Control Method in Cognitive Maps Based on Weights Increments
Когнитивные карты широко используются для моделирования сложноструктурированных многомерных систем разной природы. Особой важностью обладает вопрос управления динамикой импульсного процесса в системе, описываемой когнитивной картой. Целью данной работы является разработка и исследование такого метод...
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| Veröffentlicht in: | Кибернетика и вычислительная техника |
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Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України
2016
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| Zitieren: | Control Method in Cognitive Maps Based on Weights Increments / V.D. Romanenko, Y.L. Milyavsky // Кибернетика и вычислительная техника. — 2016. — Вип. 184. — С. 44-55. — Бібліогр.: 8 назв. — англ. |
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| author | Romanenko, V.D. Milyavsky, Y.L. |
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| citation_txt | Control Method in Cognitive Maps Based on Weights Increments / V.D. Romanenko, Y.L. Milyavsky // Кибернетика и вычислительная техника. — 2016. — Вип. 184. — С. 44-55. — Бібліогр.: 8 назв. — англ. |
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| container_title | Кибернетика и вычислительная техника |
| description | Когнитивные карты широко используются для моделирования сложноструктурированных многомерных систем разной природы. Особой важностью обладает вопрос управления динамикой импульсного процесса в системе, описываемой когнитивной картой. Целью данной работы является разработка и исследование такого метода управления, который использует приращения весовых коэффициентов ребер когнитивной карты в качестве управляющих воздействий. В статье предложена модель управляемого импульсного процесса для этого случая, а также критерий оптимальности для формирования управления. Выведен закон управления и исследована устойчивость замкнутой системы. Алгоритм промоделирован на примере когнитивной карты социально-учебного процесса студента. Результаты разработанного метода подтверждают возможность эффективного перевода вершин когнитивной карты на новые уровни.
Когнітивні карти широко використовуються для моделювання складноструктурованих багатовимірних систем різної природи.Метою даної роботи є розробка і дослідження методу управління імпульсним процесом когнітивної карти, що використовує прирости вагових коефіцієнтів ребер в якості керуючих впливів. У статті запропоновано модель керованого імпульсного процесу для цього випадку, а також критерій оптимальності для формування управління. Виведено закон керування та досліджено стійкість замкненої системи. Алгоритм змодельовано на прикладі когнітивної карти соціально-навчального процесу студента. Результати розробленого методу підтверджують можливість ефективного переводу вершин когнітивної карти на нові рівні.
New method of control of cognitive maps was developed. It is based on varying of the map’s edges weights. It was supposed that some of the vertices may affect other ones in different way, i.e. stronger or weaker. After presenting impulse process model in full coordinates weights increments were added to the difference equation. They were considered as control inputs which were generated according to the control law developed based on quadratic criterion. Stability of the closed-loop system was demonstrated. To verify the results, method was simulated using cognitive map of student’s socio-educational process. Finally we obtained that for stable cognitive map vertices’ coordinates are quickly stabilised at new levels via edges’ weights varying.
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44
УДК 681.5
CONTROL METHOD IN COGNITIVE MAPS BASED
ON WEIGHTS INCREMENTS
V.D. Romanenko, Y.L. Milyavsky
Educational and Scientific Complex "Institute for Applied Systems Analysis"
of National Technical University of Ukraine “Kyiv Polytechnic Institute”
Когнитивные карты широко используются для
моделирования сложноструктурированных многомерных систем разной
природы. Особой важностью обладает вопрос управления динамикой
импульсного процесса в системе, описываемой когнитивной картой.
Целью данной работы является разработка и исследование такого метода
управления, который использует приращения весовых коэффициентов
ребер когнитивной карты в качестве управляющих воздействий. В статье
предложена модель управляемого импульсного процесса для этого случая,
а также критерий оптимальности для формирования управления. Выведен
закон управления и исследована устойчивость замкнутой системы.
Алгоритм промоделирован на примере когнитивной карты социально-
учебного процесса студента. Результаты разработанного метода
подтверждают возможность эффективного перевода вершин когнитивной
карты на новые уровни.
Ключевые слова: когнитивная карта, закон управления,
приращения весовых коэффициентов, стабилизация на новых уровнях.
