Crop Area Management Based on Fuzzy Analysis of Historical Sensor
Readings Combined Within a Unified IoT Platform
ELCHIN ALIYEV1, RAMIN RZAYEV2, ASGAR ALMASOV1, ABULFAT RAHMANOV1
1Laboratory of Intelligent Decision-Making Methods and Computer Systems,
Institute of Control Systems,
Baku,
AZERBAIJAN
2Laboratory of Information Decision Support Systems,
Institute of Control Systems,
Baku,
AZERBAIJAN
Abstract: - The network-centric approach to building control systems using wireless technologies has shown its
effectiveness in practice. Currently, active research is underway in the field of implementing a network-centric
approach to improve the management of business entities. A network-centric control system is a distributed
control system in which its main components are integrated into a single information space. The purpose of this
research is to develop proposals for building a network-centric model for managing geographically distributed
crop areas based on a digital IoT-platform, which represents a universal info-communication environment. The
features of network-centric control using fuzzy modeling systems that provide analytical support for decision-
making under uncertainty are considered. As an example, it is considered a method of fuzzy modeling and
forecasting of segments of averaged sensor readings from web-devices, which can provide information support
for predictive and prescriptive analytical solutions. Proposed solutions can be used not only in the field of
precision agriculture, but also to build a digital network-centric management platform for any business entity.
Key-Words: - Crop area management, network-centric control, IoT platform, sensor readings, fuzzy set, fuzzy
time series, forecasting.
Received: August 11, 2023. Revised: May 19, 2024. Accepted: July 7, 2024. Published: August 8, 2024.
1 Introduction
Crop area management system includes sources and
consumers of information, telecommunications
facilities, as well as a center for processing input data
and preparing information for users. A network-
centric management system based on a unified IoT
information platform embodies the idea of creating
“Smart Agriculture”, which is a high-tech set of
solutions that allows for maximum automation of
specialized agricultural sectors, as a result of which
agricultural production becomes profitable and
economically beneficial. A huge layer of hidden and
useful information is concentrated in the form of data
that, through IoT technology, has become possible to
obtain from the operating web-devices of
agricultural enterprises. Crops, soil, irrigation
devices, agricultural equipment and web-devices that
monitor climate conditions, including temperature
and ground humidity, can accumulate, send and
process data, creating invisible images ready to be
used to make preventive, tactical and strategic
decisions.
Sensors of connected web-devices permanently
collect data in a dedicated environment necessary to
solve planned problems. At certain intervals, this
data is transmitted to an integrated information IoT-
platform using wireless technologies such as Wi-Fi,
Bluetooth, Zigbee, LoRa, cellular networks (Nb-IoT,
LTE, etc.), providing energy-efficient long-range
networks actions, or by connecting directly to the
Internet via Ethernet. The choice of connection
means depends on the scope of application of a
particular web-device within the framework of the
IoT-based remote monitoring system.
2 Crop Area Management System
Figure 1 shows the structure of a network-centric
management system (NCMS) for geographically
distributed crop areas, built on the basis of the
WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS
DOI: 10.37394/23209.2024.21.35
Elchin Aliyev, Ramin Rzayev,
Asgar Almasov, Abulfat Rahmanov
E-ISSN: 2224-3402
374
Volume 21, 2024
unified information IoT-platform, which receives
data from sensors from web-devices located directly
on controlled cultivation areas, and the results of
multispectral analysis of data from multi-copters in
the form of vegetation maps.
The correctness of the closure of individual
circuits of the proposed NCMS is determined by the
sufficient set of tools that provide the required
adequacy of information support in the process of
collecting, storing and processing sensor readings
from web-devices and multispectral data from
remote monitoring of the current state of the crop
area, carried out by multi-copters in real time. The
organization of each level of control involves the use
of the unique set of built-in knowledge compilation
models, information support, description of the
microclimate in a dedicated environment, etc.
Taking into account the latest advances in the field
of artificial intelligence and related scientific
disciplines [1], the tools for compiling knowledge in
solving management problems can and should be
subjected to significant revision. Its main essence
lies in a radical change in the point of view on the
role and place of modern intelligent technologies in
the organization of hierarchical management of
complex dynamic objects.
The main goal of this study is to develop the tool
for processing sensor data to provide information
support for making agricultural decisions based on
the identified patterns in the fuzzy paradigm.
Fig. 1: Generalized structure of a crop area
management system using IoT and unmanned
technologies
3 Fuzzy Predictive Model Based on
Humidity Sensor Readings
Figure 2 shows the time series reflecting the
dynamics of changes in ground humidity on the
specified sown area. Using this example, it is
necessary to develop a methodology for constructing
adequate predictive models of time series that reflect
the dynamics of changes in data received in the form
of sensory signals from web-devices that monitor the
state of vegetation and climatic conditions, which
have a significant impact on the yield of the crop
being grown.
