Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects
In the article substantiated the expediency of introducing the basics of systemological analysis in modeling and structuring of studies of complex objects, which allows to establish conditions for the implementation of a certain target function, which is responsible for the state and functionality o...
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nasplib_isofts_kiev_ua-123456789-1953802025-02-09T15:23:23Z Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects Використання системно-логічної основи та функції інформаційної ентропії при дослідженні в умовах невизначеності системно-структурованих об’єктів Использование системно-логической основы и функции информационной энтропии при исследовании в условиях неопределенности системно-структурированных объектов Kozulia, T.V. Kozulia, M.M. Experimental methods and processing of data In the article substantiated the expediency of introducing the basics of systemological analysis in modeling and structuring of studies of complex objects, which allows to establish conditions for the implementation of a certain target function, which is responsible for the state and functionality of the investigated object in certain conditions of the environment, taking into account the macrostate of the complex system, through experiments of microstates, and its changes in the system “object – the environment” regarding the state of external systems using an entropy func-tion according to a consistent analysis of uncertainties and their solution to establish conditions for the stabilization of the object or achieve the goal of regulation situations based on information synergetics. It was concluded that, proposed comprehensive entropy-synergy analysis of the determination of the state “the investigated system – the environment” and changes in the consequence of process transformations in systemic objects in conditions of certain uncertainty does not require additional research, characteristic of known estimates for the criteria in widespread mathematical means decision-making. Розглянуто доцільність впровадження основ системного аналізу в моделюванні та структуруванні досліджень складних об’єктів, що дозволяє встановлювати умови для здійснення певної цільової функції, яка відповідає за стан та функціональність досліджуваного об’єкта в певних умовах навколишнього середовища, з урахуванням макростану складної системи, через експерименти мікростанів, та його зміни в системі «об’єкт - навколишнє середовище» щодо стану зовнішніх систем за допомогою функції ентропії відповідно до послідовного аналізу невизначеності і їх вирішення встановленням умов для стабілізації об’єкта або досягнення мети ситуацій регулювання на основі інформаційної синергетики. Було зроблено висновок, що запропонований комплексний аналіз ентропійно-синергетиного визначення стану «досліджувана системи - навколишнє середовище» та зміни внаслідок процесів трансформацій у системних об’єктах в умовах певної невизначеності не вимагає додаткових досліджень, характеристик для відомих oцінок для критеріїв у поширених математичних засобах прийняття рішень. Рассмотрена целесообразность внедрения основ системного анализа в моделировании и структурировании исследований сложных объектов, что позволяет устанавливать условия для осуществления определенной целевой функции, которая отвечает за состояние и функциональность исследуемого объекта в определенных условиях окружающей среды, с учетом макросостояния сложной системы, через эксперименты микросостояний, и его изменения в системе «объект - окружающая середа» по состоянию внешних систем с помощью функции энтропии в соответствии с последовательным анализом неопределенности и их решения определения условий для стабилизации объекта или достижения цели ситуаций регулирования на основе информационной синергетики. Был сделан вывод, что предложенный комплексный анализ энтропийно-синергетического определения состояния «исследуемая система - окружающая среда» и изменения вследствии процессов трансформаций в системных объектах в условиях некоторой неопределенности не требует дополнительных исследований, характерных для известной oценки критериев в распространенных математических методов принятия решений. 2022 Article Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects / T.V. Kozulia, M.M. Kozulia // Problems of Atomic Science and Technology. — 2022. — № 3. — С. 118-127. — Бібліогр.: 34 назв. — англ. 1562-6016 PACS: 519.2 https://nasplib.isofts.kiev.ua/handle/123456789/195380 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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| topic |
Experimental methods and processing of data Experimental methods and processing of data |
| spellingShingle |
Experimental methods and processing of data Experimental methods and processing of data Kozulia, T.V. Kozulia, M.M. Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects Вопросы атомной науки и техники |
| description |
In the article substantiated the expediency of introducing the basics of systemological analysis in modeling and structuring of studies of complex objects, which allows to establish conditions for the implementation of a certain target function, which is responsible for the state and functionality of the investigated object in certain conditions of the environment, taking into account the macrostate of the complex system, through experiments of microstates, and its changes in the system “object – the environment” regarding the state of external systems using an entropy func-tion according to a consistent analysis of uncertainties and their solution to establish conditions for the stabilization of the object or achieve the goal of regulation situations based on information synergetics. It was concluded that, proposed comprehensive entropy-synergy analysis of the determination of the state “the investigated system – the environment” and changes in the consequence of process transformations in systemic objects in conditions of certain uncertainty does not require additional research, characteristic of known estimates for the criteria in widespread mathematical means decision-making. |
| format |
Article |
| author |
Kozulia, T.V. Kozulia, M.M. |
| author_facet |
Kozulia, T.V. Kozulia, M.M. |
| author_sort |
Kozulia, T.V. |
| title |
Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects |
| title_short |
Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects |
| title_full |
Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects |
| title_fullStr |
Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects |
| title_full_unstemmed |
Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects |
| title_sort |
using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2022 |
| topic_facet |
Experimental methods and processing of data |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195380 |
| citation_txt |
Using the systemological basis and information entropy function in the study at uncertainty conditions of system-structured objects / T.V. Kozulia, M.M. Kozulia // Problems of Atomic Science and Technology. — 2022. — № 3. — С. 118-127. — Бібліогр.: 34 назв. — англ. |
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Вопросы атомной науки и техники |
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118 ISSN 1562-6016. ВАНТ. 2022. №3(139)
https://doi.org/10.46813/2022-139-118
USING THE SYSTEMOLOGICAL BASIS AND INFORMATION
ENTROPY FUNCTION IN THE STUDY AT UNCERTAINTY
CONDITIONS OF SYSTEM-STRUCTURED OBJECTS
T.V. Kozulia, M.M. Kozulia
National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine
E-mail: mariya.kozulya7@gmail.com
In the article substantiated the expediency of introducing the basics of systemological analysis in modeling and
structuring of studies of complex objects, which allows to establish conditions for the implementation of a certain
target function, which is responsible for the state and functionality of the investigated object in certain conditions of
the environment, taking into account the macrostate of the complex system, through experiments of microstates, and
its changes in the system “object – the environment” regarding the state of external systems using an entropy func-
tion according to a consistent analysis of uncertainties and their solution to establish conditions for the stabilization
of the object or achieve the goal of regulation situations based on information synergetics. It was concluded that,
proposed comprehensive entropy-synergy analysis of the determination of the state “the investigated system – the
environment” and changes in the consequence of process transformations in systemic objects in conditions of certain
uncertainty does not require additional research, characteristic of known estimates for the criteria in widespread
mathematical means decision-making.
PACS: 519.2
INTRODUCTION
The systemology of complex objects is a means that
provides the possibility of solving various scientific,
business, managerial and production weakly structured
and weakly formalized problems with the help of mod-
ern information systems (IS) and information technolo-
gies (IT). This is of particular importance in the research
of a complex object “system – the environment” view
on technogenic and environmental safety. To solve
many security issues, it is important not only to estab-
lish a state of a complex object, but mostly its function-
ality in the conditions of presence and variability of the
environment. The ecological state of entertainment and
any economic activity does not determine the safety,
because it is the result of analytics of the information
component, which takes into account the qualitative
characteristics of the environment in contact with the
technosphere, quantitative assessments of their changes
in such interaction, the processes of creating direct in-
fluence factors on living organisms and a person.
Thus, consideration of security issues in any section
of their solution (at the level of macrosystem study,
analysis of simple systems) requires complexity in stud-
ies, which is ensured by the use of systemological foun-
dations for modeling complex structured systems using
the function of information entropy with the inclusion of
synergetics and information theory. The introduction of
a systematic approach in solving quality and manage-
ment problems is due, firstly “unsatisfactory ways to
describe the behavior of large discrete systems”, and
secondly, weak structuring and “complexity of real
subject areas”, interdisciplinary nature of research to
achieve a solution of the settlement tasks, obtaining
necessary knowledge as a basis for taking weighted
decisions.
In a practical section, it is proposed to achieve the
goal of finding solutions for problematic security issues
in general and ecological in particular in relation to the
experimental object in the form of a “system – the envi-
ronment” due to solving such tasks:
‒ substantiation of the methodological basis of
knowledge-oriented systemological analysis of the
complex of monitoring data on the search for target
decisions, taking into account the process phenomena of
internal and external nature for systems of different
nature and complexity due to the use of the entropy
approach for modeling conditions and processes;
‒ testing of the proposed synergistic and entropy an-
alytics of information analysis of objects in relation to
the self-organization of their homeostasis processes on
the example of the study of self-purification contami-
nated soils.
1. PROBLEM STATEMENT:
MODELING TECHNIQUE
In order to study objects of the type “system the
environment”, an algorithmic and software assessment
of natural and technogenic objects state is proposed by
the results of the probabilized-entropy analysis of moni-
toring data with the introduction of synergetics provi-
sions.
Methodological basis of a comprehensive study of
any object as a systematic formation of the view “object
– the environment – (object – the environment) – pro-
cesses of internal and external nature – (object – the
environment)
object” it is advisable to build a universal
integrated approach covering all stages of system analy-
sis of monitoring data and allows to state the acquisition
of knowledge about the object after the end of the cog-
nitive process (Fig. 1).
Trends in the system change to disorganization,
which determines the growth of the function of the
entropy S state, counteracts information. Increasing the
amount of information in the system contributes to
increasing its organization, and thus an increase in the
certainty of the investigated situation, obtaining
knowledge about the object.