Когнітивні карти широко використовуються для
моделювання складноструктурованих багатовимірних систем різної
природи.Метою даної роботи є розробка і дослідження методу управління
імпульсним процесом когнітивної карти, що використовує прирости
вагових коефіцієнтів ребер в якості керуючих впливів. У статті
запропоновано модель керованого імпульсного процесу для цього
випадку, а також критерій оптимальності для формування управління.
Виведено закон керування та досліджено стійкість замкненої системи.
Алгоритм змодельовано на прикладі когнітивної карти соціально-
навчального процесу студента. Результати розробленого методу
підтверджують можливість ефективного переводу вершин когнітивної
карти на нові рівні.
Ключові слова: когнітивна карта, закон керування,
прирости вагових коефіцієнтів, стабілізація на нових рівнях.
INTRODUCTION
Cognitive map (CM) is an oriented graph with vertices reflecting complex
systems coordinates (concepts) and edges describing cause–effect relations
between the vertices. We consider weighted CM where edges are weighted
depending on significance of corresponding relation.
During complex system operation under different disturbances CM
coordinates change in time. Each CM vertex iR is set to values )(kYi in discrete
times ...,2,1,0=k . The next value )1( +kYi is determined by current value )(kYi
and coordinates increments of other vertices jR connected to iR at time k .
Change of vertices jR coordinates 1),1()()()( >−−=∆= kkYkYkYkP jjjj , is
called impulse according to [1, 2, 3]. Spreading of impulses over CM vertices is
called impulse process and is described by the equation:
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
45
,,...,1),()()1(
1
nikPakYkY j
n
j
ijii =+=+ ∑
=
(1)
where ija is basic weight of edge from jR to iR .
Another way, CM vertices coordinates’ evolution rule (1) may be formulated
as first-order difference equation in increments:
.,...,1),()1(
1
nikYakY j
n
j
iji =∆=+∆ ∑
=
(2)
Equation (2) may be written in vector form:
)()1( kYAkY ∆=+∆ , (3)
where A is a transposed incidence matrix, Y∆ is a vector of coordinates
increments. Models (2), (3) describe multivariate dynamic discrete system in free
motion of CM vertices.
In [4–8] CM impulse process control automation is performed by external
control inputs generating based on vertices coordinates varying using known
control theory methods. To accomplish this forced motion equation under impulse
process was proposed:
,,...,1),()()1(
1
nikubkYakY iij
n
j
iji =∆+∆=+∆ ∑
=
(4)
where )1()()( −−=∆ kukuku iii is control input increment which is implemented
by means of varying resources of vertex iR .
Such an approach has a drawback: it may be practically unrealistic to vary CM
vertices resources a lot. The article proposes another approach.
PROBLEM DEFINITION
We consider new principle of control synthesis for CM impulse process. The
main idea is to vary CM edges weights ija to actualize controls )(kui in closed-
loop system. It is possible when we may change degree of impact of one CM
vertex on another. Decision-maker may implement weights varying by means of
changing administrative, scientific, financial, political, educational, informational
interrelations between coordinates of complex system described by CM. Control
)(kui is performed not by direct impact on the vertex to be changed on the k -th
sampling period, but by varying one of the weighting coefficients ija among edges
leading to this vertex. Thus, control )(kui should be formed not through resources
of )(kY j but through modifying degree of influence ( ija∆ ) of )(kY j on
)1( +∆ kYi . This problem is solved in the proposed article.
The purpose of the article is to develop method of CM impulse process
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
46
control based on varying edges’ weights.
METHOD OF STABLE CM IMPULSE PROCESSES CONTROL BASED ON WEIGHTS
VARYING
Consider free motion CM impulse process equation (3) not in increments but
in full coordinates (in scalar and vector forms):
,,...,1),()1()()1(
1
1 nikYaqkYkY j
n
j
ijii =−+=+ ∑
=
−
),()()1( 1 kYAqAIkY −−+=+
(5)
where 1−q is inverse discrete time shift operator.
If 0)(lim =∆
∞→
kYi
k
, for stabilization of CM vertices coordinates iY at
predefined levels iG it is necessary to generate controls influencing CM vertices
each sampling period according to designed control law by means of weights
)(kaij∆ varying.