Fig. 2: Time series “Ground humidity”
Recent advances in solving forecasting and
decision-making problems have been achieved
mainly through the use of neural-fuzzy data
processing technologies. Over the past decades,
impressive results have been obtained in the field of
forecasting volatile time series using fuzzy methods
for analyzing historical data, [2], [3], [4], [5], [6],
[7], [8], [9], [10], [11], [12], [13], [14], [15], [16],
[17].
The object of our study is the “Ground
humidity” time series, covering the set of historical
data for the period from 26.10.2022 to 24.01.2023
inclusive (Figure 2). Because the ground humidity
indicator is established by the usual arithmetic
averaging of sensor readings from several sections
of the crop area, each of its values x(t) at time t will
be considered as weakly structured historical data,
which can be interpreted in the form of a fuzzy set
(FS) Ak (k = n), characterized by the following
tuple:
{x(t) / µAk[x(t)]}, µAk[x(t)] [0, 1] 
where µAk() is the membership function of the
fuzzy set Ak. In this case, the fuzzy set Ak is the
evaluation concept and is used as a qualitative
criterion for assessing sensor readings. For each
specific time series, the number of qualitative
assessment criteria is set step by step as follows,
[13].
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Step 1. Sorting the sensor readings xt = x(t)
(t=91) into the ascending sequence {xp(i)}, where
p is a permutation that sorts the humidity readings in
ascending order: xp(i+1) xp(i). Hereinafter, sensor
readings at a given time should be understood as
averaging sensor readings from several sections of
the crop area.
Step 2. Calculation of the average value based
on the totality of all pairwise distances di = |xp(i)-
xp(i+1)| between any two consecutive values xp(t) and
xp(t+1) according to:
1
( ) ( 1)
1
1||
1
n
p i p i
i
AD x x
n


and standard deviation according to the formula
12
1
1()
1
n
AD i
id AD
n

 
Step 3. Elimination of anomalies outliers that
need to be removed. The values of pairwise
distances that do not satisfy the following condition
are subject to emission:
AD
AD di AD+
AD
Step 4. After re-calculating the average value
AD over the set of pairwise distances remaining
after the release of anomalous values, the
corresponding number of qualitative assessment
criteria (m) is calculated using the formula:
m = [D2-D1-AD]/[2AD]
where D1 = Dmin-AD; D2 = Dmax+AD; Dmin and
Dmax are the minimum and maximum values in the
humidity sensor readings, respectively.
Applying formulas (2) and (3) to sets of
humidity sensor readings (n = 91), we obtained the
average value AD = 0.67 and the standard deviation
AD = 1.14, respectively. By discarding di that do not
satisfy condition (4) or, more specifically, the
condition
-0.47 = 0.67-1.14 di 0.67+1.14 = 1.81
using formula (2), the final value of the average
value for the totality of the remaining pairwise
distances di was obtained: AD = 0.40. Then,
according to [13], the segment D = [D1, D2] is
selected as a universal set covering the range of
humidity sensor readings, where D1 = Dmin-AD =
34.02-0.40 = 33.62, D2= Dmax+AD = 94.60+0.40 =
95. Then, according to (5), the acceptable number of
criteria for assessing the humidity sensor readings
is: m = [95-33.62-0.40]/[20.40] = 75.72 76.
Now that the number of criteria for the
qualitative assessment of ground humidity sensor
readings has been established, it’s time to determine
their fuzzy formalisms, that is, their descriptions in
terms of fuzzy sets. To do this, it is necessary to
decide on the choice of a suitable membership
function.
One of such functions is the symmetric
trapezoidal membership function, which in the
context of the problem under consideration is given
in the following form:
1
1
12
21
23
4
34
43
4
0,
, ,
( ) 1, ,
, ,
0, ,
k
k
kkk
kk
A k k
kkk
kk
k
xa
xa a x a
aa
x a x a
ax
a x a
aa
xa



where ak2 ak1 = ak3 ak2 = ak4 ak3; k = m.
Starting from (6), to describe the readings of ground
humidity sensors in the form of fuzzy subsets of the
universe D = [D1, D2] = [33.62, 95], the appropriate
76 symmetric trapezoidal membership functions are
identified (Figure 3), the parameters of which are
summarized in Table 1.
Fig. 3: Trapezoidal membership functions
Fuzzification of historical data of the “Ground
humidity” time series is carried out according to the
principle, [13]: the sensor reading is described by
the fuzzy set to which it belongs to the greatest
degree. When the sensor reading belongs to the
interval [ak2, ak3] (projection of the upper base of the
k-th trapezoid onto the x-axis, see (10)), it is
relatively easy to find its fuzzy analog. For example,
the sensor reading x13 = 81.71 for the date
07.11.2022 is described by the fuzzy set A60 (Table
1), because it belongs to the interval [81.42, 81.83].
In other cases, additional calculations are required.
In particular, for the sensor reading x11 = 64.19 for
date 05.11.2022 we have: µA39(64.19) = 0.2023 and
µA38(64.19) = 0.7977 (Figure 4). Therefore, A38 is
chosen as the fuzzy analog.