ISSN 1562-6016. ВАНТ. 2022. №3(139) 119
The equilibrium functioning of all large systems
components in accordance with balanced interaction at
the level of subsystems and elements of each of them as
a whole is realized thanks to the synergistic effect of the
microstan components co-operation in the organization-
al structure that corresponds to the maximum entropy.
The functioning of such systems in the external envi-
ronment, their condition and properties at time is deter-
mined by the energy level:
txbaEE iii ,,, , (1)
where txba iii ,,, – accordingly, external and internal
data parameters indicators, managed parameters and time.
Fig. 1. Scheme of systemological modeling of a system object on an entropy-informational basis with knowledge
base: N, S, Е – natural, social, economic system; SEWX ,,, – composition, structure, energy, entropy;
U – management (author’s development)
From these positions in environmental research, the
facility is provided as a complex of interrelated natural
and social systems, technosphere “Technical shell”,
artificially transformed space that is under the influence
of human activity: SEWX ,,, – composition, structure,
energy, entropy of biosystems, organism and the envi-
ronment.
Such organizational and structural interconnection of
the components of the system object implements the
principle of self-organization in finding a sustainable
state due to co-operation, compatible actions of the
necessary factors, processes, etc., which is a synergistic
effect, causes a synergistic system when combining
individual components, supporting the systematic Dy-
namic state according to the effect of the compatible
action of each individual component in the form of their
simple sum. It is proposed to study the features of the
mutual functioning of socio-ecological and economic
systems of equal complexity combination of system
analysis elements – entropy, information and synergy
[13, 26 - 28].
The close content between entropy and information
determines the first as non-abundance of information, and
the second as counteraction to entropy, that is, the viola-
tion of the established procedure, the need to find new
knowledge about new systems and processes. These two
measures of complex systems are combined with each
other with a negentropy – a characteristic of motion to
order, organize the system. Any system interacting with
the environment to keep their natural state counteracts
surrounding chaos by importing negentropy [25].
The investigated object in this case has a systematic
representation in the form of “the object of monitoring
(the system – the environment) – data on state and func-
tionality = processes of external influence, internal
regulation – processes of self-organization – steady state
of the object, stationary (system – environment)”. For
its comprehensive study, it will be effective in the use of
an entropy approach, since for assessing the condition
and changes, statics and dynamics, deal with one func-
tion, namely entropy.
In the study of processes nature that return a disor-
ganized system from chaos to an orderly structure, ele-
ments of synergetics are involved, that is, co-operation
of factors interaction of imbalance resolution, unregu-
lated situations. The fixation of the necessary direction
of change is traced by the processes of self-organization
and the change in the entropy level in the current state
of the fixed system due to the sequential use of the ele-
ments of the entropy and synergetics in the system anal-
ysis of this system object with the inclusion of processes
that lead to changes or returning systems to the initial
Condition, and thus and the entire object determined as
an entropy-information evaluation of the state of system
objects (Fig. 2) [29].
According to Fig. 2, systems state is evaluated ac-
cording to the qualitative-quantitative characteristics of
the change in entropy by trajectory of the final structur-
ing of the object in the space of interaction with the
surrounding environment. In the conditions of nonlinear
development of events and self-existing processes “ob-
ject – external systems”, with a stable structure of the
system object of research, it is expedient to use an en-
120 ISSN 1562-6016. ВАНТ. 2022. №3(139)
tropy approach and a phenomenological basis of a con-
sistent solution of situations uncertainty regarding state
and processes. In this case, the stochastic and uncertain-
ty of the situation is overcome by the consistent repre-
sentation and analysis of quality information to obtain
results in terms of maintaining appropriate structural
stability in the research system “Object – Environment”
in accordance with changes in the entropy function ΔS
from the analysis of “state – processes”. According to
the results, with this approach, it is likely to establish
self-propelled regulation of equilibrium in the systemic
formation or transition to new equilibrium states with
changes that are associated with an increase in entropy
in the investigated system (see Fig. 2).
Fig. 2. Scheme for evaluating the state of the study system “object – environment” by entropy approach
to the analysis “state – process” (author’s proposal): 1, 2, 3, 4 – system states according to the terms
of interaction “object – environment”; 1
1
, 2
1
, 3
1
– arbitrary reverse processes of returning system to initial state,
i.e. Sx = 0; 1
2
, 2
2
, 3
2
– arbitrary processes of mutual influence “object – environment”,
which leads to ∆ S > 0; 1
3
, 2
3
, 3
3
– changes in the system “object – environment” on the state of external systems
03,2,1 yS , that lead to new states; 1
4
, 2
4
, 3
4
– self-regulation processes between the object and the environment
within the investigated system that maintain equilibrium in the system with its permissible changes 03,2,1 xS
The proposed entropy analysis of the analysis is de-
termined by the fact that the object is characterized from
the positions of achieving certain goals, observing the
permissible normative restrictions, etc. and the imple-
mentation of processes in relation to the object of influ-
ence of external environment or the possibility of re-
solving the coexistence situation “object – environ-
ment”. In this case, it is necessary to take into account a
close relation between entropy and information that is
important for interactions with the environment, which
is mostly an event of uncertainty.