Suppose that for each )1( +kYi there is no more than one coefficient iia μ that
may be varied, and that this additional weight )(μ ka ii∆ is applied directly to
coordinate )(μ kY i . Then forced motion equation for controlled impulse process for
each CM coordinate iY will be written as:
,,...,1),(ξ)()()()1()()1( μμ
1
1 nikkYkakYaqkYkY iij
n
j
ijii ii =+∆+−+=+ ∑
=
− (6)
where )1()()( μμμ −−=∆ kakaka iii iii , )(ξ ki is uncontrolled random noise with
zero mean.
Based on (5), (6) in vector form forced motion equation of CM impulse
process may be written as:
).(ξ)()()()()1( 1 kkakLkYAqAIkY +∆+−+=+ − (7)
Matrix )(kL is composed of measured CM coordinates )(μ kY i that influence
coordinates ,...,,2,1),1( nikYi =+ via edges with variable weights )(μ ka ii∆
which are in fact controls here. Strict rules for composing weights increments
vector )(ka∆ and matrix )(kL in (7) are formulated below.
a) Vector of weights increments )(ka∆ has dimension nm ≤ — it includes
only non-zero elements 0)(μ ≠∆ ka ii . If some weight in CM cannot be varied then
increment 0)(μ =∆ ka ii is not included into )(ka∆ .
b) Matrix )(kL has dimension mn × and contains no more than one element
in each i -th row equal to iYμ which affects vertex iY via weight increment iia μ∆ .
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
47
This element’s column number is equal to number of element iia μ∆ in )(ka∆ .
If any vertex iY does not have any incoming edges that may be varied then all
elements of i -th row are zero.
Optimal control vector )(ka∆ is designed on the base of the following
quadratic optimization criterion:
)},()(])1([])1({[)1( kaRkaGkYGkYEkJ TT ∆∆+−+−+=+ (8)
where G is reference input vector for CM coordinates vertices stabilizing on
predefined levels, R is diagonal positive-definite matrix, E is conditional
expectation operator as of time moment k .
After differentiating we obtain the following equation of multivariate
controller:
,0)(2])(ξ)()()())[((2
)(
)1( 1 =∆+−+∆+−+=
∆∂
+∂ − kaRGkkakLkYAqAIkL
ka
kJ T v
(9)
which leads to the control law:
].)(ξ)())[(())()(()( 11 GkkYAqAIkLRkLkLka TT −+−++−=∆ −− (10)
If )(kξ is not measured, then expression (10) is estimated as:
].)())[(())()(()( 11 GkYAqAIkLRkLkLka TT −−++−=∆ −−
Based on equations (7), (10) we get the following closed-loop equation for
CM impulse process:
).(ξ)}(])()()[({)(])()()[(
)())}((])()()[({)1(
11
11
kkLRkLkLkLIGkLRkLkLkL
kYAqAIkLRkLkLkLIkY
TTTT
TT
−−
−−
+−+++
+−++−=+
(11)
Here )(kL is time varying non-linear matrix depending on )(kY . Some
insights about stability of closed-loop system (11) are given below.
Proposition 1. Let forced motion equation of CM impulse process be
described by (7) where )(ka∆ is m -dimensional vector of weights and )(kL is
mn× matrix composed of coordinates )(μ kY l according to rule (b) ( ml ,..,1= are
numbers of respective increments in )(ka∆ ). Then mm× matrix )()( kLkLT in
control law (10) is diagonal with elements .,...,1),(2
μ mlkY
l
=
Proof. According to rule (b) matrix )(kL contains )(μ kY l in l -th column,
and all other elements in the column are zero. After transposing, element )(μ kY l is
in l -th row in )(kLT . Then after multiplying — in )()( kLkLT we will get element
)(2
μ kY
l
in l -th row and l -th column for all m rows and columns, while all other
elements are zero.
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
48
Corollary 1. As far as matrix R in (8) is m -dimensional, diagonal and
positive-definite, inverse matrix 1))()(( −+ RkLkLT in (11) is diagonal with
elements ,,...,1,
)(
1
2
μ
ml
RkY lll
=
+
that are always positive.
