-5) c. u. Low, medium, high
t2 Author’s objectivity (1-5) c. u. Low, medium, high
Informativeness of the Low, medium, high
t3 (1-5) c. u.
message context
Refutation and criticism Small, medium, significant
l1 (1-5) c. u.
(frequency)
l2 Social trust (1-5) c. u. Low, medium, high
Processing of linguistic variables according to the rules of fuzzy logic is performed at discrete
separation points ui of the term-set U . Additionally, at these points, the ranks rq ( ui ) related to
the linguistic terms of LV are specified. Thus, in the generalized notation, the universal term-set
U = {u1 , u2 ,..., un } and the preference ranks rq ( ui ) of linguistic terms in the separation quanta ui
( i = 1,..., n ) are considered as initial data.
Taking into account the expressed warnings, the linguistic term "an indicator of the information
messages reliability level" appears as a fuzzy set [17]:
µ (u ) µ (u ) µ (u )
DF = d 1 , d 2 ,..., d n , (7)
u1 u2 un
where: DF ⊂ U ; µq ( ui ) is a membership function of the element ui ∈U to the set DF .
In the expression (7) µd ( ui ) mean the normalized values of membership functions used in the
process of forming and solving fuzzy logic equations. The relationship between the membership
functions of linguistic variables and the corresponding ranks of the linguistic terms of the specified
variables is presented by the following relations:
µ1 µ2 µn
= = ...= , (8)
r1 r2 rn
where: µi = µq ( ui ) ; ri = rq ( ui ) for all i = 1,..., n .
Membership functions must satisfy the normalization condition, i.e.:
µ1 + µ2 + ... + µn =
1.
The ranks of factors (linguistic variables) are usually determined by the methods of ranking or
modelling of hierarchies, which makes it possible to calculate the membership function at five
points of the universal term set according to the following relations [17]:
r r r
−1
µ1 = 1 + 2 + 3 + ... + n ;
r1 r1 r1
−1
r1 r3 rn
µ2= + 1 + + ... + ;
r2 r2 r2 (9)
..........................................
−1
r r r
µn = 1 + 2 + 3 + ... + 1 .
rn rn rn
The specified number of control nodes determines the appropriate informativeness of the visual
graphic representation of the numerical characteristics of the membership functions.
Taking into account the specified prerequisites, the research task is formulated and voiced as
follows: to ensure the achievement of the maximum of the function that determines the
information messages reliability level with positive values of the linguistic terms of the universal
base U and the maximum values of the membership functions at the separation points of the
term-set [17]. The mathematical representation of the task is given in the following interpretation:
DF = F ( bk , t j , l p ) → max, k = 1,3; j =1,3;
bk > 0, t j > 0, l p > 0, p = 1, 2; . (10)
µd ( ui ) → max, ui ∈U , DF ⊂ U , i = 1,5.
The formalized representation of the task (10) contains the components of the universal term-
set of values bk , t j , l p , in relation to the linguistic variables of the process.
Finally, square inversely symmetric matrices A = aij ( aij = ri rj ; i, j = 1,...,5 ) in representation
(11) are constructed for each linguistic variable and its corresponding three linguistic terms of the
set H . Ranks are selected from the set of integers from 1 to 9 [20].
r2 r3 r4 r5
1 r r1 r1 r1
1
r1 r3 r4 r5
1
A = r2 r2 r2 r2 . (11)
... ... ... ... ...
r1 r2 r3 r4 1
r5 r5 r5 r5
For example, the experimental calculation of the membership functions of one of the linguistic
variables, characterized by three linguistic terms of the set H at five separation points
u1 , u2 , u3 , u4 , u5 of the term-set U is presented below.
4. Experiment, results
A random linguistic variable is selected, for example, b1 "information source", the universal base of
values of which is in the interval (1-5) of conditional units at the points U ( b1 ) = [1; 2;3; 4;5] , for which
linguistic terms determining the information source reliability are set in Table 1 – H ( b1 ) = . For the term "low", the variable rank on the interval increases. The lowest rank of LV at
the point u1 is set by the number 1. First, an inversely symmetric matrix is created for the specified
variable, which displays the value of the ranks in relation to the term "low". According to theoretical
principles, the elements of only the fifth row are specified, since the rest of the matrix elements a ji are
=
obtained based on the dependency: 5 j a5i ; i , j
a ji a= 1,5 .