In time, there is a deviation from stationary in a state
of the system, its functional capabilities, the emergence
of state stabilizing processes in self-regulation or the
course of processes, which is a factor in self-
organization, achievement of stationary in a permissible
variation. All this sequence is defined as elements of the
analytical system N, which forms a set X, which con-
tains variables x. Each element is determined by entro-
py, which, provided that changes in the system when
interacting with the environment (system in the object –
the internal environment, with the environment – exter-
nal environment) is defined as an entropy for the end
state with N probable consequences (outputs) view pn
(R.V. Hartley, 1928 [33]):
NS 2log . (2)
For independent random events X with N probable
states described probabilities Nnpn ,1 , establish
medium entropy and associate it with information I and
the conditions of a particular situation NI 2log .
Knowledge Oriented research is expedient to inter-
pret the theory of information that specifies the mathe-
matical apparatus of quantitative determination of in-
formation, which is determined by three approaches.
The combinator approach provides quantitatively in-
formation about the object through its systemic organi-
zation, which is consistent with the provision of an
object in the form of “system – environment”.
In a combinatorial concept, the amount of infor-
mation about the object X is provided with a given re-
quirement to accuracy, adheres to logical independence
from probabilistic assumptions. This approach allows
you to determine the amount of information as
-entropy KS . In order to allocate an individual
function from the grade of functions for the given con-
ditions of the analyzed system. In the same way, a cer-
tain amount of information is used as -capacity KC
to separate securely disparate elements K, the distance
from which not less [33].
ISSN 1562-6016. ВАНТ. 2022. №3(139) 121
Observation of an object conducted with a given
accuracy (measurement system, information processing
system, etc.) that determines -entropy S of an object
. By Shannon, this is defined as the speed of creating a
message. For -entropy, the theorem about the extreme
role of normal distribution is maintained: S calculat-
ed exactly in case of normal distribution .
Within the analysis of a systematic object, this
means that for inpatient and dynamic conditions, its
condition is described by a certain function, the change
of which indicates an approximation to a certain point
of homeostatic relations with the environment, namely
the entropy ( KS ) in establishing significant factors
of destabilization of the situation in the system “object –
environment” and the entropy of the inner homeostasis
( KC ) with regard to the state of the “object system
the internal object environment”.
In the case of a systematic submission of the re-
search object, namely the consideration of object system
(set Х) and system (set Y ), internal interaction
between components relative to the requirements of
their existence space YX realized on a set of possi-
ble pairs U at Xa and such y with aY , that match
the condition Uya , . Information entropy in this
case is calculated equation
aYNayS 2log| , (3)
where aYN – the number of set elements xY .
Since the study of complex systemic entities with a
system of environment from the object surroundings has
a certain degree of uncertainty, it is advisable to infor-
mation about the state of the system (according to X)
to establish relative information about (according y )
thus
xySySyxI |: . (4)
In the presence of data for a system object from var-
ious monitoring data sources and information consisting
of not bound or weakly bound information (indicators,
factors, measurement parameters, etc.), subordinated to
certain probabilistic laws, is used in the practice of sci-
entific research is probabilistic approach. Within its
limits are allowed with significant over time and volume
of observation of probabilities and frequencies mixing;
formation of mathematical expectation for entropy
xyMSW | and information yxMIW : , the value of
which can take excellent value (with a combinator ap-
proach, it is always a positive value that is taken into
account for an idea of information amount).
According to A.N. Colmogorov [33], the true meas-
ure of the amount of information is the averaged value
yxIW , , characterizing the density of communication
between systems and , state parameters х, у sym-
metrical way: 0| xxSW , xSxxI WW : ,
xyMIyxMIyxI WWW ::, with the fact that
xySW | and yxIW : are functions from х.
The amount of information to set an accurate value
In the presence of a well-known and sufficient vol-
ume of values jy is equal
ji
i
jij ppyS |2| log| ,
where ii pxP – probability of characteristics in
relation to parameters values of the systems i-th state ;
ijji pyxP , – additional distribution for a
random object with consideration of the compatible
probability distribution (in the proposed version of the
analysis according to Fig. 2
ji
i
jij ppyS |2| log| , where jip | is the
difference between the probability of obtaining data /
information on the investigated object and the actual
existing state of it with clearly defined properties or
target, that is
jiji pp || , (5)
that averaged
i
jijij pp
j
yPMS |2| log| ,
and on the suggestion
ji
ji
i
jijij
p
ppp
j
yPSM
|
||2| , log|
(6)
where |S , |S – conditional entropy and
change of conditional entropy at x ; |MS
and |SM – mathematical expectation of condi-
tional entropy and change of conditional entropy in
variable characteristics or system state [24, 28].
