Implementation of Fuzzy C-Means in Investor Group in the Stock
Market Post-Covid-19 Pandemic
AISYAH ARYANDANI1, SOLIMUN2, NURJANNAH3,
ADJI ACHMAD RINALDO FERNANDES4, ACHMAD EFENDI5
Department of Statistics, Faculty of Mathematics and Science,
Brawijaya University,
Jl. Veteran, Malang 65145 East Java,
INDONESIA
Abstract: - This study aims to implement fuzzy c-means for groups of investors in the stock market post-covid-
19 pandemic. The data used in this study is primary data generated by a Likert scale. Measurement of variables
in primary data using the average score of each item. The sample selection of 100 investors is because it
follows the central limit theory which says that the sampling distribution curve (for a sample size of 30 or
more) will center on the population parameter values and will have all the properties of a normal distribution.
This study uses an analytical method, namely fuzzy c-means. The results obtained in this study are the grouping
of data into various types depending on the data for each parameter owned by the type of stock. The number of
iterations is also very dependent on the value of the cluster center determined in the first iteration. Originality in
this study is the object of research, namely post-pandemic stock market investors using a fairly reliable data
grouping algorithm, namely Fuzzy C-Means, the algorithm groups data based on the characteristics of the data
they have.
Key-Words: - Fuzzy C-Means, Investors, Pandemic, Stock Market.
Received: August 15, 2021. Revised: May 7, 2022. Accepted: May 24, 2022. Published: June 17, 2022.
1 Introduction
According to, Solimun [1], the measurement of
population characteristics to be investigated must
be known comprehensively and very rarely
research only uses one variable. Therefore,
multivariate analysis is needed in measuring the
characteristics in this study. One of the commonly
used multivariate analysis methods is cluster
analysis. Cluster analysis has the aim of grouping
objects based on their similar characteristics.
Grouping with cluster analysis is divided into two
methods, namely Hierarchy and Non Hierarchy
Cluster Analysis methods. In the Non Hierarchy
method, one simple method that is often used is the
K-Means cluster method. The K-Means cluster
method is a hard clustering method that is often
used, where the grouping of each object is assigned
to only one cluster. However, at one time the hard
clustering method could not be carried out because
an object was located between two or more
clusters. So that a grouping method appears by
considering the degree of membership and includes
a fuzzy set as a weighting basis called fuzzy
clustering. One of the fuzzy clustering methods that
is often used is the Fuzzy C-means method
In the Fuzzy C-means method, an object tends
to become a member of a cluster based on the
highest membership degree value. The Fuzzy C-
Means method is often used in grouping because it
gives good results in determining the membership
of an object that has the potential to become a
member of two or more clusters. So with this fuzzy
cluster method, you get a deep understanding of
several investors who are grouped based on the
characteristics of the factors that affect stock
investment after the COVID-19 pandemic.
In the economic development of a country, it
takes a lot of money or funds. These funds can be
obtained from loans or own capital, which in its use
the funds can be allocated as an investment, where
investment here can be interpreted as investment
for one or more assets owned and usually for a long
period of time in the hope of getting profits in the
future. come. With regard to investment in the
capital market, the Indonesian government
considers that the capital market is a means that can
support the acceleration of Indonesia's economic
development. This is possible because the capital
market raises the movement of long-term funds
from the public (investors) which are then
channeled to productive sectors with the hope that
these sectors can develop and generate new jobs for
the community. The role of the capital market for
individuals, companies, and the economy, a
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country must have a good (healthy) capital market.
The capital market will run well if the information
needed by the parties involved can be obtained
quickly, precisely, accurately, continuously, and
efficiently. A capital market that can function
properly (healthy) will be able to improve
economic performance through increasing national
income, creating job opportunities, and distributing
development results that are felt by the community.
One aspect that will be assessed by investors is
financial performance. In principle, the better the
company's performance in generating profits, the
higher the demand for these shares, which in turn
will increase the company's share price. The stock
market price is a measure of the company's
performance index, 3 which is how far the
management has managed to manage the company
on behalf of the shareholders. Thus the stock price
in the capital market is an indicator of company
value, namely how to increase shareholder wealth
which is the company's general goal.
