Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів
The model of information support estimation of the decision maker (DM) based on a study of qualitative indicators of informedness, which characterizes the completeness, accuracy and timeliness of DM informedness , is presented. On the basis of these characteristics the level of danger situations in...
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| author | Pankratova, Nataliya D. Slota, M. R. |
| author_facet | Pankratova, Nataliya D. Slota, M. R. |
| author_institution_txt_mv | [
{
"author": "Nataliya D. Pankratova",
"institution": "The Institute for Applied System Analysis at the Igor Sikorsky Kyiv Polytechnic Institute, Kyiv"
},
{
"author": "M. R. Slota",
"institution": "The Institute for Applied System Analysis at the Igor Sikorsky Kyiv Polytechnic Institute."
}
] |
| author_sort | Pankratova, Nataliya D. |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2018-03-30T15:25:34Z |
| description | The model of information support estimation of the decision maker (DM) based on a study of qualitative indicators of informedness, which characterizes the completeness, accuracy and timeliness of DM informedness , is presented. On the basis of these characteristics the level of danger situations in the operation of complex objects is formed. In implementing the model are used the methods of one-parameter classification with operations of fuzzy sets and strong intersections, as well as methods of interval classification with the operations of union and intersection of fuzzy sets, and also with operations of strong union and intersection of fuzzy sets. The proposed methods allow classifying the situation to inform DM about the validity and security of the decision with the available information support. The proposed model is based on a study of qualitative characteristics of informedness of DM and can be used to estimate the level of danger situations in the problems of the complex objects operation. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2017.1.01 |
| first_indexed | 2025-07-17T10:20:55Z |
| format | Article |
| fulltext |
© N.D. Pankratova, M.R. Slota, 2017
Системні дослідження та інформаційні технології, 2017, № 1 7
TIДC
ТЕОРЕТИЧНІ ТА ПРИКЛАДНІ ПРОБЛЕМИ
І МЕТОДИ СИСТЕМНОГО АНАЛІЗУ
УДК 517.9, 519.816
DOI: 10.20535/SRIT.2308-8893.2017.1.01
MODEL OF THE LEVEL ESTIMATION OF DANGER
SITUATIONS IN THE PROBLEMS OF COMPLEX OBJECTS
OPERATION
N.D. PANKRATOVA, M.R. SLOTA
Abstract. The model of information support estimation of the decision maker (DM)
based on a study of qualitative indicators of informedness, which characterizes the
completeness, accuracy and timeliness of DM informedness , is presented. On the
basis of these characteristics the level of danger situations in the operation of com-
plex objects is formed. In implementing the model are used the methods of one-
parameter classification with operations of fuzzy sets and strong intersections, as
well as methods of interval classification with the operations of union and intersec-
tion of fuzzy sets, and also with operations of strong union and intersection of fuzzy
sets. The proposed methods allow classifying the situation to inform DM about the
validity and security of the decision with the available information support. The
proposed model is based on a study of qualitative characteristics of informedness of
DM and can be used to estimate the level of danger situations in the problems of the
complex objects operation.
Keywords information analysis, qualitative characteristics of informedness, classifi-
cation, recognition, danger level, integrated indicator of informedness.
INTRODUCTION
Reality constantly requires of reasonable administrative decisions, such as im-
plementation of innovative technologies, companies moving to the new markets,
complex technical systems management, and the solution of complex social is-
sues. Decision making — generally speaking, is the result of the intellectual
activity based on the specific information, their experience, knowledge and intui-
tion that allows decision-makers move to a certain conclusion on the way to the
necessary actions. Well-grounded decision should be aimed at achieving the de-
sired results in a certain field.
Modern technologies has greatly facilitated and improved the process of
forming solutions. Nowadays, there are numerous tools and software products
that are based on mathematical modeling, forecasting, prediction, which allow to
form effective management decisions. However, analysis of the global crashes
and disasters that have taken place over the past decades shows that the scale of
the losses can be substantially reduced due to the timely formation and realization
N.D. Pankratova, M.R. Slota
ISSN 1681–6048 System Research & Information Technologies, 2017, № 1 8
of the rational solutions in the emergency and critical situations. The key problem
is the timely and reliable information support of decision-makers.
Information analysis is a vital tool for formalization and solving of system
problems. Its objectives are to ensure of the necessary and technologically possi-
ble level of information support reliability and validity of the decision on applied
systems tasks, and this is an important tool for decision-makers support and the
process of decision. The issue of data analysis is quite relevant in our time and
therefore many scientists around the world bring variations of their problem vi-
sion and mathematical formulations for effective solutions that have long been
set, but still haven’t completely solved tasks.