The amount of information relative , contained in
the results obtained (task) or determined appropriately
due to characteristics for the system , equal to the
difference
|| MSSI ;
and information changes to the investigated object will
be || SMSI according to the ob-
servation data received
2| log ,
| .
ij
ij
i i j
ij
p
I p
P x P y
I f p
(7)
According to equations (2) - (5) we have the final
calculation definitions of changes for the state of the
investigated object in the field of its existence W, in
particular the information yxIW : :
xpxpxS
x
W log2 ;
xypxypxyS
i
W | log|| 2 ;
xySySyxI WWW |: . (8)
In the study “object – environment” system, it is ad-
visable to have information on changing the probability
to maintain a macro-source that is responsible for target-
,
122 ISSN 1562-6016. ВАНТ. 2022. №3(139)
ing equilibrium in space and processes in such a system
according to the statistical function of the Boltzmann
entropy (see Fig. 2):
lnkS , (9)
where k – the coefficient of proportionality, constant
Boltzmann; k = 1.38 10
–23
J/K; ∆ – changes in the
number of possible microstates (methods), which can be
compiled by this macroscopic state of the system that
identifies the number of system microstates, provided
that all microstates are equal.
Provided changes in the system when the object in-
teracts with the environment receive certain N-probable
consequences (outputs) pn, of which interesting is
changed ∆N, that determine the realization of equilibri-
um or intended purpose in accordance with changes in
Hartley entropy:
NS 2log . (10)
Such a sequence of obtaining a chain of entropy
changes in the analysis of states and processes allows
you to move in the direction of probable trajectories in
the space “object – environment”, which leads to a goal
or desired development in such a system or facility in
existing conditions. The level of knowledge about the
system state (finally accepted solution) is defined as
Shannon's information entropy for independent changes
in events X, which corresponds to ΔN-altered probable
states described by probabilities Nnpn ,1 :
n
N
n
nnx pMppS
2
1
2 loglog . (11)
The final finding result is rated in this way:
- minimum probability of change corresponding to
the implementation of the necessary macro state, unit
probability;
- maximum probability of change corresponding to
uniform probability distribution ofstates realization that
are closed to solution according to
NpNn n /1 ,,1 ;
- zero value for other cases when changing statistical
entropy by Shannon:
l
s
ii
x
N
N
N
N
S
1
ln , (12)
where iN – changes in the number of elements in the
i-th species in the total number of changes in the inves-
tigated system ∆N.
The final state is established by a structural entropy,
according to which the desire of the system to equilibri-
um is formed ( min,0 1 SS max,0 2 SS )
[24, 27, 32].
In all decisions, the system or object must reach the
attractor structure (function), which specifies (deter-
mines) stable system state (synergetics, nonlinear think-
ing). Thus, a probable state of the system is realized, a
probable purposeful action is likely to lead to the maxi-
mum ordering and self-organization of the object,
achieving the synergy of the information flow.
2. REVIEW OF THE LITERATURE
REGARDING THE METHODS
OF STUDYING COMPLEX OBJECTS SUCH
AS “SYSTEM – ENVIRONMENT”
In general, in the performance of a comprehensive
analysis of a complex research object, it is in mind that
any system with its functional properties is a conse-
quence of the functional request of the subsystem to its
specific function. Under this position in scientific re-
search, it is advisable to draw attention to the search for
decisions in accordance with the provisions and princi-
ples of systemology, which considers the object, taking
into account the level of its systematic.
The essence of systemologies as a methodology of
system analysis and the theory of complex systems,
which is an expanded principle of integration, unity and
communication, concentration, modeling, productivity,
uncertainty, decentralization, which applies to systemic
research and determines the essence of the system or-
ganization of the object [1 - 3]. The system is consid-
ered as a dynamic object, along with the process of its
emergence, formation and functioning when interacting
with surrounding external systems [1, 2].
Given the features of ecology tasks solution, which
deals with complex objects, with the lack of objective
models for obtaining a generalized assessment of al-
ternatives quality, if necessary, taking into account the
set of criteria (environmental, economic, technologi-
cal, etc.), when choosing an optimal decisions it is
relied on a decision maker (DM). To increase the DM
objectivity, it is necessary to provide an area of re-
search as objective information. Information about
objects of problem area (PA) and their properties are
proposed in the knowledge base (KB) of the intellectual
system of expert analysis of the environment state, fore-
casting and prevention (IseaFP) of emergencies. Thus,
for a weakly structured problem of choosing an optimal
environmental measure to prevent the possibility of a
emergencies on objects of industrial production, the
provisions of the systemological cognitive approach [4]
are implemented.