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Table 1. Fuzzy Sets as Criteria for Assessing Sensor
Readings
Trapezoidal membership function
parameters
ak1
ak2
ak3
ak4
33.62
33.91
34.31
34.71
34.31
34.71
35.12
35.52
35.12
35.52
35.92
36.32
35.92
36.32
36.73
37.13
36.73
37.13
37.53
37.93
37.53
37.93
38.34
38.74
38.34
38.74
39.14
39.54
……………………………………………………………………
…….
63.30
63.71
64.11
64.51
64.11
64.51
64.91
65.32
……………………………………………………………………
…….
89.07
89.48
89.88
90.28
89.88
90.28
90.69
91.09
90.69
91.09
91.49
91.89
91.49
91.89
92.30
92.70
92.30
92.70
93.10
93.50
93.10
93.50
93.91
94.31
93.91
94.31
94.71
95.00
Fig. 4: Evaluation criteria in the form of fuzzy sets
A38 and A39
Thus, guided by the principle proposed in [13],
the fuzzy analog of the “Ground humidity” time
series was constructed and summarized in Table 2.
The next step in constructing the predictive
model is to identify internal connections that
determine cause-effect relationships between sensor
readings throughout the entire observation period.
Depending on the number of prerequisites in the
fuzzy relation of the form “If <...>, then <...>”,
internal relationships are divided into groups of 1st,
2nd, and high-orders. Internal relationships (or fuzzy
relations) of the 1st order are grouped according to
the principle: if the fuzzy set At is connected with Ap
and As, then the 1st order group is localized relative
to it: At Ap, As. For example, the fuzzy set A29 is
connected with the fuzzy sets A25 и A38, then the 1st
order group A29 A25, A38 is localized relative to it
(Table 3, Group G29). The breakdowns by groups of
internal relationships of the 1st and 2nd order are
presented in Table 3 and Table 4, respectively.
Table 2. Fuzzy Time Series “Ground Humidity”
Date
xt
Data
FS
Date
xt
Data
FS
26.10.2022
x1
77.67
A55
11.12.2022
x47
88.62
A69
27.10.2022
x2
73.90
A50
12.12.2022
x48
83.09
A62
28.10.2022
x3
65.97
A41
13.12.2022
x49
88.14
A68
29.10.2022
x4
73.42
A50
14.12.2022
x50
73.79
A50
30.10.2022
x5
68.91
A44
15.12.2022
x51
87.02
A67
31.10.2022
x6
70.01
A46
16.12.2022
x52
88.62
A69
01.11.2022
x7
66.53
A41
17.12.2022
x53
89.75
A70
02.11.2022
x8
64.66
A39
18.12.2022
x54
89.23
A69
03.11.2022
x9
58.38
A31
19.12.2022
x55
80.50
A59
04.11.2022
x10
56.76
A29
20.12.2022
x56
94.60
A76
05.11.2022
x11
64.19
A38
21.12.2022
x57
90.73
A71
06.11.2022
x12
73.83
A50
22.12.2022
x58
83.48
A62
07.11.2022
x13
81.71
A60
23.12.2022
x59
87.07
A67
08.11.2022
x14
77.55
A55
24.12.2022
x60
91.48
A72
09.11.2022
x15
71.04
A47
25.12.2022
x61
82.08
A61
10.11.2022
x16
74.92
A52
26.12.2022
x62
86.69
A66
11.11.2022
x17
87.83
A68
27.12.2022
x63
83.60
A62
12.11.2022
x18
83.09
A62
28.12.2022
x64
74.86
A52
13.11.2022
x19
69.22
A45
29.12.2022
x65
66.79
A42
14.11.2022
x20
69.26
A45
30.12.2022
x66
73.19
A50
15.11.2022
x21
74.44
A51
31.12.2022
x67
72.24
A69
16.11.2022
x22
83.68
A63
01.01.2023
x68
62.00
A62
17.11.2022
x23
61.18
A35
02.01.2023
x69
49.43
A68
18.11.2022
x24
48.49
A19
03.01.2023
x70
43.34
A12
19.11.2022
x25
49.53
A20
04.01.2023
x71
42.91
A12
20.11.2022
x26
54.39
A26
05.01.2023
x72
48.47
A19
21.11.2022
x27
56.31
A29
06.01.2023
x73
59.03
A32
22.11.2022
x28
53.11
A25
07.01.2023
x74
42.49
A11
23.11.2022
x29
34.02
A1
08.01.2023
x75
90.67
A71
24.11.2022
x30
71.01
A47
09.01.2023
x76
90.46
A71
25.11.2022
x31
81.06
A59
10.01.2023
x77
86.47
A66
26.11.2022
x32
80.30
A58
11.01.2023
x78
91.18
A72
27.11.2022
x33
75.55
A52
12.01.2023
x79
85.03
A64
28.11.2022
x34
81.04
A59
13.01.2023
x80
81.73
A60
29.11.2022
x35
86.75
A66
14.01.2023
x81
81.13
A59
30.11.2022
x36
94.60
A76
15.01.2023
x82
79.92
A58
01.12.2022
x37
93.21
A74
16.01.2023
x83
81.19
A59
02.12.2022
x38
88.62
A69
17.01.2023
x84
81.59
A60
03.12.2022
x39
90.42
A71
18.01.2023
x85
82.55
A61
04.12.2022
x40
91.97
A73
19.01.2023
x86
82.78
A61
05.12.2022
x41
92.45
A73
20.01.2023
x87