Stock prices always change every day even
every second the stock price can change. Therefore,
investors must be able to pay attention to the
factors that affect stock prices. The price of a share
can be determined according to the law of supply
and demand. The more people who buy a stock, the
stock price tends to move up. Vice versa, the more
people who sell the shares of a company, the stock
price tends to move down. One form of investment
in the capital market is stocks. Prior to investing in
stocks, individuals or organizations must ensure
that the investments made are appropriate. This
means that he must assess various alternatives that
will bring positive returns in the future, both in the
form of dividends, namely withdrawals or income
based on the profits obtained by the company
whose shares we own, as well as in the form of
capital gains, namely the excess of the selling price
of the purchase price, Saleh [2].
This study will apply fuzzy c-means to groups
of investors in the stock market post-covid-19
pandemic. By conducting research, researchers
hope to know the group of investors in the stock
market from each type of stock so that they can
find out which types of stocks are sustainable after
the COVID-19 pandemic. The data used in this
study is primary data generated by a Likert scale.
Originality in this study is the object of research,
namely investors in the stock market after the
COVID-19 pandemic. Based on this description,
research on the application of fuzzy c-means to
groups of investors in the stock market after the
COVID-19 pandemic is important.
2 Literature Review
2.1 Cluster Analysis
A newly developed technique to solve data analysis
problems is the cluster analysis technique. This
technique will look for categories or patterns of
sample data (data sets) based on the process of
forming homogeneous data groups called clusters.
Cluster analysis is a class of techniques used to
classify objects or cases (respondents) into
relatively homogeneous groups, called clusters.
Objects/cases in each group tend to be similar to
each other and different (not the same) from objects
from other clusters. Cluster analysis is also called
classification analysis or numerical taxonomy,
Supranto [3].
Cluster analysis is an analytical method in
statistics that is used to build groups or clusters of
multivariate data objects, Hardle and Simar [4].
The main purpose of cluster analysis is to group
objects based on the similarity of characteristics
between these objects. According to Mattjik and
Sumertajaya, [5], cluster analysis is a method in
multiple variable analysis that aims to classify units
of observation into groups based on variables. The
characteristics of a good cluster are that it has high
homogeneity (similarity) between its members in
one cluster (within-cluster) and has high
heterogeneity (difference) between one cluster and
another (between cluster).
According to Supranto, [3] cluster analysis is
referred to as classification analysis or numerical
taxonomy, with a clustering procedure in which
each object only belongs to one cluster, there is no
overlapping or interaction. In general, cluster
analysis is divided into two methods, namely the
hierarchical method and the non-hierarchical
method. The difference between the two methods is
in determining the number of groups or clusters. If
the non-hierarchical method in determining the
number of clusters is determined in advance
according to the wishes of the researcher, then the
hierarchical method goes through a gradual
grouping process such as forming a kind of tree
with levels.
2.2 Fuzzy Logic
From one dataset, many prediction models can be
obtained either using different techniques or using
similar algorithms. Each model then produces
predictions that can differ from one another. The
ensemble learning approach combines these
various predictions into one final prediction.
Ensemble techniques that rely on variations from
the random forest and boosting approaches can
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provide predictions with excellent accuracy.
Random forest works by making ensemble
composing models in such a way that various
possibilities can be optimally accommodated while
boosting works iteratively so that unpredictable
cases are no longer a problem.
The ensemble method can reduce classification
errors effectively, and is believed to have good
performance compared to using a single classifier.
The ensemble method is an algorithm in Machine
Learning where this algorithm combines several
models to achieve a higher generalization
performance than a single model can do (Peter,
2014). The main idea of the ensemble method is to
combine several sets of models that solve the same
problem to get more accurate model (Aziz, 2020).
2.3 Fuzzy C-Means
Fuzzy clustering is a grouping technique in
determining clusters based on distance using a
fuzzy membership function. This method is a
development of partitional with fuzzy weighting
that performs grouping even though the data groups
are not clearly distributed. According to,
Kusumadewi and Purnomo [7]. Fuzzy clustering is
a technique for determining the optimal cluster in a
vector based on the Euclidian normal form for
vector distances. According to, Kusumadewi [8]
Fuzzy C-Means is a method of grouping data where
each data is in a group determined by the
membership value. According to Karim, Reda, and
Georges [9] Fuzzy C-Means is a grouping method
that allows one part of the data to have two or more
groups.
