=Paper=
{{Paper
|id=Vol-2608/paper10
|storemode=property
|title=Situational management of urban engineering networks with intelligent support for dispatching decisions
|pdfUrl=https://ceur-ws.org/Vol-2608/paper10.pdf
|volume=Vol-2608
|authors=Aleksandr Stenin,Iryna Drozdovych,Mariya Soldatova
|dblpUrl=https://dblp.org/rec/conf/cmis/SteninDS20
}}
==Situational management of urban engineering networks with intelligent support for dispatching decisions==
https://ceur-ws.org/Vol-2608/paper10.pdf
Situational management of urban engineering networks
with intelligent support for dispatching decisions
Aleksandr Stenin1[0000-0001-5836-9300], Irina Drozdovych2[0000-0002-4216-2417],
Mariya Soldatova3[0000-0003-1233-1272]
1, 3
Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine.
alexander.stenin@yandex.ua
benten1093@gmail.com
2
Institute of telecommunications and global information space NAS of Ukraine, Kyiv, Ukraine.
irina.drozdowicz@gmail.com
Abstract. To improve the efficiency of urban engineering networks manage-
ment, an intelligent system for supporting dispatching decisions (IDSS UEN)
proposed, based on a situational approach using fuzzy logic. The developed al-
gorithm for situational fuzzy control is the basis of the IDSS UEN and is based
on the original method of mixed estimates of alternatives and fuzzy situational
network UEN
Keywords: urban engineering networks, weighted graph of situations, intelli-
gent decision support system, fuzzy situation management algorithm.
1 Introduction.
The work of the dispatcher of urban engineering networks (UEN) (power grids, gas
pipelines, water pipes, sewers, etc.) is an extremely difficult task [1, 4, 5].
Decision-making by the UEN dispatcher takes place in a complex environment
characterized by the following difficulties [2]:
-impossibility to get reliable, complete and accurate information about an emer-
gency;
-the transience of changes in emerging situations in UEN;
-obsolescence of information used for decision making;
-the presence of a large number of factors;
-a multivariate approach to decision-making;
-compromise between economic benefits for the city and the quality of services
for residents based on decisions made by the dispatcher;
-responsibility for the sole decision;
It is known [1-4], when a large amount of initial information used for decision-
making, the quality of decisions significantly reduced. Research shows that decision-
makers without additional analytical support tend to use simplified and contradictory
decision-making rules. In this sense, effective decisions of the dispatcher in the work
of UEN largely depend on the capabilities of technology and software tools that im-
plement methods and methods of intellectual support for decisions. The use of the
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
intellectualization tools, which based on the experience of experts in this subject area,
can significantly improve the efficiency of UEN operation.
The most appropriate method for implementing effective solutions is an intelligent
decision support system in urban engineering networks (IDSS UEN), built on a situ-
ational approach using fuzzy logic [4, 6].
2 Problem statement
It knew [7] that the decision-making task (DMT) can represent as:
DMT T , A, Q, Y , F , G, D , (1)
where: – problem statement; – the set of alternatives; – a set of selection
criteria (evaluating the effectiveness of solution options); – multiple methods for
measuring relationships between options; – mapping a set of valid options to a set
of ratings; – the system preferences of experts; – a decision rule that reflects the
preference system.
Assume that the current situation that has developed in the process of UEN opera-
tion described as a fuzzy situation of the following type [9]:
STEK M Si xi / xi , xi X , (2)
M Si xi – the function of belonging to a linguistic variable xi , that characterizes
the current situation STEK .
Also, assume that for each linguistic variable xi corresponds to the j-th term of the
set of terms in the knowledge base. Then the formula (2) can be written as:
S i M M S xi T ji / T ji , j 1, M ; i 1, N ; xi X ,
i
(3)
T ji – j-th term i-th linguistic variable.
To determine the current state of urban engineering networks it is necessary to
compare this fuzzy situation with each fuzzy situation from a certain set of existing
situations in the knowledge base of this subject area S S i , S K The result of
the comparison should be a dispatcher's decision on the strategy for further UEN
management with the involvement of IDSS. If the current situation is "regular", the
control implemented automatically according to the existing algorithm for this situa-
tion. If occurs in an "emergency" situation, the IDSS will help you choose a manage-
ment strategy that is close to this situation, or, if one is not found, form a new man-
agement strategy.