83.78
A63
06.12.2022
x42
92.02
A73
21.01.2023
x88
80.82
A59
07.12.2022
x43
87.17
A67
22.01.2023
x89
79.05
A57
08.12.2022
x44
84.37
A63
23.01.2023
x90
73.93
A50
09.12.2022
x45
89.83
A70
24.01.2023
x91
86.75
A66
10.12.2022
x46
87.42
A67
The 1st order internal relationship between the
sensor readings xt and xt+1 can be interpreted as the
fuzzy implication
“If xt is Ak, then xt+1 is Ap”,
where t = 1÷91; k, p = 1÷76. In particular, the
internal 1st order relationship A11A71 (Table 3, G2)
between the readings x74(42.49) and x75(90.67)
(Table 2) is interpreted as “If x74 is A11, then x75 is
A71”. If the internal relationship of the 1st order is
represented in the form AkAp1, …, Apr, where k, p1,
p2,, ps = 1÷76, then in the form of the fuzzy
implication it looks like this: “If xt is Ak, then xt+1 is
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Ap or xi+1 is Ar or xi+1 is As”. In particular, the 1st
order internal relationship A52A42, A59, A68
between sensor readings x64(74.86) and x65(66.79),
x33(75.55) and x35(81.04), x16(74.92) and x17(87.83)
(Table 2), interpreted as:
“If xt is A52, then xt+1 is A42 or xt+1 is A59 or xt+1 is
A68”.
Accordingly, the 2nd order fuzzy relation, for
example, A47, A59A58 can be interpreted as the
fuzzy implication: “If xt is A47 and xt is A59, then xt+1
is A58”, or relationship A59, A58A52, A59 can be
interpreted as the fuzzy implication:
“If xt is A59 and xt is A58, then xt+1 is A52 or xt+1 is A59
Table 3. Groups of Internal Relationships of the 1st
Order
Group
Relation
Group
Relation
G1
A1A47
G16
A44A46
G2
A11A71
………………………..
G3
A12A12, A19
G31
A64A60
G4
A19A20, A32
G32
A65
G5
A20A26
G33
A66A62, A72, A76
G6
A25A1
G34
A67A63, A69, A72
G7
A26A29
G35
A68A12, A50, A62
G8
A29A25, A38
G36
A69A59, A62, A70, A71
G9
A31A29
G37
A70A67, A69
G10
A32A11
G38
A71A62, A66, A71, A73
G11
A35A19
G39
A72A61, A64
G12
A38A50
G40
A73A67, A73
G13
A39A31
G41
A74A69
G14
A41A39, A50
G42
A75
G15
A42A50
G43
A76A71, A74
Table 4. Groups of Internal Relationships of the 2nd
Order
Group
Relation
Group
Relation
G1
A55, A50A41
G16
A52, A68A62
G2
A50, A41A50
………………………..
G3
A41, A50A44
G47
A62, A68A12, A50
G4
A50, A44A46
………………………..
G5
A44, A46A41
G75
A72, A64A60
G6
A46, A41A39
G76
A64, A60A59
G7
A41, A39A31
G77
A60, A59A58
G8
A39, A31A29
G78
A58, A59A60
G9
A31, A29A38
G79
A59, A60A61
G10
A29, A38A50
G80
A60, A61A61
G11
A38, A50A60
G81
A61, A61A63
G12
A50, A60A55
G82
A61, A63A59
G13
A60, A55A47
G83
A63, A59A57
G14
A55, A47A52
G84
A59, A57A50
G15
A47, A52A68
G85
A57, A50A66
4 “Ground Humidity” Fuzzy Time
Series Forecasting
Various rules are applied to determine fuzzy
predictions and defuzzify them [8], [9]. As applied
to our task, the essence of some of them is as
follows. If the sensor reading xt is described by the
fuzzy set Aj, which within the totality of time series
data forms only one internal relationship of the 1st
order, for example, in the form of the fuzzy relation
AjAk, then the prediction for the next (t+1)-th
period is the fuzzy set Ak. In the case when there is a
group of relationships, for example, AjAk1, Ak2, …,
Akp, then the union Ak1Ak2 Akp is the fuzzy
predict for the (t+1)-th period. To defuzzify fuzzy
predicts, the following two rules can be applied.
Rule 1. In the case of a fuzzy relation of the
form AiAj, where Ai is the fuzzy analog of the
sensor reading on the i-th day, the predict in
nominal terms for the next (t+1)-th day is the
abscissa of the middle of the upper base of the
trapezoid, reflecting the fuzzy set Aj. Indeed, this is
confirmed by the defuzzification rule of the fuzzy
set A, which is implemented according to the
following formula
max
0
max
1
( ) ( )F A M A d
 
where A
={u|
A(u)
, uU} is the
-level sets
(
[0, 1]); M(A
) is powers of the corresponding
-
level sets, calculated by the formula
1
1
() n
k
k
M A u
n
, ukA
.