The main feature of the existing approaches and methods is that they are fo-
cused primarily on evaluation the amount of data only. But practically data of
quality indicators, such as completeness, reliability, timeliness, and several others
are not estimated. At the same time validity and the effectiveness of the applica-
tion system tasks solutions directly depend not only on the quantity of informa-
tion, but also on its qualitative characteristics [1].
Several authors have focused their attention on the analysis of the qualitative
characteristics of a specific information type, in particular the financial [2–4].
Some researchers have suggested methods for converting qualitative characteris-
tics into quantitative. And, as a consequence, processing of these characteristics is
made via usual for mathematicians methods [5, 6].
Development of American scientists in this direction aimed at the financial
sector and focused on the development of useful and interesting for large financial
corporations methods. For instance, the paper [4] contains some interesting ideas
about the formalization process of the selections phase of useful information for
the formation of an investment portfolio. The paper presents not only theoretical
knowledge, but also the general mathematical formulation and results of re-
searches. The authors also provided the main advantages and disadvantages of
proposed methodologies and how business can be developed using the efficiency
of their activities.
In the papers the questions of informational analysis from the perspective of
decision-maker’s study of the quantitative and qualitative characteristics of in-
formation, evaluation of their impact on the accuracy, completeness and timeli-
ness of systemic task solution were considered [8–10].
In this article, we consider the model of information support evaluation of
decision-makers that is based on qualitative indicators of their informedness, on
the basis of which the level of situation danger is formed and the decision-making
procedure is provided.
PECULIARITIES OF THE TASKS CLASSIFICATION AND CRITICAL
SITUATION RECOGNITION IN THE INFORMATION ANALYSIS
Taking into account the construction of a general theory of the mathematical
model and analysis of information, we define key features in the formulation the
problem of the situations recognitions and its classification.
In general, tasks that are under consideration in model assessment of deci-
sion-maker’s information support are also similar to a conventional pattern of
Model of assessment the level of danger situations in the tasks of functioning of complex objects
Системні дослідження та інформаційні технології, 2017, № 1 9
tasks recognition, including many mathematical classification methods. Each sit-
uation from the variety of object recognition, as well as image, may be classified
according to certain set of attributes for a specific class. The main goal is to build
such a rule (functional), which allows to classify objects of observation with the
lowest possible error.
However, within the framework of the system approach there are additional
conditions which are not considered in the conventional pattern recognition tasks.
There are some of the most essential.
1. Analysis of qualitative characteristics of information substantially de-
pends on the subject area and so each application is unique in its own way and
will require an individual approach to its formalization.
2. In the process of analysis and classification there is no guarantee of the
input data completeness.
3. Formation of the qualitative characteristics of information often has a
fuzzy character.
4. Unlimited space recognition features significantly complicates the process
of situations classification.
5. Because of the lack of criteria for assessing the critical situation there are
some difficulties with error estimation of constructed models.
Therefore, to solve such tasks it’s advisable to use a set of new models,
methods, techniques to determine the level of result consistency. Also, it is worth
considering the fact that the analysis of the qualitative characteristics of informa-
tion involves the development of methods for the transformation of these charac-
teristics in the numerical equivalents. These methods should be integrated into the
general mathematical model of system tasks, as shown in [8].
Based on the characteristics of the above we formulate the most important
requirements for the models and methods that can be applied to tasks of classifi-
cation and recognition level of danger situations.
1. Consideration of the fuzziness and incompleteness of the initial information.
2. Focusing on the processing of large quantities of data in real time.
3. Performance of methods to ensure the timely formation of the results.
4. The lack of standard training sample in the form of a finite set of data
about the characteristics of each class of the accepted classification is determined
by the principal unbounded feature space.
The concept of informedness is important for the analysis of information
support of decision-makers [8]. Under the informedness of decision-makers will
understand the change in the level of uncertainty of knowledge about a situation
or object of analysis as a result of receiving information. The level of informed-
ness of decision-makers is an indicator of the knowledge level about the subject
of analysis or research. Quantitatively, awareness of decision-makers will be
characterized by the magnitude of the level of uncertainty resulting from the
changes of knowledge information. Pay attention to the fundamentally important
factor: with receiving information knowledge level of uncertainty can be reduced,
if the information is accurate, but it may also increase if the information is inten-
tionally distorted (i.e. received misinformation) or invalid (i.e. not confirmed by
experience calculations, documents or otherwise), or contrary to the available in-
formation.