3 Literature review
Decision-making in most cases consists of generating possible alternative solutions,
evaluating them, and selecting the best option. In most cases, the choice of the opti-
mal solution made under conditions of information uncertainty and conflicting fac-
tors. Uncertainties in a particular subject area can be divided into uncertainties associ-
ated with incomplete knowledge of the problem solved and uncertainties associated
with the inability to fully account for the state of the environment [4, 5]. Inconsis-
tency occurs due to ambiguity in the assessment of situations, errors in the choice of
priorities, which greatly complicates decision-making. Research shows that decision-
makers without additional analytical support tend to use simplified and sometimes
contradictory decision-making rules. In this case, the most effective tool for making a
potentially better decision is decision support systems (DSS). DSS provides assistance
decisions make in the analysis of initial information (assessment of the current situa-
tion and restrictions imposed by the external environment). DSS provides identifica-
tion and ranking of priorities, take into account the uncertainty in the estimates of the
decision-maker and forming preferences, generation of possible solutions (forming a
list of alternatives); evaluation of possible alternatives; analysis of the possible conse-
quences of the decisions taken; selection of the potentially best solution [6,21].
Formalization of methods for analysis and generation of solutions, their evaluation
and coordination is quite a difficult task. Its solution made possible due to the wide-
spread use of computer technology and largely depends on the capabilities of techni-
cal software tools that implement methods and methods of intellectual support [8].
The decision-making process can proceed according to two main schemes: intui-
tive-empirical (based on comparing the problem situation with similar situations that
have previously occurred) and formal-heuristic (based on building and researching a
model of the problem situation for this particular subject area).
Under building a model of a problem situation, we examine the structure of the
DSS, which determined by such elements as the state of the initial data of the prob-
lem, the model of the decision-making situation, restrictions, decision options, and
their consequences, and external factors of an objective and subjective nature. The
combination of these elements forms a specific environment (system). In other words,
a DSS is a system that provides the decision-maker with the data, knowledge, conclu-
sions, and/or recommendations necessary for making a decision [10].
Considering the existing conceptual models of the DSS, the authors identify ap-
proaches based on the use of the ideology of information systems, artificial intelli-
gence, and the instrumental approach.
Within the framework of the ideology of the information approach, DSS classified
as a class of automated information systems whose main purpose is to improve the
activity of knowledge workers in organizations by using information technology.
Within the framework of the ideology of intelligent decision support systems
(IDSS), knowledge-based systems differ significantly from similar systems, primarily
expert systems (ES), in their target orientation [3, 19]. IDSS designed to help deci-
sion-makers solve problems, and ES designed to replace people in solving specific
problems [3, 18].
The tool approach, depending on the specifics of the tasks to be solved and the
technological tools used, we take into account applied DSS, which serve to support
decision-making for individual applied tasks in specific situations. Application DSS
are packages of software tools for searching and issuing data, modeling, etc., which
used by developers to create specialized systems and objects.
Modern IDSS based on the use of specialized information storage (Data Ware-
house) and OLAP (On-Line Analytical Processing) technologies - operational data
analysis. The main purpose of OLAP technologies is dynamic multidimensional data
analysis using an effective data-mining tool, modeling, and forecasting [2.20].
4 Building an IDSS based on a fuzzy situational network
The degree of proximity of a fuzzy situation STEK and situation S k k 1, K
from
the knowledge model determine as:
̶ degree of fuzzy enabling a fuzzy situation STEK in a fuzzy situation S k ;
̶ the degree of fuzzy equality STEK and S k ;
̶ degree of the fuzzy community STEK and S k ;
Setting one of the chosen proximity measures, we can set some fuzzy relationships
between situations, not only about the current one STEK but also between existing
ones in the knowledge base of this subject area.
From this subject area, the most convenient measure of proximity can be consid-
ered the degree of fuzzy inclusion of the situation, which characterized by a certain
threshold of inclusion determined by the expert, based on the conditions in which the
work of urban engineering networks takes place. The inclusion threshold is defined,
as well as the membership functions, in the normalized range [0, 1] as follows:
ton min ,1 (4)
min - the lower limit of the range of the degree of inclusion, usually
min 0.6 / 0.7 . In this case, we can talk about how fuzzy signs of the current situa-
tion STEK are included in the fuzzy values of the corresponding signs of the situation
S k (k 1, K ) [4, 15].