According to the stated conditions, the inversely symmetric matrix takes the following form:
1 6 4 1 3
9 9
9 9
9 1 4 3 1
6 6 6 6
(12)
Alow ( b1 ) = 9 6 1 3 1 .
4 4 4 4
9 6 4
3 1 1
3 3 3
9 6 4 3 1
Taking into account the elements of the matrix (12) and the expressions (9), the values of the
membership functions are calculated for the term "low" at five points of the universal term set:
µlow ( u1 ) = 0,39 ; µlow ( u2 ) = 0, 24 ; µlow ( u3 ) = 0,16 ; µlow ( u4 ) = 0,12 ; µlow ( u5 ) = 0,04 .
For the term "medium", the following inversely symmetric matrix is formed:
1 5 9 4 1
1
5 1 9 5 4 15
Amedium ( b1 ) = 1 5 1 4 1 . (13)
9 9 9 9
1 5 9 1 1
4 4 4 4
1 5 9 4 1
Similarly to the previous steps, the corresponding membership functions are obtained:
µmedium ( u1 ) = 0,05 ; µmedium ( u2 ) = 0, 25 ; µmedium ( u3 ) = 0, 45 ; µmedium ( u4 ) = 0, 20 ; µmedium ( u5 ) = 0, 05 .
The matrix for the linguistic term "high" is presented in a similar form:
1 4 5 8 9
1 1 5 8 9
3 3 3 3
1 4 1 8 9 .
Ahigh ( b1 ) = (14)
5 5 5 5
1 4 5 1 9
8 8 8 8
1 9 4 9 5 9 8 9 1
The following membership functions are obtained:
µhigh ( u1 ) = 0,037 ; µhigh ( u2 ) = 0,148 ; µhigh ( u3 ) = 0,185 ; µhigh ( u4 ) = 0, 296 ; µhigh ( u5 ) = 0,33 .
Normalization of membership functions is performed by multiplying their values by a
coefficient:
= kr 1= max µ r ( ui ) , ( i 1,...,5 ) ,
where r means ”low”, ”medium”, ”high”.
Based on the results of using the formula µr ( di =
) kr × µr ( ui ) for the linguistic variable
n
"information source" (the source reliability) with the specified terms "low", "medium", "high", the
following normalized values of the membership functions are obtained:
µlow ( u1 ) = 1 ; µlow ( u2 ) = 0, 61 ; µlow ( u3 ) = 0, 41 ; µlow ( u4 ) = 0,31 ; µlow ( u5 ) = 0,10 ;
n n n n n
µ medium ( u1 ) = 0,11 ; µ medium ( u2 ) = 0,55 ; µ medium ( u3 ) = 1 ; µ medium ( u4 ) = 0,55 ; µ medium ( u5 ) = 0,11 ;
n n n n n
µ high ( u1 ) = 0,11 ; µ high ( u2 ) = 0, 49 ; µ highn ( u3 ) = 0,56 ; µ high ( u4 ) = 0,90 ; µ high ( u5 ) = 1 .
n n n n
The normalized numerical priorities of the membership functions of LV " information source"
(reliability) relative to the terms "low", "medium", "high" are presented by the expression (7) in
fuzzy sets.
1 0,61 0, 41 0,31 0,10
low reliability = ; ; ; ; c. u.;
1 2 3 4 5
0,11 0,55 1 0,55 0,11
medium reliability = ; ; ; ; c. u.; (15)
1 2 3 4 5
0,11 0, 49 0,56 0,90 1
high reliability = ; ; ; ; c. u.
1 2 3 4 5
An important step in the application of fuzzy logic tools for the study of processes containing
uncertainties is the visualization of membership functions [18]. The purpose of visualizing the
values of the membership functions for the LV "information source" (reliability) according to the
terms "low", "medium", "high" is to graphically represent the source involvement in a certain
reliability level depending on the specified term. The visualization helps to show that reliability is
not a well-defined quantity (for example, "reliable" or "unreliable"), but varies gradually. The values
of the membership functions indicate the degree of "attachment" of the LV to each term and
determine to what extent the information source corresponds to a certain reliability level.
