=Paper=
{{Paper
|id=Vol-3126/paper17
|storemode=property
|title=Development of a method for deciding on the distribution of efforts to destroy the air enemy between anti-aircraft missile forces and fighter aircraft
|pdfUrl=https://ceur-ws.org/Vol-3126/paper17.pdf
|volume=Vol-3126
|authors=Pavlenko Maksim,Dmytro Kalinovskiy,Nataliya Garmash
}}
==Development of a method for deciding on the distribution of efforts to destroy the air enemy between anti-aircraft missile forces and fighter aircraft==
https://ceur-ws.org/Vol-3126/paper17.pdf
Development of a Method for Deciding on the Distribution of
Efforts to Destroy the Air Enemy Between Anti-Aircraft Missile
Forces and Fighter Aircraft
Maksim Pavlenko 1, Dmytro Kalinovskiy 2, Nataliya Garmash 3
1,2,3
Ivan Kozhedub Kharkiv National Air Force University, Sumska st. 77/79, Kharkiv, 61023, Ukraine
Abstract
The publication shows the possibility of using the mathematical apparatus of the multicriteria
method of analysis of hierarchies in conjunction with the theory of fuzzy sets, at the stage of
assessing the significance of selected parameters that affect the distribution of forces and means
in accordance with the conditions of the task, during the task. Binary operations of symmetric
difference and drastic sum are used to determine the set of alternatives for the joint use of fighter
aircraft and anti-aircraft missile forces, taking into account the projected loss estimate. The
conducted mathematical apparatus makes it possible to form a set of rules on the basis of which
it is possible to make a decision on the distribution of efforts to destroy the air enemy. Using
the method of analysis of hierarchies at one of the stages uses fuzzy logic to form a measure of
evaluation of the parameters being evaluated, but the end result has an exact value that requires
recalculation when changing at least one of the parameters. Instead, using set theory, namely
the operation of symmetric difference and drastic sum, it is possible to determine the set of
values that forms alternative decision-making depending on the result obtained. That is, the
target that will be in a certain range will be immediately distributed relative to the fighter aircraft
and anti-aircraft missile forces, without recalculating the parameters and their coefficients
relative to each other.
Keywords1
Method of analysis of hierarchies, fuzzy sets, evaluation criterion, symmetric difference, drastic
sum.
1. Introduction number of tasks performed by air defense, namely
[1, 2]:
destruction of enemy air attack means;
The experience of wars and armed conflicts of
gaining and maintaining an advantage in the
the twentieth and twenty-first centuries shows a
air;
significant increase in the use of air strikes [4].
destruction of unmanned aerial vehicles,
The capabilities of air strikes are evolving along
which are used in the conditions of hybrid
with scientific and technological progress, which
warfare, and represent an element of uncertainty
allows them to solve not only tactical but also
for a set of means of automation or automated
strategic tasks. Instead, the use of air defense is
control system and require a clear definition
not only a defense system against air strikes but
(shock or reconnaissance);
also a deterrent, the impact of which is assessed in
cover of important state and military facilities,
the first place. The increase in the number of tasks
their transformation into the national defense
before the means of air attack correlates with the
system of Ukraine;
ISIT 2021: II International Scientific and Practical Conference
«Intellectual Systems and Information Technologies», September
13–19, 2021, Odesa, Ukraine
EMAIL: bpgpma@ukr.net (A. 1); kalinovskyidmytro@gmail.com
(A. 2); garmash.n@ukr.net (A. 3)
ORCID: 0000-0003-3216-1864 (A. 1); 0000-0003-3184-6458 (A.
2); 0000-0002-8840-2797 (A. 3)
©️ 2021 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
increasing the level of combat capability of the (forces) but also an assessment of the relative
Armed Forces of Ukraine and other components losses that can be achieved on the one hand and
of the defense forces with the achievement and on the other, resource indicators and time
maintenance of certain capabilities for fire defeat parameters from analysis of the situation to
of the enemy. completion of the combat mission.