N.D. Pankratova, M.R. Slota
ISSN 1681–6048 System Research & Information Technologies, 2017, № 1 10
The level of uncertainty of knowledge may be evaluated on the basis of dif-
ferent approaches. In particular, it can be estimated on the basis of the adaptation
of quantitative methods described in [1, 5] or using the methods [10].
Let us note only the most essential qualitative properties of information,
which are fundamentally important in solving problems of systems analysis, in
particular, problems of estimation of the degree and level of risk in normal,
abnormal, and critical situations. Among these properties are uncertainty,
inaccuracy, incompleteness, fuzziness, untimeliness, noncredibility, and
contradictoriness. It is evident that the formed decision should have the required
level of quality and efficiency. For this, during its formation, it is necessary both
to provide appropriate levels of completeness, reliability and timeliness of
informedness of the situation in order to minimize the extent and level of risk.
Determining the most important features from the perspective of decision-makers,
in systems analysis are completeness, reliability and timeliness. Therefore, the
qualitative characteristics of decision-makers awareness will determine the
following properties [8]:
Completeness of informedness is a property that characterizes the conformity
of the quantity of information received by a decision maker to the quantity of
information required for decision making.
Timeliness of informedness is a property that determines the conformity of a
decision maker’s time resource for forming and making decisions to the time
resource from the moment of receiving information to the moment of solution
realization.
Credibility of informedness is a property that characterizes the conformity of
the information received by a decision maker to the actual state of the situation.
It should be noted that the results of the solution of system tasks are directly
dependent on the level of decision makers informedness (DMI).
In this case, proceed as follows [9].
1. Form indicators of completeness NI , timeliness TI , and credibility CI of
decision makers informedness, that will take into account the degree and the level
of influence of each of the input parameters on the degree of the decision-maker’s
objectives achievement.
2. Offer the classification of a given set of situations 0S according to a sin-
gle system of interrelated indicators CTN III ,, or according to a single integrated
indicator of DMI.
3. To develop techniques and procedures of the specific situation recogni-
tion supplies KS from a given set of situations 0S to a certain class of objects to
the introduced classification.
When forming the general level of DMI the specific properties and intro-
duced indicator’s features CTN III ,, should be taken into account. Here are the
most important properties of these indicators:
• the level of DMI is growing continuously from the increasing of all of the
indicators CTN III ,, or from one of it;
• if the level of general DMI increases in its completeness, credibility and
timeliness it changes according to non-linear law, in particular: the growth of
DMI level gradually slows down as it approaches completeness of performance
and credibility to their limits (Figure);
Model of assessment the level of danger situations in the tasks of functioning of complex objects
Системні дослідження та інформаційні технології, 2017, № 1 11
• the level of DMI of the integral index in case of reducing the value of a
private performance below a certain threshold value cannot be compensated by
increasing the values of other indicators;
• with zero meaning of any of the indicators CTN III ,, general level of
DMI of the integral index is also zero.
During the solution formation, which starts at the moment 0== fntt and
ends at the moment crtt = , the
additional information is re-
ceived, and this leads to an
increase in the completeness,
credibility and the amount of
information. It follows that the
completeness and credibility
indicators CN II , in general are
the increasing functions of time.
However, for the indicator of
timeliness TI the dependence is
qualitatively different, due to the
tight interrelation since the end
of the formation of decision and
the moment of its implementa-
tion. Given the fact that the time
realization is fixed and it is
determined by external factors, it
is possible to state that the index of timeliness is a decreasing function of time [8].
From the above it follows that there is a contradiction between the level of
completeness and credibility of DMI on the one hand, and the level of timeliness
on the other. Therefore practically important task is to find a rational compromise
between the levels CTN III ,, in the process of decision formation taking into ac-
count the requirements of the reduction of time during its formation. To solve this
task it is needed to take into account the dependence CTN III ,, from time that is
to put )(),(),( tIItIItII CCTTNN === .