Taking into account the above and the needs of envi-
ronmental research in ecological methods, in the paper,
a proposal for consideration of the research object in the
form of a systemic formation “System – environment”
is supplemented by the system of processes that ensure
the interaction of these components as integrity, provid-
ing equilibrium and stability.
The specific manifestation of the systemic principle
of systemicity in a complex system organization of the
experimental object is a phenomenon or synergy law.
The basis of the analytical research system of such an
object is the theory of self-organization, which is a sci-
ence of complicated and steady unequal, non-stationary
and structures associated with synergetics as a theory of
self-organization, dissipative structures, dynamic chaos
[7 - 9].
The research object in case of the use of such an in-
terdisciplinary on the essence of the approach is the
system of the real environment of socio-ecological and
economic purposes, which are for the target problem – a
scientific understanding of complexity and rational
ISSN 1562-6016. ВАНТ. 2022. №3(139) 123
explanation of the relationship between the complexity
with the laws of nature [10 - 20].
In these works, the synergistic approach is prospec-
tive for scientific research of open systems in various
areas of knowledge about the state, functional abilities
and development of natural, humanitarian systems and
objects of technosphere. In general, in most cases, under
synergetics understand (from gr. Synerge-Tikos a
common, coherent, active) scientific direction, which
studies the links between elements of the structures that
are formed in open systems due to intensive (streaming)
metabolism and energy from the environment by non-
equilibrium conditions. In such systems, the behavior of
subsystems is determined by coherence, which is asso-
ciated with the phenomenon of self-organization when
the degree of their ordering with a decrease in entropy is
increased. In the study of environmental systems and
the use of natural resources, an index based on entropy
is proposed to establish an optimal species, for example,
a hydraulic system and its water mitigation, an entropy
assessment on the tasks of avoiding natural and man-
made hazards [21 - 23].
Within the complex scientific research of a system-
atic object as a “system – environment” principles of
systemological analysis inhibit (dynamics) systems and
in accordance with the provisions of synergetics as the
theory of achieving a system of target destination (equi-
librium), and as a consequence of the acquisition of
scientific Knowledge about the research object in the
conditions of this environment. In the proposed natural-
man-made objects of the study as systemic formations
used entropy, which is an evolutionary function of the
state within the field of synergetics, that is, the basis of
system self-organization from chaos in accordance with
the directions of its target implementation [23 - 28]. The
paper proposes to use the entropy approach of scientific
search from the position of the universality of entropy
function as a characteristic of the state of the object as a
whole, the state of components and processes that pro-
vide equilibrium coexistence of systems within the
object (internal homeostasis) and with systems of envi-
ronment (external homeostasis).
3. MATERIALS AND METHODS
According to the proposed systemological infor-
mation and entropy approach based on the theory of
system analysis and synergetics of a complex study of a
complex object in the sequence of “system state – exci-
tation – the process – stabilized system state”, experi-
ments on the possibilities of soil abilities realization to
self-cleaning due to the growth of heterogeneity of the
factor are conducted. External influence on this natural
system, including man-made sources (the basis for anal-
ysis, served as many years of study by the author about
the features of the behavior of anthropogenic loaded
soils by their state on the territory of the Zmiyivan land-
fill and in Kharkiv (Ukraine) 1995-2009 [32]).
The paper proposes a systemological model of a
complex object of the species “soil external environ-
ment influence factors processes (results of change)
perception of external actions synergy space equi-
librium (soil environment)” (Fig. 3).
Fig. 3. Systemological model of self-cleaning of contaminated soils in accordance with synergistic and entropy
analysis: 1 – soil as an external system according to the distribution systems of pollutants in certain layers
of soils (2) in the form of mobile forms: cations (set X1 (3
1
)) and anions (set X2 (3
2
)), which is an internal system
of research (pollution zone where the condition of pollutants is determined through the entropy value of violations
of maximum permissible values); 4 – the effective system of chemical transformations as information synergy,
which is the process of self-cleaning
To describe the transformation in the migration
stream of heavy metals (HM), which are soil pollutants,
used entropy analysis of arbitrary processes of formation
of insoluble compounds, and as a result of the accumula-
tion of HM in the soil and the absence of them in the
biomaterial. Self-cleaning of the soil, thus, is determined
by the probability of binding of pollinants into insoluble
compounds (system 4 processes (changes in changes)
perception of external actions 4 in Fig. 3).
124 ISSN 1562-6016. ВАНТ. 2022. №3(139)
Violation of the discrepancy between the state of
environmental safety of soils at the accepted level of
changes in the HM content in them is an internal system
of research, characterized by certain entropy load – the
entropy value of discrepancies with the established
safety standards (formulas (8-12)). This system is a
geochemical subspace of the soil system mAAA ,..., , 21
( m – dimension), for which mxxx ,..., , 21 components
make up factors of influence in the form of
2211 , AxAx , that is the subject space from cationic
and anionic forms of HM UAAA m ...21 :
21
VCr,Mo,,CuSr,Pb,Ni,Co,Zn,
xx
U .