Corollary 2. Matrix )(])()()[()( 1 kLRkLkLkLIkB TT −+−= in closed-loop
equation (11) is nn × diagonal matrix with main diagonal elements equal to
ll
ll
ll RkY
R
RkY
kY
ll
l
+
=
+
−
)()(
)(
1 2
μ
2
μ
2
μ in rows that correspond to non-zero rows of )(kL
and equal to 1 otherwise. Thus, eigenvalues of )(kB are always
.,...,1,1λ0 nii =≤<
It is important that despite being time varying and non-linear with respect to
)(kY matrix )(kB is never unstable because its eigenvalues are always positive
and less or equal than 1.
Consider stable CM, i.e. amplitude of eigenvalues of incidence matrix A are
less than 1. Closed-loop system (11) is stable if absolute values of roots of its
characteristic equation are less than 1, too. This equation is written as
,0)))((det( 11 =−+− −− qAqAIkBI (12)
where )(])()()[()( 1 kLRkLkLkLIkB TT −+−= .
We already know that )(kB is diagonal matrix with elements in ]1;0( interval.
If )(kB were identity matrix, system could not be unstable because
),)(1()( 1111 −−−− −−=−+− AqIqqAqAII and roots of 0)det( 1 =− −AqI are
eigenvalues of A which is stable. If instead of identity matrix we multiply the
same expression by diagonal matrix some elements of which are positive and less
than 1 (and some are still equal to 1), it cannot become unstable. For simplicity it
will be demonstrated below in case of triangular matrix A . In this case
determinant in (12) is calculated easily because )))((( 11 −−−+− qAqAIkBI is
also triangular matrix, so its determinant equals to product of diagonal elements.
Thus, in fact we need to prove only scalar case, i.e., that absolute values of roots of
equation
0)1(1 11 =−+− −− qaqab (13)
are not greater than 1 if 10,1|| <<< ba (for 1=b it’s obvious).
Let us solve (13) as quadratic equation with respect to 1−q :
.01)1( 12 =++− −− qabbaq
If discriminant 04)1( 22 <−+= baabD then roots are
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
49
,
2
)1(4)1( 22
1
2,1 ba
abbaiab
q
+−±+
=− then absolute value is 1
||
1|| 1
2,1 >=−
ab
q , so
1|| 2,1 <q . If 0≥D , that is possible when 0<a , then
.1
2
1
2
1
2
4)1()1( 222
1
2,1 aba
a
a
a
ba
ababab
q −
+
±
+
=
−+±+
=− It is easily seen that
aba
a
a
aq 1
2
1
2
1 2
1
1 −
+
+
+
=− monotonically increases with b increasing from 0
to 1, and maximal value is 11
2
11
−<=
−++
aa
aa ;
aba
a
a
aq 1
2
1
2
1 2
1
2 −
+
−
+
=−
monotonically decreases and minimal value is 1
2
11
=
+−+
a
aa . Anyway,
1||1|| 2,1
1
2,1 <⇒>− qq .
STABILISATION OF STUDENT’S SOCIAL-EDUCATIONAL PROCESS VIA COGNITIVE
MAP WEIGHTS VARYING
As an example of application of control law proposed above consider
stabilization of CM of a student, specifically, of social-educational process of a
student. The following concepts are selected as vertices of this CM:
1. Time spent on study.
2. Success in studies.
3. Time spent on work.
4. Success in work.
5. Money earned.
6. Health (time and finance spent on health care).
7. Family welfare.
8. Hobby (time and money spent on leisure and entertainment).
This CM with basic edge weights set by experts can be seen on fig. 1.
Fig. 1. CM of student
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
50
Equation (3) is written in this case as:
.
)(
)(
)(
)(
)(
)(
)(
)(
04.003,006.003.0
3.065.005.00000
5.008.02,004.005.0
00004.0000
3.005,004.08,002.0
03.0000006.0
004.0004,04.08.0
15.07,000025.02.00
)1(
)1(
)1(
)1(
)1(
)1(
)1(
)1(
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
∆
∆
∆
∆
∆
∆
∆
∆
−−
−
−−
−
−−
−
−−−
=
+∆
+∆
+∆
+∆
+∆
+∆
+∆
+∆
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
kY
(14)
Suppose decision-maker (student) can vary the following weight coefficients:
a) 13a — how time spent on work affects time spent on study;
b) 23a — how time spent on work affects success in studies;
c) 31a — how time spent on study affects time spent on work;
d) 41a — how time spent on study affects success in work;
e) 65a — how earned money affects health level;
f) 75a — how earned money affects family welfare;
g) 83a — how time spent on work affects hobby.