The Fuzzy C-Means algorithm was first
proposed by Dunn in 1973 and then updated by
Bezdek in 1981. This algorithm is one of the most
popular soft clustering techniques using a data
point approach where the center point of the cluster
will always be updated according to the
membership value of the cluster. existing data and
besides that the fuzzy c-means algorithm is also an
algorithm that works using a fuzzy model so that it
allows all data from all group members to be
formed with different membership degrees between
0 and 1, Bora and Gupta [10]; Sanmorino [11]. The
Fuzzy C-Means method basically has the aim of
minimizing the function and getting the center of
the cluster which will later be used to find out the
data that enters a cluster.
The basic concept in Fuzzy C-Means is to
determine the center of the cluster, which will mark
the average location for each cluster. Each data
point has a degree of membership for each cluster
that is formed. In the initial conditions, the cluster
center is still not accurate, therefore, improvements
are made to the cluster center and the degree of
membership of each data point repeatedly until it is
at the right point. This iteration is based on the
minimization of the objective function that
describes the distance from a given data point to
the center of the cluster which is weighted by the
degree of membership of the data point. From this
iteration, it can be seen that the longer the cluster
center will move to the right location, Kusumadewi
[7]. In fuzzy theory, membership of a data is not
expressly stated by giving a value of 1 if it is a
member, and 0 if it is not a member, but is
expressed by a degree of membership whose value
range is between 0-1. The value is 0 if it is not a
member at all and 1 if it is a full or partial member
in a set. A data can be a member in several sets
which is expressed by the value of the degree of
membership of a set, Prasetyo and Sutisna [12].
Fuzzy C-Means relates to the concept of the
similarity of functions of adjacent objects and finds
the center point of the cluster as a prototype. For
some data objects, there is no limitation on only
one class, but the data can be grouped based on the
degree of membership, which is between 0 and 1
which indicates partial membership of the data,
Merliana [13]. Fuzzy C-Means cluster analysis is a
cluster technique that is widely used in cluster
applications. Fuzzy C-Means applies fuzzy
grouping, each object can be a member of several
clusters with different degrees of membership in
each cluster. Fuzzy C-Means is an iterative
algorithm that applies iteration to the data cluster
process. The purpose of Fuzzy C-Means is to get
the center of the cluster which will later be used to
find out the data that enters a cluster. In fuzzy logic
there is a fuzzy cluster which is one method to
determine the optimal cluster in a vector space
based on the Euclidean normal form for the
distance between vectors.
2.4 Stock Market
Stock Market is an activity related to the public
offering and trading of Securities, public
companies relating to the securities they issue, as
well as institutions and professions related to
Securities. The stock market consists of the
primary/primary market and the secondary market
(Law no. 21 of 2011 concerning OJK). The primary
market is the market for newly issued securities.
The secondary market is the market for trading
securities that have existed (old securities) on the
stock exchange and as a means of buying and
selling securities between investors.
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Economic growth, which includes economic
growth, purchasing power of the society,
investment prospects in the area of operations.
Social and political situations, which includes
demography, social conditions, culture, politics,
stability in terms of security of the area of
operations, Fernandes and Solimun [14]. In the
stock market, the most important thing investors
should know is the stock price. Share price is the
price of a share that occurs on the stock market at a
certain time determined by market participants and
determined by the demand and supply of the
relevant shares in the capital market, Jogiyanto
[15]. The share price determines shareholder
wealth. Maximizing shareholder wealth translates
into maximizing the company's share price. The
stock price at any given time will depend on the
cash flows expected to be received in the future by
the "average" investor if the investor buys the
stock, Houston [16].