To assess the safety of НM receipt in environmental
objects in accordance with the soil, a characteristic is
given in the form of relations: 21, xx 2m ,
CuSr,Pb,Ni,Co,Zn,1 A , VCr,Mo,2 A , then
21 AAS there is a pairs set of view 21 , xx , for
which ratio are formed by the value of the entropy state,
that is, the analysis of changes in changes and self-
organization capabilities of the soil system as a whole.
Relationships that are parts of the same space, single-
type, implemented operations: association disjunction
“or”; section conjunction “and”. To ana-
lyze the state of heavy metals in the soil adopted for envi-
ronmental safety values, the probability of deviationing
their number in the soil from the normatively established
limitation of small risk 20%, which is a system for
evaluating ecological well-being in the form of
1
1, if 0.2;
0, if 0.2
n
x
P x x
x .
(13)
4. EXPERIMENTS. RESULTS
In order to identify the unauthorized processes of
binding heavy metals in the soil take into account that
the entropy assessment of the established bonds be-
tween the defined forms of HM in the soil should in-
crease in negative values. In accordance with this, an
assessment of soil condition is provided polluting
elements are in a bound state, which reduces their mi-
gration capabilities in the adjacent medium (Table 1).
Table 1
Comparator Identification of heavy metals under
the entropy of the violations of safety requirements
Element Entropy
state
Comparator Cr V
Zn -2.265 1 1 1
Co -1.619 0 1 1
Nі -1.616 0 1 1
Pb -2.042 1 1 1
Sr -1.687 0 1 1
Cu -1.844 0 1 1
Mo -1.462 0 1 1
Cr -2.639 1 1 1
V -2.434 1 1 1
Reflection “Excess” of the natural level of HM con-
tent due to the technogenic “receipt”, “interaction” in
the soil with its components (sorption) and among
themselves in a migration flow, taking into account the
combination of these processes for each element (con-
junction QP ) determine based on safety assessment
in the form 4030201000 yxyxyxyxyxP (where
x
0
, y
0
– Zn, y
1
– Ni, y
2
–Pb, y
3
– Sr, y
4
– Cu) According to
the formed base of their identified state (Table 2).
Table 2
Comparator identification of elements state
by the results of combining processes
Zn Ni Pb Sr Cu
Zn 1 1 1 1 1
Ni 0 0 0 0 0
Pb 1 1 1 1 1
Sr 1 1 1 1 1
Cu 0 0 0 0 0
According to the resulting perfect disjunctive normal
form (PDNF) form
4030201000 yxyxyxyxyxP
(where x
0
, y
0
– Zn, y
1
– Pb, y
2
–Sr, y
3
– Cr, y
4
– V) pro-
vide data of HM state in the soil (Table 3).
Table 3
Assessment results of heavy metals in the soil
Zn Pb Sr Cr V
Zn 0 0 0 1 1
Pb 0 0 0 1 1
Sr 0 0 0 1 1
Cr 1 1 1 0 0
V 1 1 1 0 0
Taking into account the section of Zn states in ac-
cordance with the state of other heavy metals present is
determined, PCNF of the form
.241404231303
423241314030
yxyxyxyxyxyx
yxyxyxyxyxyx
The random processes of HM accumulation are rec-
orded, with a small P deviation from the minimum con-
tent; The stability of the provision of a “positive state”
is determined by a significant deviation from the per-
missible limitation of the presence of an element in the
soil and the course of the compounds-forming process-
es: 2.3ix , if 0.1P and 2.99jy , if 0.05 ,
0.95P . Taking into account the data in Table 1 and
the above expression, PCNF has such an assessment of
elements state by comparative identification [14]:
Zn x
0
=–2.78 1111 1
Pb x
1
=–2.04 1010
0
Sr x
2
=–2.02 1010
0
Cr x
3
=–2.7 111111 1
V x
4
=–2.46 111111 1
Thus, phenomenological knowledge about the HM
behavior in environment objects, taking into account
arbitrary processes by entropy-synergistic analysis of
the situation, allow to substantiate their state and con-
firm the results of comparator identification, taking into
account “state – process” due to the use of PDNF and
DСNF and experimental measurements [32]. This al-
ISSN 1562-6016. ВАНТ. 2022. №3(139) 125
lows you to establish a risk factor, the probability of
leveling its negative influence due to the processes of
transformation of the urgent flows in the presence of
other negative components.
In order to implement in practice, the safety control
of natural-man-made territorial formations on the meth-
od provided by the method of assessing the quality of
complex systems was formed. To implement these tasks
in practice, such a sequence of automated information
processing (Fig. 4) [34] is proposed.