The functional dependence of the parameters is determined for variety of sit-
uations 0S . It is more convenient to represent this relationship in the form of pol-
ynomials. Firstly, it makes it possible to determine the polynomial coefficients by
usage of known techniques of interpolation, and secondly, according to the theo-
rem of Weierstrass any continuous function polynomial can be approximated by
polynomial with any desired accuracy. Therefore, hereinafter:
∑
=
=
CN
k
kCC tatI
0
)( (1)
∑
=
=
NN
k
kNN tatI
0
)( . (2)
∑
=
=
TN
k
kTT tatI
0
)( . (3)
Distribution of qualitative characteristics of
awareness
qI TI NI
CI
crt t
N.D. Pankratova, M.R. Slota
ISSN 1681–6048 System Research & Information Technologies, 2017, № 1 12
THE CONSTRUCTION OF THE MODEL FOR DETERMINING
THE RISK SITUATION
Construction of the task solution model for the classification and determination of
the danger level of the situation involves the following steps.
Step 1. Classification of hazard classes of possible situations and the defini-
tion of a set of risk factors. Depending on the subject area and the specific appli-
cation task the first stage it is necessary to carry out procedures that will imple-
ment the peculiarities of the classification. First of all, we need to create classes
on the level of danger of the critical situations that denote the variety
}..1,{ Kkk =ω=Ω . (4)
Each class of danger should be characterized by a certain criterion in the
form of membership function. Universal set is determined. Most often, the uni-
versal set Х is defined by time interval ],0[ crT , where crT is the time of decision
making. After this point of time even the most reliable information is of no value.
During the system operation there is an influence of its sets of uncontrollable
risk factors
}...1|{ mjj =Φ=Φ . (5)
The final step for the first stage is to define a set of situations
}...1|{ niSS i == . (6)
Each situation iS from the variety (6) under the influence of risk factors (5)
may move to a different danger class kω (4). Such change may occur over a pe-
riod of time, and its duration is unknown a priori, and that depends on the amount
and duration of exposure properties Φ∈Φ j .
It is necessary to define a valid period of time 0T for the formation and im-
plementation of solutions for which the probability of a transition situation iS in
one of the danger classes (4) will not exceed the predetermined value adη=η .
Step 2. The construction of a situational factor grid of connections and
influences. By situational factor grid will mean:
]1;0[: ⎯→⎯×Φ SA . (7)
Where Φ is a multiple risk factors Φ∈Φ j (5), S is a set of situations of
DMI Ssi ∈ (6).
Since the sets (5) and (6) are finite, mapping (7) can be set in the form of a
matrix nmA ×|| , which elements are Boolean variables that are showing the effect
of risk factors jΦ on situation iS .
Step 3. Definition of private indicators for situational informedness-factorial
components. The definition and formation of private indicators informedness fun-
damentally are not formalized for arbitrary domains. Each task requires an indi-
vidual approach, as input data, which is owned by the decision-maker may
Model of assessment the level of danger situations in the tasks of functioning of complex objects
Системні дослідження та інформаційні технології, 2017, № 1 13
have a different specificity and semantic foundation that significantly affect the
determination of the level of awareness of DMI. In addition, specific tasks may
include an analysis of additional indicators of private DMI except imposed (1)–
(3). This step is a separate task of information analysis and requires the usage of
additional mechanisms.
Later on we shall assume that for each situational factor component of the
vector of private DMI indicators in the form of (1)–(3).
Step 4. Determining the danger level of current situation. The danger level
of the current situation Ssi ∈ is characterized by the vector of private DMI indi-
cators and risk factors. Denote )(tI ij
C is the indicator of the completeness of DMI
of the i-th situation under the influence of the risk factor j. Similarly )(tI ij
N is the
reliability indicator of DMI and )(tI ij
T is the timeliness indicator of DMI. The
transition probability of the situation iS under the influence of factor Φ∈Φ j in
danger class Ω∈ωk depends from the change in time completeness )(tI ij
C , credi-
bility )(tI ij
N and timeliness )(tI ij
T of DMI. The probability ijη of such event de-
termines the following ratio
))(1(lg1 tIa ijijij +−=η ,
)()()()( tItItItI TNCij = .
To make a decision, it is needed to find a rational compromise between the
levels )(),(),( tItItI TNC to reduce the time for its formulation and implementa-
tion. Indicators of completeness )(tI ij
N and credibility )(tI ij
C of DMI grow with
time. Along with the increased time of risk exposure level Φ∈Φ j the level of
timeliness DMI reduces )(tI ij
T according to its properties. And, as a consequence,
the length of formation time, acceptance and implementation of solutions is re-
ducing, to prevent transition of the researched situation in one of the danger clas-
ses Ω∈ωk (4).