The nation’s competitiveness means the role of
existing human resources in Indonesia in
contributing to world market through products
and/or services produced by the ability of
Indonesian human resources through mastery of
technology, science and skills, Sumardi and
Fernandes [17]. Stock prices in the market are
always fluctuating, or always changing. Several
studies link stock prices with company
performance. If the company's performance is
good, the stock price will also increase. The
company's performance can be seen from its
financial statements. Usually companies that have
gone public have an obligation to publish their
financial statements at least once every three
months. When there is publication of financial
statements, investors will see the performance of
the financial statements of the company. If the
company's profits increase, investors will be
interested in buying the shares, the demand for
these shares will also increase, so the stock price
will rise. This applies vice versa, if the company
suffers a loss then the stock price will tend to fall.
The article that regulates the stock market is
stated in Law no. 8 of 1995 article 1 point 13, "the
stock market is a public offering activity carried out
in securities trading, political companies,
institutions and professions related to securities
have been issued", Dyasartika [18]. Tandelilin [19],
defines the stock market as a place used to trade
securities between people who have a lot of funds
or excess funds and people who lack funds or need
funds which usually have an age of more than 1
year.
Shares are a sign of participation or ownership
of individual investors or institutional investors or
traders on investments or a number of funds
invested in a company, Musdalifah, Mintarti and
Maryam [20]. The stock market is a place where
government and industry can raise long-term
capital and investors can buy and sell securities,
Saraswati [21]. In addition, there is a positive
relationship between an efficient stock market and
economic growth in both the short and long term.
This is in line with the statement that the stock
market will not be able to run away from the
economic conditions of a country, Filbert and
Prasetya [22].
2.5 Covid-19
In December 2019, the corona virus or known as
Covid-19 appeared in Wuhan, China. This virus
spreads very quickly and infects not only Chinese
citizens but spreads to all corners of the world
including Indonesia. In Indonesia, the first case of
death due to COVID-19 occurred in March 2020,
after which new victims emerged, both positive for
COVID-19, as well as PDP (Patients Under
Supervision) and ODP (People Under Supervision).
Until now, the number of positive patients
continues to increase (Covid-19, 2020). Covid-19
has an incubation period of 2-14 days in the human
body with complaints resembling the flu, ranging
from fever, cough, runny nose, chest pain,
shortness of breath, to pneumonia, acute respiratory
distress syndrome, skepticism, and even death. The
pandemic has caused the International Monetary
Agency (IMF) to predict a global economic
slowdown will occur.
During the Covid-19 pandemic, which spread
all over the world. At first this did not affect the
stock market, but with more confirmed victims the
stock market reacted negatively, Khan, Ali, Shi,
Siddique, Nabi, Hu & Han [23]. This also caused
prices in the stock market to decline, especially
after WHO declared that Covid-19 was a pandemic
and caused negative abnormal returns, Alali [24].
3 Results and Discussion
3.1 Research Method
The statistical application should not be
complicated and difficult, it but must rather be
simple and easy, so that it is user-friendly, Solimun
and Fernandes [25]. The data used in this study is
primary data. The variables used in this study are as
follows: Rupiah Exchange Rate Fluctuations,
Government Policy and Market Manipulation
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Factors. The time of data collection was on January
2, 2022. The data was obtained by simulation by
generating data using a Likert scale. Measurement
of variables in primary data using the average score
of each item. The sampling technique used is
purposive sampling. The object of observation is
investors in the stock market as many as 100
respondents. The sample selection of 100 investors
is because it follows the central limit theory which
says that the sampling distribution curve (for a
sample size of 30 or more) will center on the
population parameter values and will have all the
properties of a normal distribution. This study uses
the fuzzy c-means method. The research path
diagram of the fuzzy c-means method is shown in
Figure 1.
Data Acquisition Data Analysis with
FCM Clustering Result
Fig. 1: Research Path Diagram Fuzzy C-Means.
3.2 Data Acquisition
Grouping will be carried out on the data that has
been generated as many as 10000 investors into 3
groups where the definition of each group is
determined by the researcher. Grouping is done
based on parameters according to the case to be
analyzed. For example, to group investors by type
of stock against Fluctuations in the Rupiah
Exchange Rate and the value of parameters such as
the number of investors from before the pandemic
and the number of investors who dare to invest
post-pandemic will be calculated. More details can
be seen in Table 1.
Table 1. Number of investors after the pandemic on
Rupiah Exchange Rate Fluctuations in Indonesia.
No.