So, according to rule (a)
( )Taaaaaaaa 83756541312313 ∆∆∆∆∆∆∆=∆
and according to rule (b):
.
)(000000
0)(00000
00)(0000
0000000
000)(000
0000)(00
00000)(0
000000)(
)(
3
5
5
1
1
3
3
=
kY
kY
kY
kY
kY
kY
kY
kL
All eigenvalues of A are less than 1 by absolute value, the system is stable.
All vertices coordinates are measured in scale from 0 to 10 and initial values are set
to 5 for illustrative purpose. Suppose that initial impulse is negative: success in
studies and health decrease from 5 to 4 level. Our goal is to increase success in
studies and health up to 6 level. Having applied control law (10) with R equal to
identity 77× matrix, we obtain the following impulse process (Fig. 2).
V.D. Romanenko, Y.L. Milyavsky, 2016
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51
Fig. 2. Controlled impulse process
Weights increments generated by the control law are the following (Fig. 3).
V.D. Romanenko, Y.L. Milyavsky, 2016
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52
Fig. 3. Weights increments
RESULTS
As we can see from the simulation results proposed algorithm allows setting
CM vertices coordinates in impulse process at new adjusted levels. Coordinates
converge to reference inputs quickly, amplitude is small enough for practical
implementation. This is achieved only via selected CM edges weights varying.
Range of the weights change is reasonably small, so that decision-maker can
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
53
physically vary them in real life impulse process. Thus, if CM impulse process is
stable, using given quadratic criterion and having edges weights that can be varied
it is possible to generate control law which moves selected vertices coordinates to
any desired values.
CONCLUSION
The article considers new control method of impulse process in CM. This
method uses CM edges weights increments as control inputs as opposed to all other
methods that require external controls. This makes it possible to change state of
dynamic system described by stable CM without varying resources associated with
CM vertices. Instead the proposed method is based on changing degree of impact
of one CM vertex on another which is more preferable in lots of practical cases.
For stabilization quadratic optimality criterion is proposed and explicit formula for
optimal control law is derived. Stability of the closed-loop system after applying
this law was demonstrated. For illustrative purposes CM of student’s socio-
educational process was considered. It was shown that by means of the proposed
method several vertices coordinates of this CM are easily stabilized on new levels
via weights varying. Simulation proved practical applicability of the proposed
method.
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V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
54
UDC 681.5
CONTROL METHOD IN COGNITIVE MAPS BASED
ON WEIGHTS INCREMENTS
V.D. Romanenko, Y.L. Milyavsky
Educational and Scientific Complex "Institute for Applied Systems Analysis"
of National Technical University of Ukraine “Kyiv Polytechnic Institute”
Introduction. Cognitive maps are widely used for modeling large
multidimensional systems. These are weighted oriented graphs that represent
concepts and relations between them. When external or internal disturbances affect
the system impulse process is initiated. It is described by first-order equation in
increments of vertices coordinates. A number of articles solved a problem of
control in cognitive map’s impulse process by means of control theory methods.
But all of them used external control inputs, i.e. resources of the vertices, for this
purpose.
The purpose of the article is to develop new method of control where
cognitive map’s edges weights are used as controls for impulse process
stabilisation.
Results. New method of control of cognitive maps was developed. It is based
on varying of the map’s edges weights. It was supposed that some of the vertices
may affect other ones in different way, i.e. stronger or weaker. After presenting
impulse process model in full coordinates weights increments were added to the
difference equation. They were considered as control inputs which were generated
according to the control law developed based on quadratic criterion. Stability of the
closed-loop system was demonstrated. To verify the results, method was simulated
using cognitive map of student’s socio-educational process. Finally we obtained
that for stable cognitive map vertices’ coordinates are quickly stabilised at new
levels via edges’ weights varying.
Conclusion. Applying the proposed method of control based on weights
varying to impulse process of cognitive map allows setting vertices coordinates on
desired levels.