As a result, to determine the danger level of the situation, it is necessary to
define the acceptable time resource in a period ],;[ 210 TTT = XT ∈0 , where X is
the universal set. For this the following inequality is solved
adij tI η≤+−≤ ))(1(lg10 . (8)
Step 5. Classification of the situations in accordance with the imposed dan-
ger classes. At this stage it is necessary to formalize a fuzzy classification of the
situation, considering the previous step of acceptable time resource or the imple-
mentation of solutions.
At the universal set X for each danger class Ω, the fuzzy characteristics are
introduced Xxxk ∈μ ),( in the form of membership functions for Ω∈ωk .
The general approach to the classification of situations can be described by
an algorithm that consists of three basic steps:
N.D. Pankratova, M.R. Slota
ISSN 1681–6048 System Research & Information Technologies, 2017, № 1 14
Step 1. The fuzzification of the input parameters.
Step 2. Fuzzy composition of situational factor components.
Step 3. Defuzzification of internal parameters and outputs activation.
The first step involves the classification of fuzzification, what is the reduc-
tion to fuzziness of input parameters, namely resource of the acceptable time 0T .
After fuzzification the vector of affiliation degrees:
KkTkk ..1),( 0 =μ=μ ,
to danger classes (4) are be obtained.
The second step is to assess the impact of each risk factor Φ∈Φ j on situa-
tion Ssi ∈ and the formation of average or maximum rate, which is transmitted
to the next stage (the input of the activation function) to activate the exit. In the
offered model this process is called a process of internal factor of the composition
(or convolution).
For composition, is possible to use the operations defined on fuzzy sets.
Given peculiarity of the process, the most consistent operation will be at the in-
tersection of attitude fuzzy sets [11]. In this case analysis of the results will
also include the ratio of the strong intersection. As a result we get a set of convo-
lution ikμ .
This stage has a great deal of flexibility, as there are many options for setting
fuzzy relation on the set of parameters for the composition.
There is the union of fuzzy sets of A and B with the following membership
function
}),(),({max)( Xxxxx BAC ∈μμ=μ . (9)
The strong union of fuzzy sets of A and B with membership function is used
⎩
⎨
⎧
≥μ+μ
<μ+μμ+μ
=μ
.1)()(,1
,1)()(),()(
)(
xxif
xxifxx
x
BA
BABA
C (10)
The intersection of fuzzy sets of A and B with membership function is used
}),(),({min)( Xxxxx BAC ∈μμ=μ . (11)
Strong intersection of fuzzy sets of A and B with membership function in the
following form is applied
Xxxxx BAC ∈μ⋅μ=μ ),()()( . (12)
For activation of the output it is necessary to set parameters ikμ via activa-
tion function for each kω .
As the function of activation will take the Heaviside function
⎩
⎨
⎧
η≥
η<
=ρ
,,1
,,0
)(
max
max
i
i
x
x
x where }{maxmax ikki
μ=η . (13)
Danger class (4), to which corresponds the value of the function (13) 1=ρ is
model’s output parameter.
As a part of the proposed classification methodology we can identify two
classification algorithms.
Model of assessment the level of danger situations in the tasks of functioning of complex objects
Системні дослідження та інформаційні технології, 2017, № 1 15
Simpler algorithm is a one–parameter classification of situations. For the en-
trance to the classification one parameter is supplied. According to the general
model of tasks solving, in the early stages for each danger class (4) a personal
membership function is formed. The set of functions is received
}..1|]1;0[:{ KkXI k =⎯→⎯μ= , where ||Ω=K . (14)
Often for this type of classification as the only parameter is taken the length
of time interval, that is the time which the decision-maker has for solution forma-
tion and implementation.
Another algorithm is the interval classification of situations. This algorithm
takes into account the situation that can be characterized by a vector of intervals
that are obtained by solving the inequality (8). Interval classification of situations,
according to the general model, is includes three steps. If the interval is described
with beginning and the end, that is two-dimensional case for (14). We describe
the input parameter by ratio
];[},..1,..1,..1|{ +−===== ijlijlijlijl TTTLlmjniTT .
After fuzzification step and finding the )( ijlkijlk TT μ= the following parame-
ters are determined
−− = ijkl
l
ijk TT min ,
++ = ijkl
l
ijk TT max .
Further, in accordance with the general model for solving problems, the
fuzzy relations (9)–(12) are used. In result we get a vector of intervals ],[ +−
ikik TT .
These values are passed to input of the activation function (13).
The method of classifying interval takes into account subjective assessment
of the membership function which is not only a resource of time, but also other
factors such as the desired time of the beginning of formation of a decision or
a planned time of solutions realization. This method, as well as the previous one,
include several variations and allow adjusting the classification logic of the spe-
cifics of the task.