Stock Type
Number of
investors
after the
pandemic
1
Blue Chip
Stocks
429
2
Income Stocks
456
3
Growth Stocks
6676
4
Speculative
Stocks
1031
5
Counter
Cylical
885
Meanwhile, the grouping of investors based on
the type of stock against Government Policy will be
calculated based on the parameters of the number
of investors from before the pandemic and the
number of investors who dare to invest after the
pandemic. More details can be seen in Table 2.
Table 2. Number of investors after the pandemic on
Government Policy in Indonesia.
No.
Stock Type
Number of
investors from
before the
pandemic
Number of
investors
after the
pandemic
1
Blue Chip
Stocks
2847
1057
2
Income Stocks
774
280
3
Growth Stocks
1339
1021
4
Speculative
Stocks
5040
1277
5
Counter Cylical
2983
2034
The grouping of investors based on the type of
stock against the Market Manipulation Factor will
be calculated based on the parameters of the
number of investors from before the pandemic and
the number of investors who dare to invest after the
pandemic. More details can be seen in Table 3.
Table 3. Number of investors after the pandemic on
Market Manipulation Factors in Indonesia
No.
Stock Type
Number of
investors from
before the
pandemic
Number of
investors
after the
pandemic
1
Blue Chip
Stocks
3471
1272
2
Income Stocks
441
380
3
Growth Stocks
1739
1421
4
Speculative
Stocks
3240
2147
5
Counter Cylical
3923
1834
3.3 Data Analysis with Fuzzy C-Means
Fuzzy logic is an appropriate way to map an input
space into an output space, for example:
1) The warehousing manager tells the production
manager how much inventory is at the end of
this week, then the production manager will
determine the number of items that must be
produced tomorrow.
2) Restaurant services provide services to guests,
then guests will give appropriate tips on whether
or not the services provided.
3) You tell me how cool you want the room to be,
I will adjust the rotation of the fan in this room.
Fuzzy clustering is a technique to determine
the optimal cluster in a vector space based on the
Euclidian normal form for the distance between
vectors. Fuzzy clustering is very useful for fuzzy
modeling, especially in identifying fuzzy rules. The
clustering method is a grouping of data and their
parameters in groups according to the tendency of
the nature of each data (similarity of properties).
The concept of Fuzzy C-Means first is to
determine the center of the cluster, which will mark
the average location for each cluster. In the initial
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conditions, the center of this cluster is still not
accurate. Each data point has a degree of
membership for each cluster. By fixing the center
of the cluster and the degree of membership of each
data point repeatedly, it will be seen that the center
of the cluster will move to the right location. This
iteration is based on the minimization of the
objective function that describes the distance from
a given data point to the center of the cluster which
is weighted by the degree of membership of the
data point.
The FCM algorithm flowchart is as follows:
1) Entering the data to be grouped x, in the
form of a matrix measuring n x m serves to
determine the amount of data and the
attributes of each data to be used:
n = number of data samples
m = attribute of each data
(i 1,2,...n)atribute j(j 1,...,m)
ij
X sampledata i
2) Determine:
Number of clusters = c;
Weight power = w;
Maximum Iteration = Maxlter
Smallest expected error =
Initial Objective Function =
00P
Initial iteration = t = 1
Based on to determine the initial value of
the equation, before processing the data.
3) Generating random numbers
: , 1,2,... ; 1,2,...
ik i n k c
; function as
elements of the initial partition matrix U.
Counting the number of each column
(attribute):
1
c
j ik
k
Q
(1)
Calculate:
ik
ik
j
Q
(2)
4) Calculate the center of the -th cluster:
kj
V
,
with k=1,2,...c; and j=1,2,...,m; The
determination of the cluster center is used
to mark the average location for each
cluster with inaccurate initial conditions.
*
1
1
nw
ik kj
k
kj nw
ik
k
X
V
(3)
5) Calculating the objective function in the
iteration = t, Pt : the calculation of the
objective function is used to describe the
distance from a given data point to the
center of the cluster which is weighted by
the degree of membership of the data point.