The effectiveness of joint combat use of troops Determine the sequence of calculations using
(forces) in repelling air strikes is achieved by the method of analysis of hierarchies (MAH) [5,
realizing their combat capabilities under the 6, 7], which includes the steps:
condition of coordinated interaction and 1. Selection of troops (forces) of fighter
centralized management, a single automated aircraft and anti-aircraft missile forces in
control system using the decision support system accordance with the existing ones;
(DSS). It is also necessary to take into account the 2. Determination of sets of parameters that
scale, nature of the actions of the means of air characterize certain troops (forces) (tactical and
attack, combat composition, combat capabilities, technical capabilities; time of readiness to
weather and geographical conditions. perform the task; means of destruction used;
The decision on the distribution of efforts in training of personnel; preparation for re-use;
the destruction of air between the anti-aircraft others);
missile forces and fighter aircraft is made by the 3. The choice of quality indicators that are
decision-maker on the basis of proposed compared (quality indicators in turn can be both
alternative solutions to DSS. However, the local and global, which directly affects the priority
decision-maker will use the received of the parameter);
recommendations only if he trusts this system, 4. Calculation of the generalized criterion
and his trust can be built on the degree of validity (global assessment for each fighter or anti-aircraft
of the recommendations. missile system, fighter aircraft and anti-aircraft
Therefore, at present, the question of choosing missile forces in general relative to others).
a mathematical decision-making apparatus Since MAН is based on estimates of the degree
remains relevant, with the possibility of of influence of lower hierarchy factors on the
explaining the recommendations in DSS, which criteria and indicators of higher levels of the
provides proposals for the distribution of efforts hierarchy, we assume that the more factors and
in the destruction of air strikes between anti- indicators will be taken into account, the more
aircraft missiles and fighter aircraft. accurate the final result will be. On the other hand,
the assessment of the significance of some
2. The main part parameters may be insignificant in comparison
with other estimates of parameters, which implies
the effect of insignificance of the selected
The distribution of efforts is carried out in
parameters, which will give a negligible
order to achieve the maximum effect in the advantage to the parameters that should not be
destruction of air attack means by joint efforts, as considered at all.
well as to ensure the safety of their aircraft. Given To select the optimal grouping of troops
the fact that anti-aircraft missile forces can be (forces) that will be tasked, we use the algorithm
used for ground (surface) purposes, it follows that of expert assessment of the impact of the
the scope is common. characteristics of complex technical systems on
Depending on the combat capabilities and the quality indicators, proposed by T. Saaty using a
nature of the tasks to be solved, fighter aircraft and nine-point scale for comparing alternatives
anti-aircraft missile forces share efforts: Tab. 1. However, this measure of comparison is
in space (in directions, boundaries, not a dogma and, if necessary, it is possible to use
areas, strips, sectors, zones, altitudes); your own.
by time; If several experts take part in the assessment,
method of performing the task [3]. the assessment is agreed by consensus, or each
The distribution of goals according to the expert builds his own table, and the estimates are
forces that must be allocated for their destruction presented as geometric averages.
is carried out by the decision-maker from a It is important to emphasize the importance of
particular point of control. To make such choosing the right priorities, because in the case
decisions requires not only a preliminary of a gross mistake, the priority may not be
assessment of the conditions of use of troops important, but important will be ignored, which
will lead to the accumulation of error or even error reliability, as well as take into account possible
and making the wrong decision. Therefore, for a errors.
more accurate assessment, you need to specify a
more accurate set of input data, assess their
Table 1
Comparison of alternatives
Relative
Definition Explanation
importance
Equal contribution of two indicators to the
1 Equal importance of indicators
assessment
A slight advantage of one over Experience and research give a slight advantage of
3
the other one indicator over another
Experience and research give a great advantage of
5 Great advantage
one indicator over another
The advantage is so strong that it becomes
7 A significant advantage
significant
9 Full advantage The obvious advantage is most fully confirmed
2,4,6,8 Intermediate values Used as an alternative
After calculations, we obtain a matrix of unless they operate jointly in one area but
priorities in accordance with certain conditions separated by sometimes.
(known). This will allow you to make a decision Therefore, it would be rational to apply a
on the distribution of effort on the basis of the symmetrical difference (drastic product A B )
average value, or using special data analysis [9, 10, 11] of two sets where A is the set of targets
software [8] to determine at what level of the that will be attributed to the targets of fighter
hierarchy the defined indicators have the greatest aircraft and B is the set of targets that will be
impact. attributed to the targets of anti-aircraft missile
For example, using a color gradation of the forces.
appropriate range. However, changing the Also ( A B ) based on the definition
conditions of the task, taking into account the ( A B) \ (A B) can be described as Fig.1., that
risks or making a decision in conditions of is, a set that includes all elements of both sets that
complete uncertainty requires a recalculation of are not common to the two sets or
the priorities of the parameters on the basis of new ( A \ B) (В\ А) , a set that includes all elements
input data.
of the first set that are not included in the second
Although the set of comparative alternatives is
set, as well as elements of the second set that are
used at the stage of expert evaluation in MAH, it
not included in the first set.
affects only the initial level of evaluation of
coefficients, which does not allow to determine
the set of alternatives of the final result.