Further, for the existing knowledge base of this subject area and the conditions of
GIS operation in different operating modes, we form typical "regular" situations for
which control actions on the UEN are developed in detail on the expert methods. In
this case, the possible transition from one "regular" situation S k to another S i carried
out using some R ki solution. In this case, each possible solution determined by the
degree of preference for this solution kl ( S k , R kl ) In this way, you can build a fuzzy
situational network (Fig. 1), which clearly shows possible transitions from one "regu-
lar" situation to another and the degree of preference for these transitions [10, 15].
It notes that both the knowledge base of this subject area and the situation network
are evolutionary and are periodically updated both when a new "regular" situation
appears (in fact, this is a variant of the "non-standard" situation developed by experts)
and new requirements for the UEN operation.
As a result, based on the knowledge base of this subject area and conditions robots
UEN fuzzy situational network is a fuzzy directed graph, whose vertices correspond
to existing "regular" fuzzy situations, arc-weighted possible solutions required to
transition situations, and degrees of preference of these decisions (fig.1).
R24 R4K
R12 S2 S4
ɣ24(S2 ,R24) ɣ4K(S4 ,R4K)
S1 R43
Sl
R13 Rkl
S3 Sk SK
R3K
ɣ3K(S3 ,R3K)
Fig. 1. Fuzzy situational network
The degrees of preference for solutions in each situation either unchanged and deter-
mined by an expert survey, or depended in some way on the situation and determined
by the preferred solution in this situation. The control solution corresponding to the
current state is a sequence of decisions necessary for the transition from the current
situation to a given target situation along the "optimal route" in a fuzzy situation net-
work. The criteria for minimizing time and/or energy costs can be used as a prefer-
ence for solutions in the case of UEN. Then the "optimal route" corresponds to the
minimization of the total time and/or energy costs when moving along this route. In
this case, you can use the dynamic programming method.
Thus, the output of the solution is divided into setting a goal (target situation) and
building a management strategy that corresponds to the optimal translation of the
UEN to the target state. This conclusion of the decision is valid if the current situation
can be included in one of the "regular" situations.
Otherwise, if the current situation has a degree of fuzzy inclusion less than αmin in
the formula (4), then this "non-regular" situation presented to the experts to bring it to
the rank of "regular" and form variants of transition situations. Thus, the existing
fuzzy situational network corrected, which ensures its evolution. In fig.2 shown a
block- scheme of the IDSS UEN containing the main blocks (modules) of the soft-
ware: a knowledge base (KB), a block for generating control solutions, a block of
hints, a knowledge acquisition block and an intelligent interface presented.
The intelligent interface combines linguistic, information, and software tools for
interaction between the dispatcher, knowledge engineer (analyst), and UEN experts
with the corresponding components of the Toolkit. The hint block is intended to
show, if necessary, in a form that is understandable to the dispatcher, the progress of
the" reasoning" (working scenario) of the output mechanism to justify the manage-
ment decision made by it.
Before the main work, IDSS UEN creates a knowledge base (KB). KB UEN in-
cludes two components: long-term knowledge about UEN, which can be represented
as a set of rules of logical inference, hierarchical frame structures, semantic networks,
or other information structures that combine the above; operational knowledge (op-
erational data) that describes the current situation.
Note once again that the UEN database is evolutionary and is periodically updated
either with new information in this subject area or with the emergence of new situa-
tions in the management of UEN.
The formation KB of the UEN is as follows. In the knowledge acquisition block,
goals (sub-goals), criteria, requirements, and working conditions of the GIS formed.
Next, the term sets of the domain formed based on the descriptors of this domain, i.e.
UEN, which defined according to the work [11].
Fig. 2. Block-scheme IDSS UEN
From the selected set of descriptors, the most significant ones are selected, which are
used in the software module according to the work [12] for the intelligent multi-agent
subsystem (IMS) for searching information on the Internet, which one of the main
components of the database (DB), for accumulating the UEN knowledge base. In this
IMS synthesizes a generalized model of data collection and analysis based on a ge-
netic approach and a multi-agent method for synthesizing decision trees and a neural
network [13] that uses the decision-making specificity index. The decrease in search
time in IMS is due to an algorithm for selecting control solutions that use estimates of
sets of types of situations and specifics of logics, rather than the sets themselves. Im-
proving the quality of information achieved at each iteration by selecting behaviors
with a high frequency of use and cutting off the area of superposition estimates by the
logic specificity index and the situation index, which increases the level of ontological
representation of information.