Fig. 4. Data stream chart
Developed a program application in the language
Python. As a result of the software application, the
structure of knowledge-oriented base (Fig. 5) is deter-
mined.
Fig. 5. Python program realisation
Thus, the proposed comprehensive entropy-synergy
analysis of the determination of the state “the investi-
gated system the environment” and changes in the
consequence of process transformations in systemic
objects in conditions of certain uncertainty does not
require additional research, characteristic of known
estimates for the criteria in widespread mathematical
means decision-making; Data processing results are
invariant with respect to the data processing method, in
accordance with reality, while using known means of
criterion evaluation of environmental protection level,
the result depends on the analytical method and subjec-
tive experiences of the researcher.
CONCLUSIONS
1. In the article substantiated the expediency of in-
troducing the basics of systemological analysis in mod-
eling and structuring of studies of complex objects,
which allows to establish conditions for the implemen-
tation of a certain target function, which is responsible
for the state and functionality of the investigated object
in certain conditions of the environment, taking into
account the macrostate of the complex system, through
experiments of microstates, and its changes in the sys-
tem “object – the environment” regarding the state of
external systems ∆Sy
1,2,3
(see Fig. 2) using an entropy
function according to a consistent analysis of uncertain-
ties and their solution to establish conditions for the
stabilization of the object or achieve the goal of regula-
tion situations based on information synergetics.
2. An example of a solution of problematic issues to
stabilize the state of impaired soil pollution under cer-
tain conditions for probabilistic entropy, obtaining in-
formation on the safety probability of this situation in
the implementation of synergistic effects of self-
cleaning, and thus solving the issues of environmental
friendliness of the functioning of natural-territorial ob-
jects socioeconomic purpose (see Figs. 3-6).
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Article received 07.02.2022
ВИКОРИСТАННЯ СИСТЕМНО-ЛОГІЧНОЇ ОСНОВИ ТА ФУНКЦІЇ
ІНФОРМАЦІЙНОЇ ЕНТРОПІЇ ПРИ ДОСЛІДЖЕННІ
В УМОВАХ НЕВИЗНАЧЕНОСТІ СИСТЕМНО-СТРУКТУРОВАНИХ ОБ’ЄКТІВ
Т.В. Козуля, М.М. Козуля
Розглянуто доцільність впровадження основ системного аналізу в моделюванні та структуруванні
досліджень складних об’єктів, що дозволяє встановлювати умови для здійснення певної цільової функції,
яка відповідає за стан та функціональність досліджуваного об’єкта в певних умовах навколишнього
середовища, з урахуванням макростану складної системи, через експерименти мікростанів, та його зміни в
системі «об’єкт навколишнє середовище» щодо стану зовнішніх систем за допомогою функції ентропії
відповідно до послідовного аналізу невизначеності і їх вирішення встановленням умов для стабілізації
об’єкта або досягнення мети ситуацій регулювання на основі інформаційної синергетики. Було зроблено
висновок, що запропонований комплексний аналіз ентропійно-синергетиного визначення стану
«досліджувана системи навколишнє середовище» та зміни внаслідок процесів трансформацій у системних
об’єктах в умовах певної невизначеності не вимагає додаткових досліджень, характеристик для відомих
oцінок для критеріїв у поширених математичних засобах прийняття рішень.
ИСПОЛЬЗОВАНИЕ СИСТЕМНО-ЛОГИЧЕСКОЙ ОСНОВЫ И ФУНКЦИИ
ИНФОРМАЦИОННОЙ ЭНТРОПИИ ПРИ ИССЛЕДОВАНИИ
В УСЛОВИЯХ НЕОПРЕДЕЛЕННОСТИ СИСТЕМНО-СТРУКТУРИРОВАННЫХ ОБЪЕКТОВ
Т.В. Козуля, М.М. Козуля
Рассмотрена целесообразность внедрения основ системного анализа в моделировании и
структурировании исследований сложных объектов, что позволяет устанавливать условия для
осуществления определенной целевой функции, которая отвечает за состояние и функциональность
исследуемого объекта в определенных условиях окружающей среды, с учетом макросостояния сложной
системы, через эксперименты микросостояний, и его изменения в системе «объект окружающая середа»
по состоянию внешних систем с помощью функции энтропии в соответствии с последовательным анализом
неопределенности и их решения определения условий для стабилизации объекта или достижения цели
ситуаций регулирования на основе информационной синергетики. Был сделан вывод, что предложенный
комплексный анализ энтропийно-синергетического определения состояния «исследуемая система
окружающая среда» и изменения вследствии процессов трансформаций в системных объектах в условиях
некоторой неопределенности не требует дополнительных исследований, характерных для известной oценки
критериев в распространенных математических методов принятия решений.
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