In particular, for the fuzzy set (Table 2) A71=
{0/89.88, 1/90.28, 1/90.69, 0/91.09}, which is the
predict in the conjunction A11A71, for 0 <
< 1 we
have:
= 1, A71,
= {89.88, 91.09},
M(A71,
) = (89.88+91.09)/2 = 90.485.
Then, according to (7), the prediction in
nominal terms is:
1
10 71 71
0
( ) ( ) ( ) 90.485 1
90.485.
F A M A d M A


Rule 2. In the case of the fuzzy relation AtAj,
Ai, Ap, where At is the fuzzy analog of the sensor
reading for the t-th day, the crisp prediction for the
next (t+1)-th day is calculated as the arithmetic
mean of the abscissa of the midpoints of the upper
bases of the trapezoids, corresponding to the fuzzy
sets Aj, Ai and Ap, [2], [3]. In particular, according to
the internal relationship A68 A12, A50, A62 the
predicts for the dates 12.11.2022, 14.12.2022 and
03.01.2023 are calculated as follows (Table 2):
42.77 43.17 73.37 73.77 83.03 83.44
2 2 2 66.59
3

.
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Thus, the predictions obtained using Rules 1 and
2 for the 1st and 2nd order predictive models are
summarized in Table 5 and Table 6 in Appendix.
The corresponding geometric interpretations of the
forecasting results are presented in Figure 5.
At the end of Table 5 and Table 6 (Appendix), the
values of statistical criteria for assessing the
adequacy of predictive models are presented, [18]:
MSE (Mean Squared Error), MAPE (Mean Absolute
Percentage Error) and MPE (Mean Percentage
Error), which are calculated using the corresponding
formulas:
2
1
1
MSE ( )
m
tt
tFR
m

,
1
||
1
MAPE 100%
mtt
tt
FR
mR

,
1
1
MPE 100%
mtt
tt
FR
mR

,
where m is the length of the time series; Rt is the
actual indicator of the ground humidity at the t-th
moment of observation; Ft is the predict of Rt.
When interpreting these metrics, their
characteristics should be taken into account. For
example, MSE being one of the most common
metrics of forecast errors, allows to evaluate the
accuracy of the forecast in absolute units of
measurement, while MPE and MAPE show the
deviation as a percentage. In particular, MAPE can
be useful for comparing the forecast accuracy of
different models processing different ranges of data.
Fig. 5: Time series predictive models of 1st and 2nd
orders
As can be seen from Table 5 and Table 6 in
Appendix, the MSE indicators for the 1st and 2nd order
predictive models are equal to MSE1 = 49.16 and
MSE2 = 30.52, respectively. According to the MAPE
criterion, which demonstrates the percentage of the
forecast error in comparison with the actual values of
the time series, the identified errors MAPE1 = 6.44%
and MAPE2 = 2.53% also demonstrate the
preference of the 1st and 2nd order predictive models
over the exponential smoothing model, for which
MAPE = 9.18%. According to the MPE indicator,
which is a more informative criterion for assessing
the adequacy of the forecasting model, acceptable
“biases” of these predictive models were obtained as
MPE1 = -2.03% and MPE2 = -1.68%, which does not
exceed the normative 5%-th threshold to the left of
zero.
5 Conclusion
In the process of implementing IoT technology,
unique challenges arise that entail the use of signals
from multiple web-devices in real-time. To solve
them, it is necessary to develop new methods for
processing signals and information. The result
presented in the article is only one minor fragment
in the general methodology for processing sensory
signals carried out as part of the application of IoT
technology in precision agriculture. This or similar
methodology has the potential to enable an
intelligent IoT platform despite being overshadowed
by other aspects of IoT technology such as
communications architecture, sensor technologies,
and power management. The approach proposed in
this paper is capable of supporting predictive and
prescriptive analytical decisions by linking
previously collected data from smart sensors,
equipment, and other agricultural assets. This
approach facilitates the creation of tools for
monitoring the current state of crops and controlling
the growing environment and is aimed at increasing
the yield of the crop as a whole. By anticipating
undesirable situations, one can permanently
maintain a high level of care for the crop area.
References:
[1] A. M. Abbasov, R. R. Rzayev, “Artificial
intelligence and digital economy:
development prospects”, Lecture Notes in
Networks and Systems, vol. 610, pp. 147-153,
2023.
[2] S. M. Chen, and N. Y. Chung, “Forecasting
enrollments of students by using fuzzy time
series and genetic algorithms”, International
Journal of Information and Management
Sciences, vol. 17, no. 3, pp. 1-17, 2006.
[3] S. M. Chen, and N. Y. Chung, “Forecasting
enrollments using high order fuzzy time series
and genetic algorithms”, International
Journal of Information and Management
Sciences, vol. 21, pp. 485-501, 2006.