Information obtained from the Internet and other sources based on latent semantic
analysis form the most significant content of the UEN KB [11] following the purpose
and conditions of the UEN operation.
Next, a fuzzy situational network of this subject area, i.e. UEN, built in the inter-
preter of working scenarios for finding solutions in the block for generating control
solutions. To do this, we extract a set of "regular" fuzzy situations from the UEN
database, for which possible transitions between situations are determined based on
information about the goals/sub-goals of GIS work, criteria for work, and require-
ments for UEN work. The result is a fuzzy situational network that is a fuzzy oriented
weighted graph. The fuzzy situational network, as the KB UEN periodically updated
with new information, clarifying objectives, criteria and the emergence of "nonstan-
dard" situations missing BRS in GIS, i.e. in effect, the training of IDSS UEN.
The mechanism for fuzzy inference of management decisions based on operational
data about the current situation, based on long-term knowledge, predicts the actions
required by the current situation, planning a step-by-step working scenario for finding
a solution. The block for forming management decisions implements the fuzzy situ-
ational management algorithm shown below (Fig.3) [15].
5 The algorithm of fuzzy situational control
In fig.3 shows a block-scheme of the UEN fuzzy situational management algorithm,
which, if an "emergency" situation occurs, will help you choose a management strat-
egy that is close to this situation, or, if one is not found, form a new management
strategy.
In block 1, enter information about the current situation in the GIS, which charac-
terized by many factors. In this case, some factors entered into the system automati-
cally based on the readings of the corresponding measuring instruments, and some are
targeted monitoring information. In General, information about the current situation
will be characterized by both quantitative and qualitative values of factors. In block 2,
the situation compared with a set of "regular" situations that are in the knowledge
base (KB) and characterized by the same set of factors as the current one. Thus, this
block allows you to limit the number of possible situations for which you need to
calculate the degree of proximity to the current situation. This will significantly re-
duce the running time of the algorithm. In block 3, the degree of proximity ton of
the current situation is calculated and the "regular" situations from block 2 that are
close to it are determined. Determining the degree of proximity of fuzzy situations
necessary to provide the required data for the algorithm for selecting control solutions
that operate on the control decision matrices stored in the database of "regular" fuzzy
situations. In block 4 compares the calculated degree of proximity ton (the degree
of belonging) to the specified normalized inclusion interval according to the formula
(4), where ton . This makes it possible to select the "regular" situations that are
closest to the current one.
Fig. 3. Block-scheme of the fuzzy situational control algorithm
In block 5, management decisions generated that correspond to the "regular" situa-
tions selected in block 4. In blocks 6.7, the effectiveness of control actions ranked in
descending order within a subset of selected "regular" situations and the optimal one
is determined among them. In block 8 the optimal control and the corresponding
situation are entered as "regular" in the knowledge base about the functioning of the
UEN. In block 9 the operation mode is adjusted to take into account the current situa-
tion and the criteria for the effectiveness of the UEN.
In block, 10 the current situation is placed in the expert environment (ES) and the
knowledge base of the subject area. In block 11, possible control actions are re-
quested from experts in this subject area placed in the knowledge base. In block 12,
possible situations and relevant management decisions generated and entered into the
knowledge base. On the method of mixed assessments developed by the authors, new
"regular" situations are formed and entered into the knowledge base about the func-
tioning of UEN.
6 Mixed assessment method
The proposed method differs from the known methods PARK, ZAPROS, ORCLASS,
and SHNUR [14] in that the entire set of alternatives evaluated for each criterion at
once. The main stages of the method include:
Stage1. Construction of a set of hypotheses-bases Z i corresponding to a set of
criteria K i and a set of hypotheses-consequences zij corresponding to a set of
criteria values.
Stage2. Formation of quantitative and linguistic scales of criteria for evaluating al-
ternatives.
Stage3. Drawing up a block structure of the questionnaire and filling it out on the
hypotheses-bases and hypotheses-consequences.
Stage4. Normalization of scales of criteria for evaluating alternatives.
Attributes that form alternatives to Ai contain both numeric (quantitative) and
linguistic (qualitative) variables. The membership function μ:x→[0,1] quantitatively
grades the membership of elements of the set of alternatives A to the fuzzy set A ,
~
with normalized variables, i.e. A x, A ( x) x X .