Keywords: cognitive map, control law, weights increments, stabilisation at
new levels.
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V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
55
complex system under unstable impulse process // System Research & Information
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cognitive maps vertices' ratios in impulse mode // System Research & Information
Technologies. — 2015. — №3. — P. 109–120 (in Russian).
Получено 24.03.2016
V.D. Romanenko, Y.L. Milyavsky, 2016
ISSN 0452-9910. Кибернетика и вычисл. техника. 2016. Вып. 184
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| id | nasplib_isofts_kiev_ua-123456789-110367 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0452-9910 |
| language | English |
| last_indexed | 2025-12-07T16:52:29Z |
| publishDate | 2016 |
| publisher | Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України |
| record_format | dspace |
| spelling | Romanenko, V.D. Milyavsky, Y.L. 2017-01-03T18:34:11Z 2017-01-03T18:34:11Z 2016 Control Method in Cognitive Maps Based on Weights Increments / V.D. Romanenko, Y.L. Milyavsky // Кибернетика и вычислительная техника. — 2016. — Вип. 184. — С. 44-55. — Бібліогр.: 8 назв. — англ. 0452-9910 https://nasplib.isofts.kiev.ua/handle/123456789/110367 681.5 Когнитивные карты широко используются для моделирования сложноструктурированных многомерных систем разной природы. Особой важностью обладает вопрос управления динамикой импульсного процесса в системе, описываемой когнитивной картой. Целью данной работы является разработка и исследование такого метода управления, который использует приращения весовых коэффициентов ребер когнитивной карты в качестве управляющих воздействий. В статье предложена модель управляемого импульсного процесса для этого случая, а также критерий оптимальности для формирования управления. Выведен закон управления и исследована устойчивость замкнутой системы. Алгоритм промоделирован на примере когнитивной карты социально-учебного процесса студента. Результаты разработанного метода подтверждают возможность эффективного перевода вершин когнитивной карты на новые уровни. Когнітивні карти широко використовуються для моделювання складноструктурованих багатовимірних систем різної природи.Метою даної роботи є розробка і дослідження методу управління імпульсним процесом когнітивної карти, що використовує прирости вагових коефіцієнтів ребер в якості керуючих впливів. У статті запропоновано модель керованого імпульсного процесу для цього випадку, а також критерій оптимальності для формування управління. Виведено закон керування та досліджено стійкість замкненої системи. Алгоритм змодельовано на прикладі когнітивної карти соціально-навчального процесу студента. Результати розробленого методу підтверджують можливість ефективного переводу вершин когнітивної карти на нові рівні. New method of control of cognitive maps was developed. It is based on varying of the map’s edges weights. It was supposed that some of the vertices may affect other ones in different way, i.e. stronger or weaker. After presenting impulse process model in full coordinates weights increments were added to the difference equation. They were considered as control inputs which were generated according to the control law developed based on quadratic criterion. Stability of the closed-loop system was demonstrated. To verify the results, method was simulated using cognitive map of student’s socio-educational process. Finally we obtained that for stable cognitive map vertices’ coordinates are quickly stabilised at new levels via edges’ weights varying. en Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України Кибернетика и вычислительная техника Интеллектуальное управление и системы Control Method in Cognitive Maps Based on Weights Increments Спосіб управління в когнітивних картах на основі приростів вагових коефіцієнтів Article published earlier |
| spellingShingle | Control Method in Cognitive Maps Based on Weights Increments Romanenko, V.D. Milyavsky, Y.L. Интеллектуальное управление и системы |
| title | Control Method in Cognitive Maps Based on Weights Increments |
| title_alt | Спосіб управління в когнітивних картах на основі приростів вагових коефіцієнтів |
| title_full | Control Method in Cognitive Maps Based on Weights Increments |
| title_fullStr | Control Method in Cognitive Maps Based on Weights Increments |
| title_full_unstemmed | Control Method in Cognitive Maps Based on Weights Increments |
| title_short | Control Method in Cognitive Maps Based on Weights Increments |
| title_sort | control method in cognitive maps based on weights increments |
| topic | Интеллектуальное управление и системы |
| topic_facet | Интеллектуальное управление и системы |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110367 |
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