One of the key points in the practical application of the visualization is that the membership
functions can overlap, that is, the same source can have some degree of membership in several
terms at the same time. This provides flexibility in reliability classification and avoids rigid
boundaries between terms.
The presented paper uses Gaussian membership functions, which, unlike triangular ones, have a
smoother version, in which the membership changes more smoothly, which is useful for simulated
processes where changes in reliability occur more gradually.
A visual graphic representation of fuzzy sets (15) of the linguistic variable "information source"
by the terms "low", "medium", "high" is presented in Fig. 2.
Similarly, in a more complete interpretation, a graphical representation of the membership
functions of the remaining linguistic variables is carried out, the absence of which in this paper
does not change the essence of the general approach to the research problem.
The next step in the practical implementation of the task concerns the formation of a fuzzy
knowledge base and the design of fuzzy logic equations. The formation of a fuzzy knowledge base
ensures the construction of effective models for complex systems and processes where uncertainty
and inaccuracy are inherent characteristics, providing flexibility and accuracy in decision-making.
The basis for the formation of a fuzzy knowledge base is the model of logical inference in Figure
1, which determines the sequence of actions regarding the process of establishing an indicator of
the information messages reliability level. Fuzzy logical inference is a process in which, on the
basis of fuzzy rules and fuzzy data (linguistic variables), results are calculated that may also be
fuzzy.
low reliability medium reliability higt reliability
1,2
Values of the memebership function
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5
Values of the term-set
Figure 2: Visualization of membership functions of the linguistic variable “information source”.
This allows for decision-making and analysis in situations where the information is incomplete,
uncertain or unclear. According to the formalized interpretation of the task expressed by the entry
(10), the indicator of the information reliability level is identified by the authors as the linguistic
variable of the highest level D , for which a set of linguistic terms H ( D ) = is
formed. According to the model hierarchy, the basic sets of linguistic variables of the next
hierarchy level relate to the author’s, organizational, and user’s parts of the IM reliability level, for
which similar fuzzy sets receive the following expression:
H ( B ) = – the organizational part of the IM reliability;
H (T ) = – the author’s part of the IM reliability;
H ( L ) = – the user’s part of the IM reliability.
The basis of a fuzzy knowledge base is a set of fuzzy rules, which have the form: "if A, then C",
where A and C are fuzzy sets. Such rules define relationships between linguistic variables.
Therefore, the fuzzy knowledge base for the linguistic variable, which determines the generalized
level of reliability of the information message, takes the following form:
IF ( B = low) AND ( B = medium) AND ( B = high)
AND ( T = low) AND ( T =medium) AND ( T =high)
AND ( L = low) AND ( L =medium) AND ( L =high),
THEN ( D = low) AND ( D =medium) AND ( D = high).
The knowledge matrix based on the fuzzy knowledge base is presented in Table 2.
Table 2
Knowledge matrix for the linguistic variable D
Organizational part of Author’s part of User’s part of Generalized IM
the IM reliability the IM reliability the IM reliability reliability level
(B) (T) (L) (D)
low low medium
low
low medium low
low high medium
medium
medium low high
high medium high
high
high high medium
The knowledge matrix became the basis of fuzzy logical equations, the solution of which led to
obtaining membership functions for the specified terms of the linguistic variable D :
µlow ( D ) = µlow ( B ) ∧ µlow (T ) ∧ µmedium ( L ) ∨ µlow ( B ) ∧ µmedium (T ) ∧ µlow ( L ) ;
µmedium ( D ) = µlow ( B ) ∧ µhigh (T ) ∧ µmedium ( L ) ∨ µmedium ( B ) ∧ µlow (T ) ∧ µhigh ( L ) ;
µhigh ( D ) = µhigh ( B ) ∧ µmedium (T ) ∧ µhigh ( L ) ∨ µhigh ( B ) ∧ µhigh (T ) ∧ µmedium ( L ) .
According to the logical inference model, similar procedures are performed for the next-level
MF, i.e. B = FB ( b1 , b2 , b3 ) , T = FT ( t1 , t2 , t3 ) , L = FL ( l1 , l2 ) , for which corresponding logical statements,
knowledge matrices, and fuzzy logical equations are formed alternately.