A value of 0 means that the element not included in the fuzzy set, and 1 means that
the element is fully described by the given set. Among the most well-known and used
auxiliary functions, the most convenient and universal for the variables under consid-
eration is a triangular function of the form [7,18]:
а) for the max-min preference scale of the Ai alternative
0, if x aij ;
x aij
xij ij , if aij xbij ; (5)
bij aij
1, if x bij ,
where aij x ; bij xmax ij
min ij
б) for the min-max preference scale of the Ai alternative
1, if xij aij ;
b xij
xij ij , if aij xij bij ; (6)
aij bij
0, if xij bij ,
where aij x ; bij xmax ij
min ij
Rationing of estimates of the compared alternatives carried out on the formulas (5)
and (6). For this:
─ for all quantitative estimates the maximum and minimum values of the variable
under consideration determined;
─ for all linguistic (qualitative) assessments, the maximum and minimum verbal
value of the variable determined;
─ the values of the criteria are determined following formulas (5) and (6).
Stage5. Identifying a potentially better alternative
The values of ratings on the normalized scale according to the formulas (5) and
(6) are formed as follows:
ij ' ij , (7)
where i – alternative number, j –index of the value of a quantitative or linguistic
scale.
Then the sum of s-th alternative can be calculated by adding the sum of
scores for each j-th question, which is summed across all issues of the i-th block and
all blocks of the questionnaire:
n m k
rS ij' (8)
S 1 i 1 j 1
As a result, can formulate for the initial set of alternatives As an ordered set
of their ranks R r1 , r2 ,..., rn . If it is necessary to take into account the importance
of a particular criterion (question), it is necessary to enter weight coefficients in for-
mula (8), which can be determined on the known methods of expert assessments [18].
7 Modeling optimal transitions in a fuzzy situational
network
Let be a weighted oriented graph (Fig.4) is a fragment of a fuzzy situational network
(Fig.1). Necessary to transfer the UEN from the" regular "situation S1 to the "regular"
situation S10 with the minimum total value of the preference func-
tions ij S i , Rij , i 1,...,10; j 1,...,10 , which reflect the time and material costs of
the transition from S i to S j . Numerical values of preference functions indicated on
the arcs of the graph in conventional units.
Fig.4. Fragment of a fuzzy situational network
To simplify and systematize the compilation of Bellman functions will number the
vertices of Si so that the arc leaves the vertex with a smaller number. In this case, we
consistently find the fi functions for each vertex of the oriented graph from the Bell-
man functional equation
f 1 minS 4 f 1
f1 0 , f 2 minS 21 f1 min3 0 3,
f 3 minS 31 f1 min4 0 4
f 4 minS 41 f1 min2 0 2,
S 54 f 4 3 2
f1 min S 53 f 3 min 6 4 5
S f 3 3
52 2
S 64 f 4 1 2
f 6 min min 3,
S 65 f 5 1 5
S 76 f 5 6 3
f 7 min min 9
S 75 f 5 8 5
f 8 minS 36 f 6 min12 3 15,
S 75 f 5 7 5
f 9 min min 12
S 98 f 6 6 15
S10,7 f ? 14 9
f10 min S10,9 f ? min 3 12 15
S f 11 5
10,8 8
The sum of costs for the optimal trajectory is 15 conventional units. To determine it,
the fi functions viewed in reverse order. In this instance
S10,7 f ? 14 9
f10 min S10,9 f ? min 3 12 15
S f 11 5
10,8 8
The minimum selected amount of 3+12=15 corresponds to the vertex S9.
S 75 f 5 7 5
f 9 min min 12
98
S f 6 6 15
When calculating f 9 , the vertex S 5 selected. Continuing in the same way, we get the
shortest path from a vertex S1 to vertex S10 ( S1 , S 4 , S 5 , S 9 , S10 ) . In fig.6 arcs of the
optimal trajectory shown in bold lines.
8 Conclusion
The principle of building IDSS, similar to the UEN IDSS developed in this article, is
universal for other subject areas and can serve as a powerful incentive for creating
intelligent information technologies and developing innovative systems for managing
urban development in the territory of a municipality [14-16]. The situational algo-
rithm of fuzzy control given in the article is the basis of the ISPR and based on the
automated method of mixed assessments and the expert method of generating and
evaluating alternatives to management decisions [17]. Optimal trajectories of transi-
tions from one situation to another, taking into account the preference functions, im-
plemented on the dynamic programming method.