Using instead of the specified exact value, a fuzzy
unlimited multivalued estimate, we can increase
the set of values, all values of which satisfy the
task and are within acceptable limits. However,
when considering the distribution of efforts in one
area, the security of their troops (forces) remains
essential, so the set of targets set for fighter Figure 1: Image of the symmetric difference of
aircraft should not intersect with multiple targets sets A and B using Euler circles
that will apply to anti-aircraft missile forces,
Using a system of algebraic equations can be Symmetrical difference, respectively.
represented as follows: Given the safety of joint use, we define the set
mB ( x), if mA ( x) 1 for x X C - the estimated estimate of the loss of fighter
aircraft and D - the estimated estimate of the loss
mAB ( x) mA ( x), if mB ( x) 1 for x X , (1) of anti-aircraft missile forces in joint use. Based
0 in other cases
on the above use, we must take into account that
where X is the set of real numbers, mA ( x) is the the projected loss estimate will be relative to the
set of common use, so similarly use the symmetric
set of targets of fighter aircraft, mB ( x) is the set of
difference and the drastic sum to determine
targets of anti-aircraft missile forces. kCD ( x) and kCD ( x) where kC ( x) and kD ( x) - the
From the point of view of the use of fighter
set of projected losses.
aircraft and anti-aircraft missile forces, it can be
To determine the set of decision-making
described as used jointly in one area but divided
alternatives, taking into account the projected
into ranges, in the purpose for which fighter
estimate of losses when used together, consider
aircraft are used, anti-aircraft missile forces are
not considered and vice versa. max( AB ) , min( AB ) and max(CD ) ,
On the other hand, it is necessary to consider min( CD ) , in the figure it will look like a limit,
the whole set of purposes for which fighter aircraft and its division is described by determining the
and anti-aircraft missile forces can be used based maximum of the maximum allowable value and
on their capabilities, given the limit of joint use to the minimum of the minimum allowable. We get:
determine this set, we use a drastic sum ( AB ) max( AB ) max(max(mB ( x)) max(max(mA ( x)) (6)
which can be written as: min( AB ) min(min(mB ( x)) min(min(mA ( x)) (7)
mB ( x), if mA ( x) 0 for x X Accordingly, for max(CD ) , min( CD ) . Using
mAB ( x) mA ( x), if mB ( x) 0 for x X , (2) Euler's circles, the set of decisions takes the form
1 in other cases of Fig.2
In the case of the use of a symmetric sum, a set
of purposes became known which can be
considered for joint use, and in the case of the use
of a drastic sum using the previously described
max( AB ) , we define the boundaries of joint use,
which can be described as:
max(mB ( x)), if min(mA ( x)) 0 for x X
mAB ( x) max(mA ( x)), if min(mB ( x)) 0 for x X , (3)
1 in other cases
then the symmetric difference can be written
as:
min(mB ( x)), if max(mA ( x)) 1 for x X Figure 2: A variant of many decision-making
alternatives
mAB ( x) min(mA ( x)), if max(mB ( x)) 1 for x X , (4)
0 in other cases
To describe the knowledge for decision-
Using a symmetrical difference and a drastic making based on the given set of values, we use
sum to determine the boundaries of alternatives to the production model [12, 13]. In our case we can
the decision to use fighter aircraft and anti-aircraft form the following rules:
missile forces, there are other cases in which joint
1. If max( AB ) max(CD ) then use fighter
use will take place.
Let us denote the joint application by , since aircraft;
it is necessary to consider all possible cases, then 2. If min( AB ) min(CD ) then use anti-
the system of equations of the drastic sum takes aircraft missile forces;
the form: 3. If max( AB ) min( AB ) then joint use.
mB ( x), if mA ( x) 0 for x X Otherwise, it is possible to form a set of
hierarchically dependent rules depending on the
mAB ( x) mA ( x), if mB ( x) 0 for x X , (5)
level of the production model, or the level of
AB hierarchy of the method of analysis of hierarchies.
3. Conclusions [9] Mathematical apparatus of artificial
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