[4] S. M. Chen, and J. R. Hwang, “Temperature
prediction using fuzzy time series”, IEEE
Trans. Systems, Man, and Cybernetics, Part B:
Cybernetics, vol. 30, no. 2, pp. 263-275, 2000.
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E-ISSN: 2224-3402
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Volume 21, 2024
[5] S. M. Chen, and P. Y. Kao, “TAIEX
forecasting based on fuzzy time series,
particle swarm optimization techniques and
support vector machines”, Information
Sciences, vol. 247, pp. 62-71 2013.
[6] S. M. Chen, and N. Y. Wang, “Fuzzy
forecasting based on fuzzy-trend logical
relationship groups”, IEEE Trans. Systems,
Man, and Cybernetics, Part B: Cybernetics,
vol. 40, no. 5, pp. 1343-1358, 2010.
[7] S. M. Chen, “Forecasting enrollments based
on fuzzy time series”, Fuzzy Sets and Systems,
vol. 81, pp. 311-319, 1996.
[8] S. M. Chen, “Forecasting enrollments based
on high-order fuzzy time series”, Cybernetics
and Systems, vol. 33, no. 1, pp. 1-16, 2002.
[9] C. H. Cheng, J. R. Chang, and C. A. Yen,
“Entropy-based and trapezoid fuzzification
fuzzy time series approaches for forecasting
IT project cost”, Technological Forecasting &
Social Change, vol. 73, pp. 524-542, 2006.
[10] Y. L. Huang, S. J. Horng, M. He, P. Fan, T.
W. Kao, M. K. Khan, and I. H. Kuo, “A
hybrid forecasting model for enrollments
based on aggregated fuzzy time series and
particle swarm optimization”, Expert Systems
with Applications, vol.38, no. 7, pp. 8014-
8023, 2011.
[11] K. Huarng, “Heuristic models of fuzzy time
series for forecasting”, Fuzzy Sets and
Systems, vol. 123, no. 3, pp. 369-386, 2001.
[12] N. Kumar, S. Ahuja, V. Kumar, and A.
Kumar, “Fuzzy time series forecasting of
wheat production”, International Journal on
Computer Science and Engineering, vol. 2,
no. 3, pp. 635-640, 2010.
[13] D. Ortiz-Arroyo, and J. R. Poulsen, “A
weighted fuzzy time series forecasting
model”, Indian Journal of Science and
Technology, vol. 11, no. 27, pp. 1–11, 2018.
[14] J. R. Poulsen, Fuzzy Time Series Forecasting
Developing a New Forecasting Model
Based on High Order Fuzzy Time Series.
AAUE: CIS 4, 2009.
[15] Q. Song, and B. S. Chissom, “Forecasting
enrollments with fuzzy time series part I”,
Fuzzy Sets and Systems, vol. 54, pp. 269-277,
1993.
[16] Q. Song, and B. S. Chissom, “Forecasting
enrollments with fuzzy time series part II”,
Fuzzy Sets and Systems, vol. 62, pp. 1-8.,
1994.
[17] V. R. Uslu, E. Bas, U. Yolcu, and E. Egrioglu,
“A fuzzy time series approach based on
weights determined by the number of
recurrences of fuzzy relations”, Swarm and
Evolutionary Computation, vol. 15, pp. 19-26,
2014.
[18] K. D. Lewis, Methods for Forecasting
Economic Indicators. Moscow: Finance and
Statistics, 1986 (in Russian).
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APPENDIX
Table 5. 1st Order Time Series Predictive Model
Date
Data
FS
Fuzzy output
Predict
26.10.2022
77.67
A55
-
-
27.10.2022
73.90
A50
A47 A50
72.36
28.10.2022
65.97
A41
A41A44A60 A66A67A69
79.88
29.10.2022
73.42
A50
A39 A50
69.14
30.10.2022
68.91
A44
A41 A44A60 A66 A67A69
79.88
31.10.2022
70.01
A46
A46
70.35
01.11.2022
66.53
A41
A41
66.32
02.11.2022
64.66
A39
A39 A50
69.14
03.11.2022
58.38
A31
A31
58.27
04.11.2022
56.76
A29
A29
56.66
05.11.2022
64.19
A38
A25 A38
58.67
06.11.2022
73.83
A50
A50
73.57
07.11.2022
81.71
A60
A41A44A60A66A67A69
79.88
08.11.2022
77.55
A55