EVALUATION OF DANGER LEVEL OF SITUATIONS DURING POWER
TURBOGENETATOR OPERATIONS
The use of the proposed model is considered on the example of the classification
system task, recognition and prevention of critical and catastrophic situation func-
tioning turbine generator power. There were determined the set of risk factors and
situations.
Risk factors are }6...1|{ =Φ=Φ jj :
• decrease of the frequency to 49,7 Hz;
• increase of the frequency to 50,1 Hz;
• erroneous actions of the operating personnel;
• the failure of emergency control;
• natural phenomena;
N.D. Pankratova, M.R. Slota
ISSN 1681–6048 System Research & Information Technologies, 2017, № 1 16
• emergency shutdown of high power.
Situations are }4..1|{ == iSS i :
• changing Power Electric;
• transfer Power Electric units on its sources;
• asynchronous Power Electric mode;
• separation of the power systems into parts.
For this task, a lot of danger classes has been formed as follows:
},..,{ 41 ωω=Ω :
1ω —secure situation;
2ω — critical situation;
3ω — emergency;
4ω — catastrophic situation.
For the problem of recognition and prevention of critical and catastrophic
situations on the example of the functioning of turbine generator power is
impossible to form the training set as a finite set of data, so analysis methods will
use the methods of matching results. Other words, we will classify the critical
situation.
For the study (8) the parameter adη has changed in range of [0,5; 0,95].
Also, there were observed fluctuations in the result of the classification after
changing the type of membership function and its settings.
It should be noted that the four classification algorithms were implemented
in the study. The first two are variations of the one-parameter classification
method, while the other two are the methods of interval classification. Next, the
following definitions are accepted:
M1 is a one-parameter classification methods with the operation of the
intersection of fuzzy sets;
M2 is a one-parameter classification method with the operation of a strong
crossing;
M3 is a method of interval classification with the operations of union and
intersection of fuzzy sets;
M4 is a method of interval classification with the operations of a strong
union and intersection of fuzzy sets.
The first stage of the analysis was to study the results with fixed parameters
and types of phase transitions and changes. This step allowed to determine
whether results are consistent with the classification of the real situation. With
increase of adη the time on the formation and implementation of solutions
reduces, therefore, must increase the danger of the situation. Aggregated results
for all methods in the fixed parameters of membership function are given in Table 1.
T a b l e 1 Classification results of the change adη
adη
M
0,5 0,6 0,7 0,8 0,9 0,95
M1 1ω 1ω 1ω 2ω 2ω 2ω
M2 1ω 1ω 1ω 2ω 2ω 3ω
M3 1ω 1ω 2ω 2ω 3ω 3ω
M4 1ω 1ω 2ω 3ω 3ω 3ω
Model of assessment the level of danger situations in the tasks of functioning of complex objects
Системні дослідження та інформаційні технології, 2017, № 1 17
All the methods are responding on increasing of the value access adη . How-
ever, as follows from the results above, methods of interval classifications are
more sensitive.
The second stage of the study was application of a sensitivity analysis meth-
ods to the membership function type. Worth noting that the various membership
functions have a number of excellent options, and therefore a change of the mem-
bership function requires a small adjustment of the dispersion parameter. At this
stage, there was a slight change in the classification of the results, especially for
large values adη . Summary results in Table 2 reflect these changes.
T a b l e 2 . The study of the classification sensitivity according to the type of
membership function
M
M1 M2 M3 M4
adη MF
0,5 0,8 0,95 0,5 0,8 0,95 0,5 0,8 0,95 0,5 0,8 0,95
Triangular MF 1ω 2ω 2ω 1ω 2ω 3ω 1ω 3ω 3ω 1ω 3ω 3ω
Gaussian MF 1ω 2ω 2ω 1ω 2ω 2ω 1ω 2ω 3ω 1ω 2ω 3ω
Bell-MF 1ω 2ω 3ω 1ω 2ω 3ω 1ω 2ω 3ω 1ω 2ω 3ω
Also, an analysis of classification sensitivity to a change of membership
function parameters of the fixed type took place. It has been studied how changes
the result of classification of the situation at a constant level of information sup-
port of decision-makers, if the informedness requirements changes. Of course, the
change of the criteria of danger class should significantly affect the classification.
Results of the study are shown in Table 3 for cases of selecting a permanent form
of membership function — Gaussian MF. At the same time the variance 2σ and
mathematical expectation of a for danger classes 2ω , 3ω and its 1ω , 4ω . Four
sets of parameter were used for each danger class.