References
1. Soloviev, N.A., Nabatov, N.N.: System analysis of problems of emergency dispatching
service of housing and communal services. Questions of technical, physical, and mathe-
matical Sciences in the light of modern research. Novosibirsk, Sibak, (2018). pp. 5-12.
2. Kirakovski, V.V.: Geoinformation technologies in the diagnostics of engineering net-
works. GEOPROFI. Moscow: Geoprofi. (2005). No. 2. pp. 52-53.
3. Basalin, P.D., Bezruk, K.V., Radaeva, M.V.: Models and methods of intellectual support
of decision-making processes: A textbook. Nizhny Novgorod: Nizhny Novgorod State
University, (2011).
4. Demidova, L.A., Kirakovski, V.V., Pylkin, A.N.: Algorithms and fuzzy inference system
in the diagnostics of city engineering communications. Moscow: Hotline-Telecom. (2005).
592p.
5. Kuzin, E.S.: Information complex problems and technology of their solution. Artificial in-
telligence news. (2003). No. 1. pp. 24-29.
6. Melikhov, A.N.: Situational advising systems with fuzzy logic. Moscow. Nauka, (1990).
272p.
7. Bodrov, V.I.: Mathematical methods of decision-making. Taganrog. TSTU, (2004). 124p.
8. Trahtengerts, E.A.: Computer-aided decision support. Moscow. Nauka, (1998). 376p.
9. Averkin, A.N., Batyrshin, I.Z., Blishun, A.F., Silov, V.B., Tarasov, V.B.: Fuzzy sets in
control and artificial intelligence models. Moscow. Nauka, (1986). 312p.
10. Chekinov, G.P.: Application of situational management in information support of decision-
making in the design of organizational and technical systems. Information technologies in
design and production. (2003). 215p.
11. Stenin, A.A.: Latent semantic method for extracting information from Internet resources.
Eastern European journal of advanced technologies. (2013). No. 4(9). pp. 19-22.
12. Stenin, A.A., Pasko, V.P., Lemeshko, V.A.: Neurosemantic approach to building auto-
mated information retrieval systems. Adaptive automatic control systems. KPI. (2019). №.
1(34). pp. 125-130.
13. Subbotin, S.A., Oleynik, A.A., Hoffman, E.A., Zaitsev, S.A., Oleynik, A.A.: Intelligent in-
formation technologies for designing automated systems for diagnostics and image recog-
nition. Kharkiv. Smith Company, (2012). p. 318
14. Stenin, A. A.: Automation of the process of making innovative decisions in sociotechnical
systems. Problems of information technologies. (2016). No. 19. pp. 51-57.
15. Stenin, A.A., Lisovichenko, O.I., Drozdovich, I.G., Stenin, S.A.: Analysis of passenger
traffic and situational management of urban transport Bulgarian Journal for Engineering
Design issue. The Mechanical Engineering Faculty. Technical University-Sofia. No.40.
(2019). pp. 7-12.
16. Vdovenko, A.V., Protasevich, E.V.: Information technologies in the management system
of urban development of the territory of the municipality. Vestnik TOGU. Khabarovsk,
(2009), no. 4(15). pp. 81-88.
17. Naikhanova, L.V., Dambaeva, S.V.: The Question-answer relationship in the method of
knowledge retrieval a Survey. Theoretical and practical issues of modern information
technologies. Ulan-Ude publishing house of VSGTU. (2003). pp. 37-41.
18. Orlov, A.I.: Organizational and economic modeling. Part II Expert assessments. Moscow.
Publishing house of Moscow state University Bauman, (2011). 486p.
19. Ashikhmin, I.V., Furems, E.M.: UniComBos intellectual DSS for comparison and selec-
tion of multi-criteria objects. Proceedings of ISA RAS. (2005), vol. 12. pp. 16-25.
20. Barsegyan, A.A., Skupinou, M., Stepanenko, V.V., Holod, I.I.: Technology of data analy-
sis. Data Mining, Visual Mining, Text Mining, OLAP. (2007). pp. 384
21. Trofymchuk, O.M., Bidyuk, P.I.: Decision support systems, modeling, forecasting, risk es-
timation. LAP LAMBERT Academic Publishing. (2019). 179p.