A55 A59 A61
80.28
09.11.2022
71.04
A47
A47 A50
72.36
10.11.2022
74.92
A52
A52 A59
78.00
11.11.2022
87.83
A68
A42 A59 A68
78.67
12.11.2022
83.09
A62
A12 A50 A62
66.59
13.11.2022
69.22
A45
A45 A52 A67 A68
80.01
14.11.2022
69.26
A45
A45 A51
71.96
15.11.2022
74.44
A51
A45 A51
71.96
16.11.2022
83.68
A63
A63
84.04
17.11.2022
61.18
A35
A35 A59 A70
77.33
18.11.2022
48.49
A19
A19
48.61
19.11.2022
49.53
A20
A20 A32
54.24
20.11.2022
54.39
A26
A26
54.24
21.11.2022
56.31
A29
A29
56.66
22.11.2022
53.11
A25
A25 A38
58.67
23.11.2022
34.02
A1
A1
34.11
24.11.2022
71.01
A47
A47
71.16
25.11.2022
81.06
A59
A52 A59
78.00
26.11.2022
80.30
A58
A57 A58 A60 A66 A76
84.36
27.11.2022
75.55
A52
A52 A59
78.00
28.11.2022
81.04
A59
A42 A59 A68
78.67
29.11.2022
86.75
A66
A57 A58 A60 A66 A76
84.36
30.11.2022
94.60
A76
A62 A72 A76
89.68
01.12.2022
93.21
A74
A71 A74
91.69
02.12.2022
88.62
A69
A69
88.87
03.12.2022
90.42
A71
A59 A62 A70 A71
86.05
04.12.2022
91.97
A73
A62 A66 A71 A73
88.07
05.12.2022
92.45
A73
A67 A73
89.68
06.12.2022
92.02
A73
A67 A73
89.68
07.12.2022
87.17
A67
A67 A73
89.68
08.12.2022
84.37
A63
A63 A69 A72
88.07
09.12.2022
89.83
A70
A35 A59 A70
77.33
10.12.2022
87.42
A67
A67 A69
88.07
11.12.2022
88.62
A69
A63 A69 A72
88.07
12.12.2022
83.09
A62
A59 A62 A70 A71
86.05
13.12.2022
88.14
A68
A45 A52 A67 A68
80.01
14.12.2022
73.79
A50
A12 A50 A62
66.59
15.12.2022
87.02
A67
A41A44A60A66A67A69
79.88
16.12.2022
88.62
A69
A63 A69 A72
88.07
17.12.2022
89.75
A70
A59 A62 A70 A71
86.05
18.12.2022
89.23
A69
A67 A69
88.07
19.12.2022
80.50
A59
A59 A62 A70 A71
86.05
20.12.2022
94.60
A76
A57 A58 A60 A66 A76
84.36
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Date
Data
FS
Fuzzy output
Predict
21.12.2022
90.73
A71
A71 A74
91.69
22.12.2022
83.48
A62
A62 A66 A71 A73
88.07
23.12.2022
87.07
A67
A45 A52 A67 A68
80.01
24.12.2022
91.48
A72
A63 A69 A72
88.07
25.12.2022
82.08
A61
A61 A64
83.64
26.12.2022
86.69
A66
A61 A63 A66
84.31
27.12.2022
83.60
A62
A62 A72 A76
89.68
28.12.2022
74.86
A52
A45 A52 A67 A68
80.01
29.12.2022
66.79
A42
A42 A59 A68
78.67
30.12.2022
73.19
A50
A50
73.57
31.12.2022
72.24
A69
A41A44A60A66A67A69
79.88
01.01.2023
62.00
A62
A59 A62 A70 A71
86.05
02.01.2023
49.43
A68
A45 A52 A67 A68
80.01
03.01.2023
43.34
A12
A12 A50 A62
66.59
04.01.2023
42.91
A12
A12 A19
45.79
05.01.2023
48.47
A19
A12 A19
45.79
06.01.2023
59.03
A32
A20 A32
54.24
07.01.2023
42.49
A11
A11
42.16
08.01.2023
90.67
A71
A71
90.48
09.01.2023
90.46
A71
A62 A66 A71 A73
88.07
10.01.2023
86.47
A66
A62 A66 A71 A73
88.07
11.01.2023
91.18
A72
A62 A72 A76
89.68
12.01.2023
85.03
A64
A61 A64
83.64
13.01.2023
81.73
A60
A60
81.63
14.01.2023
81.13
A59
A55 A59 A61
80.28
15.01.2023
79.92
A58
A57 A58 A60 A66 A76
84.36
16.01.2023
81.19
A59
A52 A59
78.00
17.01.2023
81.59
A60
A57 A58 A60 A66 A76
84.36
18.01.2023
82.55
A61
A55 A59 A61
80.28
19.01.2023
82.78
A61
A61 A63 A66
84.31
20.01.2023
83.78
A63
A61 A63 A66
84.31
21.01.2023
80.82
A59
A35 A59 A70
77.33
22.01.2023
79.05
A57
A57 A58 A60 A66 A76
84.36
23.01.2023
73.93
A50
A50
73.57
24.01.2023
86.75
A66
A41A44A60A66A67A69
79.88
MSE1
49.16
MAPE1
6.44
MPE1
-2.03
Table 6. 2nd Order Time Series Predictive Model
Date
Data
FS
Fuzzy output
Predict
26.10.2022
77.67
A55
-
-
27.10.2022
73.90
A50
-
-
28.10.2022
65.97
A41
A41
66.32
29.10.2022
73.42
A50
A50
73.57
30.10.2022
68.91
A44
A44
68.74
31.10.2022
70.01
A46
A46
70.35
01.11.2022
66.53
A41