T a b l e 3 . Parameters of Gaussian membership function
iω
1ω 2ω 3ω 4ω N
a 2σ a 2σ a 2σ a 2σ
1 0 10 20 20 60 20 100 10
2 0 20 40 20 70 15 100 20
3 0 20 50 10 50 30 100 15
4 0 50 50 10 75 10 100 25
The results of the application of these four methods for fixing 7,0=ηad and
different set of Gaussian parameters of membership function (from table 3, sets
1–4) are shown in Table 4. The right selection of parameters is one of the most
important steps for effective and correct classification. It is important to create the
requirements for danger classes as fuzzy marks from which, actually, the relevant
membership functions are formed.
N.D. Pankratova, M.R. Slota
ISSN 1681–6048 System Research & Information Technologies, 2017, № 1 18
T a b l e 4 . The effect of the membership functions of the classification results
N M1 M2 M3 M4
1 2ω 2ω 2ω 2ω
2 2ω 2ω 2ω 2ω
3 2ω 3ω 3ω 3ω
4 1ω 1ω 1ω 2ω
From the results shown in Table 2 and Table 4 we can summarize that the
selection of the membership function parameters significantly affects the
classification results. Note, that this process is fundamentally non-formalized, and
therefore the task of correct choice of membership function depends on the
intuition and experience of the investigator.
Also it has been proposed to determine the overall risk assessment for all
situations is (6). In the proposed task were allocated 4 independent situations.
Therefore, an overall assessment can be formed by an absolute majority. It was
found that in most cases the algorithm gave consistent results. Table 5 shows the
results in the form nm / , where m is the number of consistent results, 16=n the
total number of situations. For this experiment were selected from membership
function with the first set of parameters from Table 3.
T a b l e 5 . Consistency of assessment classification
MF/( nm / ) 0,5 0,8 0,95
Triangular MF
16
14
16
13
16
11
Gaussian MF
16
14
16
12
16
12
Bell-MF
16
13
16
14
16
12
Thus, the proposed model has been applied to solve the systemic problems
of classification and identification of critical and catastrophic situations, operation
of turbo generator plant. The research was conducted on the basis of DMI figures
about the functioning of the turbine generator. Classification results showed the
effectiveness of the quality DMI of analysis methods for complex danger
detection task situations. It can be concluded that the classification of the result
depends essentially on the correct choice of the type of membership function and
internal parameters. This process is essentially non-formalized and or this reason
the problem of correct choice of membership function depends on the intuition
and experience of the decision-maker.
CONCLUSIONS
The problem of classification and recognition of the danger level of critical situa-
tions, which is important for the formation of the necessary and technologically
possible level of information to ensure the reliability and validity of the decision
of applied system tasks, was under the consideration. The paper presents model of
classification and the danger level of the situation recognition, as a part of a sys-
tem methodology.
Model of assessment the level of danger situations in the tasks of functioning of complex objects
Системні дослідження та інформаційні технології, 2017, № 1 19
Considering the features of the tasks of qualitative information analysis,
traditional methods of classification and pattern recognition cannot be applied in
this field. So, a classification model and recognition of critical situations, which is
fully compatible with the general theory of information analysis, were proposed.
The model is based on an analysis of private decision-maker’s indicators of in-
formedness, defined as a function of time. On the basis of these qualitative
characteristics the danger level of the situation is formed, that is, how balanced,
rational and appropriate the solutions will be based on available information. In
case of poor informedness indicators, decision-maker will be notified that a
decision is taken at the existing information support is undesirable or even
dangerous. The proposed methods allow classifying the situation for reporting it
to decision-maker about validity and safety of a decision with the available
information support.
Analysis of the results of classification on the example of the real task
revealed the strengths and weaknesses of the proposed model and algorithms of
its realization. It was revealed that the classification algorithms are sensitive to
fluctuations in the parameters of membership function and essentially depend on
the particular application.
The proposed model of classification and recognition of dangerous situations
in tasks of informational analysis may be applied in conditions of incompleteness
and fuzziness of the initial information, when taken into account expert
assessment, as well as the presence of a certain amount of data in the domain
that is being investigated.
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Received 12.11.2016
From the Editorial Board: the article corresponds completely to submitted manuscript.