22
1 1 1
n c m
ij kj ik
k i j
P X V




(4)
6) Calculate the partition matrix change
1
21
1
1
21
11
mw
ij kj
j
ik
cm w
ij kj
kj
XV
XV








(5)
With: i=1,3,…,n; and k=1,2,…,c
7) Check stop condition
a. If
1tt
P P atau t MaxIter
then the
iteration stops
b. Otherwise: t=t+1, repeat step 4
3.4 Clustering Results
Clustering results in the form of grouping investors
based on the similarity of the data they have, the
types of shares will be grouped into 3 groups.
Optimum clustering results will depend on the
value of the initial partition matrix which has a
range of 0-1.
4 Result and Discussion
The results and discussion in this study refer to the
Fuzzy C-Means algorithm which has been
described in the Research Methodology section.
The grouping of investors here is based on the type
of stock against Rupiah Exchange Rate
Fluctuations, Government Policies and Market
Manipulation Factors in Indonesia. Number of
Investors After The Pandemic On Rupiah
Exchange Rate Fluctuations in Indonesia:
1) The data to be entered is as shown in Table 1
2) Determine:
Number of clusters = 3;
Weight power = 2;
Maximum Iteration = MaxIter=100
Smallest expected error = 0.1
Initial Objective Function = Po = 0;
Initial iteration = t=1;
3) Generating random numbers to fill the
elements in the partition matrix, the value
range is 0-1. The number of random numbers
is the number of data multiplied by the number
of clusters, so the number is 20 values, it can
be seen in Table 4.
4)
Table 4. Initial Pertition Matrix
0.90
0.83
0.27
0.21
0.86
0.76
0.28
0.07
0.52
0.70
0.48
0.15
0.52
0.68
0.96
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5) Calculating the cluster center with Equation
(3), then the following results are obtained
Table 5. Center Cluster -i
14.993
28,936.519
4,167.959
19.562
43,088.531
7,439.156
17.829
41,863.591
10,837.832
6) Calculating the objective function can be
calculated using Equation (3), the value
obtained is 4,318,556,757.28
7) Calculating the change in the partition matrix
using Equation (5), we get a value as shown in
Table 6. The value in this partition matrix
change will then be used as the center of the
cluster in the next iteration
Table 6. Changes in the partition matrix
0.12
0.61
0.27
0.15
0.47
0.38
0.23
0.39
0.38
0.48
0.22
0.30
0.64
0.17
0.19
8) Check the stop condition, where the objective
function value in the current iteration is
reduced by the objective function value in the
previous iteration. If the value is greater than
0.1 then the iteration will continue, otherwise
the iteration will stop. From the results of the
calculation of the objective function of the
current iteration minus the previous iteration,
it turns out that the value is still greater than
0.1 so that the iteration continues.
The grouping of investors based on the type of
stock against fluctuations in the rupiah exchange
rate stops until the 60th iteration with the difference
in the value of the objective function obtained at
0.089. The cluster center in the last iteration can be
seen in Table 7. While the results of grouping types
of shares can be seen in Table 8, this grouping is
based on the value of the change in the partition
matrix or better known as the degree of
membership in the last iteration. A type of stock
will enter a cluster if the cluster has the highest
degree of membership.
Table 7. Center of Last Iteration Cluster
9.792091037
16142.46007
5034.628031
22.04496233
50337.02905
4265.125708
31.9057002
91543.68445
16617.23902
Table 8. Investor cluster results by type of stock on
fluctuations in the rupiah exchange rate
Stock Type
Degree of data membership in
the th cluster-
Cluster
1
2
3
1
2
3
Blue Chip
Stocks
0.0526
0.8416
0.1057
*
Income
0.0000
0.0001
0.9998
*
Stocks
0.5062
0.4494
0.0443
*
Growth
Stocks
0.9850
0.0123
0.0026
*
Speculative
Stocks
0.4103
0.5490
0.0406
*
For the case of grouping investors by type of
stock against Government Policy and Market
Manipulation Factors using the same calculation
steps as in the case of grouping investors by type of
stock against fluctuations in the rupiah exchange
rate. The initial partition matrix for each case can
be seen in Table 9 and Table 10. Determination of
the initial partition matrix is done randomly, so the
results will greatly affect the number of iterations.