Taking into account that the applied aspects of the research are carried out for the linguistic
variable b1 "information source", the following representation is focused on the linguistic variable
B = FB ( b1 , b2 , b3 ) .
A fuzzy knowledge base for qualitative assessment of the linguistic variable ( B ) is presented
below.
IF ( b1 ) = (low, medium, high)
AND ( b2 ) = (infrequent, frequent, constant)
AND ( b3 ) = (small, medium, big)
THEN ( B ) = (low, medium, high).
The following data regarding the knowledge matrix are presented in Table, as above.
Table 3
Knowledge matrix for the linguistic variable B
Organizational part of
Information source Fact checking Multiple publication
the reliability
(reliability) ( b1 ) ( b2 ) ( b3 )
of IM ( B )
low infrequent medium
low
medium infrequent small
high infrequent medium
medium
low frequent big
medium constant big
high
high constant medium
Table 3 provides the construction of a system of fuzzy logical equations for calculating the values of
membership functions of the linguistic variable B for the terms "low, medium, high":
µlow ( B ) =
µlow ( b1 ) ∧ µinfrequent ( b2 ) ∧ µmedium ( b3 ) ∨ µmedium ( b1 ) ∧ µinfrequent ( b2 ) ∧ µ small ( b3 ) ;
µmedium ( B ) = µhigh ( b1 ) ∧ µinfrequent ( b2 ) ∧ µmedium ( b3 ) ∨ µlow ( b1 ) ∧ µ frequent ( b2 ) ∧ µbig ( b3 ) ; (16)
µhigh ( B ) = µmedium ( b1 ) ∧ µconst ( b2 ) ∧ µbig ( b3 ) ∨ µhigh ( b1 ) ∧ µconst ( b2 ) ∧ µmedium ( b3 ) .
To solve the system of fuzzy equations (16) in order to obtain the numerical values of the
membership functions of the variable B
B , i.e. b2 and b3 , at the points of the
universal base of values U, which determines the areas of their existence, are calculated similarly to
the above for the variable b1 .
Omitting similar procedures for linguistic variables T and L , the final stage concerns the
linguistic variable D , which determines the integral value of the indicator of the prognostic
reliability level of information messages. The fuzzy set of the variable D is described by
membership functions with three fuzzy terms "low", "medium", "high". Numerical values D are
formed at three points of the basic universal set. On the basis of (7), the value of the variable at the
separation points of the set U is obtained from the expression:
𝜇𝜇 (𝐷𝐷) 𝜇𝜇𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 (𝐷𝐷) 𝜇𝜇ℎ𝑖𝑖𝑖𝑖ℎ (𝐷𝐷)
𝐷𝐷(𝐵𝐵, 𝑇𝑇, 𝐿𝐿) = � 𝑙𝑙𝑙𝑙𝑙𝑙
𝑑𝑑
, 𝑑𝑑2
, �, (17)
1 𝑑𝑑3
where d1 , d 2 , d3 are quantitative values of the variable D regarding the terms "low", "medium",
"high". The formation of a fuzzy logical conclusion, knowledge matrix and fuzzy logical equations
in relation to the linguistic variable D is carried out according to actions similarly applied to the
linguistic variable B . Under the condition of obtaining the values of the membership functions
µlow ( D ) , µmedium ( D ) and µhigh ( D ) , of the linguistic variable D , defuzzification of the fuzzy set (17),
i.e., the calculation of the indicator of the prognostic reliability level of information messages, is
carried out according to the expression, which is considered the basis of the method of the centre
of mass of a flat figure, limited by the abscissa axis and the graph of the membership function of
the linguistic variable D [17]:
𝐷𝐷−𝐷𝐷
∑𝑚𝑚
𝑖𝑖=1�𝐷𝐷+(𝑖𝑖−1) �𝜇𝜇 (𝐷𝐷)
𝑚𝑚−1 𝑖𝑖
𝑃𝑃 = ∑𝑚𝑚
, (18)
𝑖𝑖=1 𝜇𝜇𝑖𝑖 (𝐷𝐷)
where: P is a numerical indicator of the reliability level of information messages; D, D are
respectively, the lower and upper quantitative value of the variable D ; m is a number of
qualitative terms of assessing the variable D . When performing the calculations according to
formula (17), the following initial data are recommended: m = 3 ; µ1 ( D ) = µlow ( D ) ,
µ2 ( D ) = µmedium ( D ) , µ3 ( D ) = µhigh ( D ) ; quantitative values of the variable D regarding the terms
"low", "medium", "high" – (1, 50, 100); lower and upper values D – D = 1 , D = 100 . The value of
the indicator P is obtained as a percentage.