A41
66.32
02.11.2022
64.66
A39
A39
64.71
03.11.2022
58.38
A31
A31
58.27
04.11.2022
56.76
A29
A29
56.66
05.11.2022
64.19
A38
A38
63.91
06.11.2022
73.83
A50
A50
73.57
07.11.2022
81.71
A60
A60
81.63
08.11.2022
77.55
A55
A55
77.60
09.11.2022
71.04
A47
A47
71.16
10.11.2022
74.92
A52
A52
75.18
11.11.2022
87.83
A68
A68
88.07
12.11.2022
83.09
A62
A62
83.24
13.11.2022
69.22
A45
A45
69.54
14.11.2022
69.26
A45
A45
69.54
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382
Volume 21, 2024
Date
Data
FS
Fuzzy output
Predict
15.11.2022
74.44
A51
A51
74.38
16.11.2022
83.68
A63
A63
84.04
17.11.2022
61.18
A35
A35
61.49
18.11.2022
48.49
A19
A19
48.61
19.11.2022
49.53
A20
A20
49.41
20.11.2022
54.39
A26
A26
54.24
21.11.2022
56.31
A29
A29
56.66
22.11.2022
53.11
A25
A25
53.44
23.11.2022
34.02
A1
A1
34.11
24.11.2022
71.01
A47
A47
71.16
25.11.2022
81.06
A59
A59
80.82
26.11.2022
80.30
A58
A58
80.01
27.11.2022
75.55
A52
A52 A59
78.00
28.11.2022
81.04
A59
A59
80.82
29.11.2022
86.75
A66
A66
86.46
30.11.2022
94.60
A76
A76
94.51
01.12.2022
93.21
A74
A74
92.90
02.12.2022
88.62
A69
A69
88.87
03.12.2022
90.42
A71
A71
90.48
04.12.2022
91.97
A73
A73
92.10
05.12.2022
92.45
A73
A73
92.10
06.12.2022
92.02
A73
A73 A67
89.68
07.12.2022
87.17
A67
A73 A67
89.68
08.12.2022
84.37
A63
A63
84.04
09.12.2022
89.83
A70
A70
89.68
10.12.2022
87.42
A67
A67
87.26
11.12.2022
88.62
A69
A69
88.87
12.12.2022
83.09
A62
A62
83.24
13.12.2022
88.14
A68
A68
88.07
14.12.2022
73.79
A50
A12 A50
58.27
15.12.2022
87.02
A67
A67
87.26
16.12.2022
88.62
A69
A69
88.87
17.12.2022
89.75
A70
A70
89.68
18.12.2022
89.23
A69
A69
88.87
19.12.2022
80.50
A59
A59
80.82
20.12.2022
94.60
A76
A76
94.51
21.12.2022
90.73
A71
A71
90.48
22.12.2022
83.48
A62
A62
83.24
23.12.2022
87.07
A67
A67
87.26
24.12.2022
91.48
A72
A72
91.29
25.12.2022
82.08
A61
A61
82.43
26.12.2022
86.69
A66
A66
86.46
27.12.2022
83.60
A62
A62
83.24
28.12.2022
74.86
A52
A52
75.18
29.12.2022
66.79
A42
A42
67.13
30.12.2022
73.19
A50
A50
73.57
31.12.2022
72.24
A69
A69
88.87
01.01.2023
62.00
A62
A62
83.24
02.01.2023
49.43
A68
A68
88.07
03.01.2023
43.34
A12
A12 A50
58.27
04.01.2023
42.91
A12
A12
42.97
05.01.2023
48.47
A19
A19
48.61
06.01.2023
59.03
A32
A32
59.08
07.01.2023
42.49
A11
A11
42.16
08.01.2023
90.67
A71
A71
90.48
09.01.2023
90.46
A71
A71
90.48
10.01.2023
86.47
A66
A66
86.46
11.01.2023
91.18
A72
A72
91.29
12.01.2023
85.03
A64
A64
84.85
13.01.2023
81.73
A60
A60
81.63
14.01.2023
81.13
A59
A59
80.82
15.01.2023
79.92
A58
A58
80.01
16.01.2023
81.19
A59
A52 A59
78.00
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383
Volume 21, 2024
Date
Data
FS
Fuzzy output
Predict
17.01.2023
81.59
A60
A60
81.63
18.01.2023
82.55
A61
A61
82.43
19.01.2023
82.78
A61
A61
82.43
20.01.2023
83.78
A63
A63
84.04
21.01.2023
80.82
A59
A59
80.82
22.01.2023
79.05
A57
A57
79.21
23.01.2023
73.93
A50
A50
73.57
24.01.2023
86.75
A66
A66
86.46
MSE2
30.52
MAPE2
2.53
MPE2
-1.68
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This work was supported by the Azerbaijan Science
Foundation - Grant AEF-MQM-QA-1-2021-
4(41)-8/04/1-M-04.
Conflict of Interest
The authors have no conflicts of interest to declare.
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WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS
DOI: 10.37394/23209.2024.21.35
Elchin Aliyev, Ramin Rzayev,
Asgar Almasov, Abulfat Rahmanov
E-ISSN: 2224-3402
384
Volume 21, 2024