The case of grouping investors by type of stock
against Government Policy ended in the 34th
iteration with a difference in the value of the
objective function of 0.0954, the results of the
grouping can be seen in Table 11. Meanwhile, the
case of grouping investors by type of stock on
Market Manipulation Factors ended at number 33,
with the difference the objective function value is
0.0374, the results of the grouping can be seen in
Table 12.
Table 9. Initial Partition Matrix of Government
Policy
0.75
0.71
0.91
0.89
0.66
0.30
0.71
0.14
0.25
0.20
0.94
0.84
0.54
0.97
0.04
Table 10. Initial Partition Matrix of Market
Manipulation Factors
0.52
0.02
0.65
0.92
0.35
0.16
0.95
0.98
0.02
0.05
0.21
0.07
0.10
0.51
0.56
Table 11. Investor cluster results by type of stock
on Government Policy
Type Stock
Degree of data membership in
the th cluster-
Cluster
1
2
3
1
2
3
Blue Chip
Stocks
0.5315
0.1344
0.3339
*
Income
0.0036
0.0019
0.9943
*
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DOI: 10.37394/23206.2022.21.49
Aisyah Aryandani, Solimun, Nurjannah,
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Stocks
0.7608
0.2197
0.0194
*
Growth
Stocks
0.0798
0.9116
0.0084
*
Speculative
Stocks
0.9586
0.0357
0.0055
*
Table 12. Investor cluster results by type of stock
on Market Manipulation Factors
Type Stocks
Degree of data membership in
the th cluster-
Cluster
1
2
3
1
2
3
Blue Chip
Stocks
0.5315
0.3339
0.1344
*
Income
0.0036
0.9943
0.0019
*
Stocks
0.7608
0.0194
0.2197
*
Growth
Stocks
0.0798
0.0084
0.9116
*
Speculative
Stocks
0.9586
0.0055
0.0357
*
5 Conclusion
Based on the results and discussion, it can be
concluded that the Fuzzy C-Means method can be
used to classify investors based on the type of stock
on Rupiah Exchange Rate Fluctuations,
Government Policies and Market Manipulation
Factors in Indonesia. The Rupiah Exchange Rate
Fluctuations data groups Stocks and Growth Stocks
in the same group. The other group consists of Blue
Chip Stocks and Speculative Stocks. The type of
Income share becomes its own member in the next
group.
Another case places these types of shares in
different groups, it really depends on the value of
the parameter that is the basis for the grouping.
Because the grouping here is based on the
similarity of the characteristics of the parameters
possessed by these types of shares. The number of
iterations is quite similar in numbers 30 to 35, only
in the case of hypertension the number of iterations
reaches 60. The number of iterations depends on
the value of the initial cluster center. The use of
methods to optimize the determination of cluster
values at the beginning is very necessary so that the
grouping results become more accurate).
References:
[1] Solimun. 2010. Metode Partial Least Square-
PLS. CV Citra Malang, Malang.
[2] Saleh, M. (2009). Penilaian saham PT.
Unilever Indonesia Tbk. pasca akuisisi bisnis
kecap Bango (Doctoral dissertation,
Universitas Gadjah Mada).
[3] Supranto, J. (2004). Analisis Multivariat Arti
dan Interpretasi. Jakarta: Rineka Cipta.
[4] Hardle, W., & Simar, L. (2003). Applied
Multivariate Statistical Analysis, version
29th.
[5] Mattjik, A. A., & Sumertajaya, I. M. (2002).
Design of Experiments with SAS and
Minitab applications.
[6] Syafitri, A., Iwa, G. M., Gunawan, R., &
Ardita, I. M. (2016, November). Fuzzy-PID
simulation on current performance for
Modern Elevator. In 2016 6th IEEE
International Conference on Control System,
Computing and Engineering (ICCSCE) (pp.
403-406). IEEE.
[7] Kusumadewi, S., & Purnomo, H. (2010).
Aplikasi logika fuzzy untuk sistem
pendukung keputusan. Andi Offset,
Yogyakarta.
[8] Kusumadewi, S. (2007). Klasifikasi
Kandungan Nutrisi Bahan Pangan
Menggunakan Fuzzy C-Means. In Seminar
Nasional Aplikasi Teknologi Informasi
(SNATI).