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| id | journaliasakpiua-article-101629 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:20:55Z |
| publishDate | 2017 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/72/dc06406521f460aa4e5783702c0b6672.pdf |
| spelling | journaliasakpiua-article-1016292018-03-30T15:25:34Z Model of the level estimation of danger situations in the problems of complex objects operation Модель оценивания уровня опасности ситуаций в задачах функционирования сложных объектов Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів Pankratova, Nataliya D. Slota, M. R. information analysis qualitative characteristics of informedness classification recognition danger level integrated indicator of informedness информационный анализ качественные характеристики информированности ЛПР классификация распознавание уровень опасности интегральный показатель информированности інформаційний аналіз якісні характеристики інформованості ОПР класифікація розпізнавання рівень небезпеки інтегральний показник інформованості The model of information support estimation of the decision maker (DM) based on a study of qualitative indicators of informedness, which characterizes the completeness, accuracy and timeliness of DM informedness , is presented. On the basis of these characteristics the level of danger situations in the operation of complex objects is formed. In implementing the model are used the methods of one-parameter classification with operations of fuzzy sets and strong intersections, as well as methods of interval classification with the operations of union and intersection of fuzzy sets, and also with operations of strong union and intersection of fuzzy sets. The proposed methods allow classifying the situation to inform DM about the validity and security of the decision with the available information support. The proposed model is based on a study of qualitative characteristics of informedness of DM and can be used to estimate the level of danger situations in the problems of the complex objects operation. Предложена модель оценивания информационного обеспечения лица, принимающего решения (ЛПР), основанная на исследовании качественных показателей информированности: полноты, достоверности и своевременности информированности ЛПР. На основе этих показателей сформирован уровень опасности ситуаций при функционировании сложных объектов. Для реализации модели использовались методы однопараметрической классификации с операциями пересечения нечетких множеств и сильного пересечения, методы интервальной классификации с операциями объединения и пересечения нечетких множеств, а также с операциями сильного объединения и пересечения нечетких множеств. Предложенные методы позволяют классифицировать ситуации для информирования ЛПР об обоснованности и безопасности принятия решения при имеющемся информационном обеспечении. Разработанная модель базируется на исследовании качественных показателей информированности ЛПР и может быть применена для оценивания уровня опасности ситуаций в задачах функционирования сложных объектов. Запропоновано модель оцінювання інформаційного забезпечення особи, що приймає рішення (ОПР), яка ґрунтується на дослідженні якісних показників інформованості: повноти, достовірності та своєчасності інформованості ОПР. На основі цих показників сформовано рівень небезпеки ситуації під час функціонування складних об’єктів. Для реалізації моделі використовувалися методи однопараметричної класифікації з операціями перетину нечітких множин і сильного перетину, методи інтервальної класифікації з операціями об'єднання і перетину нечітких множин, а також з операціями сильного об'єднання і перетину нечітких множин. Запропоновані методи дозволяють класифікувати ситуації для інформування ОПР про обгрунтованість і безпеку прийняття рішення за наявного інформаційного забезпечення. Розроблена модель базується на дослідженні якісних показників інформованості ОПР і може бути застосована для оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2017-03-21 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/101629 10.20535/SRIT.2308-8893.2017.1.01 System research and information technologies; No. 1 (2017); 7-19 Системные исследования и информационные технологии; № 1 (2017); 7-19 Системні дослідження та інформаційні технології; № 1 (2017); 7-19 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/101629/96896 Copyright (c) 2021 System research and information technologies |
| spellingShingle | інформаційний аналіз якісні характеристики інформованості ОПР класифікація розпізнавання рівень небезпеки інтегральний показник інформованості Pankratova, Nataliya D. Slota, M. R. Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| title | Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| title_alt | Model of the level estimation of danger situations in the problems of complex objects operation Модель оценивания уровня опасности ситуаций в задачах функционирования сложных объектов |
| title_full | Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| title_fullStr | Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| title_full_unstemmed | Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| title_short | Модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| title_sort | модель оцінювання рівня небезпеки ситуацій в задачах функціонування складних об'єктів |
| topic | інформаційний аналіз якісні характеристики інформованості ОПР класифікація розпізнавання рівень небезпеки інтегральний показник інформованості |
| topic_facet | information analysis qualitative characteristics of informedness classification recognition danger level integrated indicator of informedness информационный анализ качественные характеристики информированности ЛПР классификация распознавание уровень опасности интегральный показатель информированности інформаційний аналіз якісні характеристики інформованості ОПР класифікація розпізнавання рівень небезпеки інтегральний показник інформованості |
| url | https://journal.iasa.kpi.ua/article/view/101629 |
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