To confirm the effectiveness of the application of the expression (18), the message reliability
level indicator is calculated. In addition to the above-mentioned initial data, the values of the
membership functions of the linguistic variable D are set: = µ1 ( D ) µ=
low ( D ) 0,10 ;
µ2 ( D ) µ=
= medium ( D ) µ3 ( D ) µ=
0, 45 ; = high ( D ) 0,65 . Substituting them into formula (18), the
following expression is obtained:
1 ⋅ 0,10 + 50 ⋅ 0, 45 + 100 ⋅ 0,65
=P = 72,92%.
0,10 + 0, 45 + 0,65
The result of the calculation shows that with the specified initial data of the membership
functions of the linguistic variables, significantly related to the process of prognostic assessment of
the information data veracity, the indicator of the reliability level of media and printed messages is
quite high. Provided there is a simulation model for calculating this indicator, the possibility of
predicting the messages objectivity level through a change in the initial parameters, the essence of
which is determined by the linguistic terms of the universal base of values, becomes real.
At the same time, the software gives an opportunity to provide feedback, the essence of which
is that the user enters the value of the indicator acceptable to him into the system and receives at
the output the characteristics of linguistic variables (the process factors) that determine the desired
information reliability level.
5. Conclusions
Summarizing the above, it is claimed that as a result of the growth of information flows, there is a
need to apply a scientific approach to assessing the reliability of data, which are generally
characterized by fuzziness and ambiguity. This toolkit includes the tools of the fuzzy set theory and
its applied direction – fuzzy logic, which ensures the creation of more flexible and adaptive models
for data analysis and practical application. As a result of the review of literary sources and the
general problems of modern society in determining the information messages veracity and
objectivity, linguistic variables – generalized factors of influence on the data content veracity, which
serve as the basic information basis of the subject under study – are singled out and grouped by type
and functional characteristics. These include linguistic variables focused on factors of organizational
orientation (information source, fact checking, multiple publication); concerning the author’s
professionalism, objectivity and the context informativeness; which express the attitude (loyalty) of
users (refutation and criticism, social trust) in relation to the received news. A universal term-set of
values of linguistic variables and their corresponding linguistic terms containing a descriptive
identification of the importance level of the variable in the separation quanta of the set of values is
designed. The term-set is considered a key concept in fuzzy systems, which allows working with
values that do not have distinctive boundaries. A graphic multi-level model of logical inference is
developed, which reflects the hierarchical dependency of the information messages veracity degree
on the values of linguistic terms of linguistic variables, and becomes the basis for calculating the
indicator of prognostic assessment of the news reliability level.
The model "works" according to the "bottom-up" principle. Inversely symmetric factor rank
matrices are constructed for the linguistic variables of the process of formation of the IM reliability
level indicator and the linguistic terms assigned to them. Based on the results of the processing of the
matrices, the values of the membership functions of the linguistic variables at the separation points of
the term-sets are calculated. One of the essential tools of fuzzy logic in the study of information
processes is the visualization of membership functions, which determines the graphical
representation of the involvement of a linguistic variable to a certain reliability level depending on
the specified term. A graph of the LV "information source" is constructed, which clearly demonstrates
how an information source is assessed by the reliability level in conditions of uncertainty, using fuzzy
logic. The practical implementation of the task concerns the design based on the fuzzy logical
inference of the fuzzy knowledge base. Knowledge matrices are constructed and the general form of
fuzzy logic equations is designed for linguistic variables, which determine the numerical indicator of
the information message’s reliability level. The expression and initial data for calculating the
indicator of the prognostic reliability level of information messages are presented.
Declaration on Generative AI
The author(s) have not employed any Generative AI tools.
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