[9] Karim, T., Reda, B., & Georges, H. (2011).
Multi-objective supervisory flow control
based on fuzzy interval arithmetic:
Application for scheduling of manufacturing
systems. Simulation Modelling Practice and
Theory, 19(5), 1371-1383.
[10] Bora, D. J., Gupta, D., & Kumar, A. (2014).
A comparative study between fuzzy
clustering algorithm and hard clustering
algorithm. arXiv preprint arXiv:1404.6059.
[11] Sanmorino, A. (2012). Clustering batik
images using fuzzy c-means algorithm based
on log-average luminance. Computer
Engineering and Applications Journal
(ComEngApp), 1(1), 25-31.
[12] Prasetyo, H., & Sutisna, U. (2014).
Implementasi Algoritma Logika Fuzzy untuk
Sistem Pengaturan Lampu Lalu Lintas
Menggunakan Mikrokontroler. Techno
(Jurnal Fakultas Teknik, Universitas
Muhammadiyah Purwokerto), 15(2), 01-08.
[13] Merliana, N. P. E. (2015). Perbandingan
metode K-Means dengan fuzzy C-Means
untuk analisa karakteristik mahasiswa
berdasarkan kunjungan ke perpustakaan
(Studi kasus Sekolah Tinggi Agama Hindu
Negeri Tampung Penyang Palangka Raya)
(Doctoral dissertation, UAJY).
[14] Fernandes, A. A. R. and Solimun. (2017).
Moderating effects orientation and
innovation strategy on the effect of
uncertainty on the performance of business
WSEAS TRANSACTIONS on MATHEMATICS
DOI: 10.37394/23206.2022.21.49
Aisyah Aryandani, Solimun, Nurjannah,
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E-ISSN: 2224-2880
422
Volume 21, 2022
environment. International Journal of Law
and Management, 59(6), 1211-1219.
[15] Jogiyanto, H. M. (2008). Metodologi
penelitian sistem informasi. Yogyakarta:
Andi Offset.
[16] dan Houston, B. (2010). Dasar-dasar
Manajemen Keuangan. Penerbit Salemba
Empat, Jakarta.
[17] Sumardi, S. and Fernandes, A.A.R. (2018).
The mediating effect of service quality and
organizational commitment on the effect of
management process alignment on higher
education performance in Makassar,
Indonesia. Journal of Organizational Change
Management, 31(2), 410-425.
[18] Dyasartika, D. (2021). Pengaruh Covid-19
Terhadap Perubahan Harga Dan Volume
Perdagangan Saham (Studi Kasus Pada
Perusahaan Farmasi Di Bei Periode
September 2019 s/d SEPTEMBER 2020)
(Doctoral dissertation, Universitas
Muhammadiyah Ponorogo).
[19] Tandelilin, E. (2010). Dasar-dasar
Manajemen Investasi. Diambil dari
http://repository. ut. ac.
id/3823/1/EKMA5312-M1. pdf.
[20] Musdalifah Azis, S. E., Mintarti, S., &
Maryam Nadir, S. E. (2015). Manajemen
Investasi Fundamental, Teknikal, Perilaku
Investor dan Return Saham. Deepublish.
[21] Saraswati, H. (2020). Dampak Pandemi
Covid-19 Terhadap Pasar Saham Di
Indonesia. JAD: Jurnal Riset Akuntansi dan
Keuangan Dewantara, 3(2), 153-163.
[22] Filbert, R., & Prasetya, W. (2017). Investasi
Saham ala Fundamentalis Dunia. Jakarta: PT
Elex Media Komputindo.
[23] Khan, S., Ali, A., Shi, H., Siddique, R., Nabi,
G., Hu, J., ... & Han, G. (2020). COVID-19:
Clinical aspects and therapeutics responses.
Saudi Pharmaceutical Journal, 28(8), 1004-
1008.
[24] AlAli, M. S. (2020). The effect of who
COVID-19 announcement on Asian Stock
Markets returns: an event study analysis.
Journal of Economics and Business, 3(3).
[25] Solimun and Fernandes, A.A.R. (2017),
Investigation the mediating variable: What is
necessary? (case study in management
research), International Journal of Law and
Management, 59(6), 1059-1067.
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