ADI International Conference Series Vol 4 January 2022 p-ISSN : 2774-9576 e-ISSN : 2747-2981 Cheng's Fuzzy Time Series Method Implementation In Predicting The Number Of Covid-19 Positive Cases In Indonesia Andi Rafianto1.
Rum Mohamad Andri2.
Bernadhed3.
Istiningsih4 Information System1,2.
Information Technology3.
Economics4.
AMIKOM Yogyakarta University1,2,3,4 Jl Ringroad Utara.
Condongcatur.
Depok.
Sleman.
Yogyakarta Indonesia
552831,2,3,4
Indonesia1,2,3,4 e-mail: andi.
rafianto@students.
id1, andri@amikom.
bernadtagger@amikom.
id3, istiningsih@amikom.
To cite this document:
Rafianto.
Rasyid.
Bernadhed, & Istiningsih.
ChengAos Fuzzy Time Series Method Implementation In Predicting The Number Of Covid-19 Positive Cases In Indonesia.
Conference Series, 4.
, 15Ae24.
https://doi.
org/10.
34306/conferenceseries.
Hash:ABCIarZm8DR2pMElLeBgPOQJiowrCzsEOgof5XFmwevYEkE8duDE7E76x3d9G Abstract At the beginning of 2020, citizens all around the world were streaked by the Corona Virus (Covid-.
pandemic which caused terror far and near.
Millions of people were infected and thousands more died ever since the World Health Organization or WHO has declared the Corona Virus (Covid-.
as a global pandemic.
Following up on this, the Indonesian government also stated that the Corona Virus problem had become a non-natural national disaster.
The President of the Republic of Indonesia and the Regional Government along with their staffs worked hand in hand to take several tactical steps as an effort to prevent the spread of the Corona Virus (Covid-.
in the community.
In this study, authors use one method to make predictions or forecasting, that is the Cheng Fuzzy Time Series method, to predict the number of Covid-19 cases in Indonesia so that the government can take tactical steps after knowing the predicted number of the case.
The actual data used is the number of Covid-19 case from July 2020 up until October 2020.
From the results of calculations that have been carried out using this method, the conclusion is that the performance is splendid, in the range of MAPE <10, whose error value is 5%.
With 95% value of accuracy.
Keywords: Fuzzy Time Series Cheng.
Prediction.
Covid-19 Cheng's Fuzzy Time Series MethodA n 15 ADI International Conference Series Vol 4 January 2022 p-ISSN : 2774-9576 e-ISSN : 2747-2981 Introduction The outbreak of Coronavirus Diseases 2019 (COVID-.
is currently becoming horrendous news globally.
The World Health Organization (WHO) has declared that the virus is a global pandemic.
Millions of people were infected and thousands died as a result of this Policies such as lockdowns have even been carried out in several countries to prevent the spread of Covid-19.
In Indonesia, the government is trying to take various actions or policy measures to prevent the spread of Covid-19 cases.
If the government can predict the number of positive cases of Covid-19 in the future, it will be easier to make tactical steps to reduce the number of positive cases of Covid-19 that occurred in the country.
In case there were research on methods or algorithms such as Cheng's Fuzzy Time Series to predict the number of positive cases of Covid-19 that occurred in Indonesia, it would be useful for the government to combat the Covid19 outbreak that occurred in Indonesia.
However, there has been no research conducted yet on the FTS Cheng method that has been carried out to predict the number of positive cases of Covid-19 in Indonesia.
From the many existing methods or algorithms, the Fuzzy Time Series Cheng could possibly be By using data on positive cases of Covid-19 in Indonesia in the form of numeric and time series models, it is possible that the Fuzzy Time Series Cheng method is suitable to be But currently there is no research on the use of this method in predicting the number of positive cases of Covid-19 that occurred in Indonesia.
With this description of the problem, authors are conducting a research entitled AuCheng's Fuzzy Time Series Method Implementation in Predicting the Number Of Covid-19 Positive Cases in Indonesia.
Ay Research Method 1 Covid-19 Coronavirus disease 2019 (Covid-.
is a new disease that is caused by a virus from the Coronavirus group, that is SARS-CoV-2 and is often called the Corona Virus.
This disease was first discovered in Wuhan City.
China at the end of December 2019.
The Corona Virus or Covid19 was then transmitted between humans and is spreadring to dozens of countries rapidly, including Indonesia in just a few months .
In Indonesia, the number of positive cases of Covid-19 has infected more than 300,000 people in October 2020.
The usual symptoms of Covid-19 are fatigue, fever, and dry cough.
Then there are colds, sore throats, aches and pains, diarrhea, and nasal congestion.
Some are healthy without symptoms .
2 Fuzzy Time Series Fuzzy Time Series (FTS) was first developed by Song and Chissom in 1993.
FTS is using the Fuzzy principle and it is one of the forecasting methods.
Usually the fuzzy set is equated as a class whose numbers have fuzzy boundaries.
If U is a universal set, then its equation function yaycn = yuNyaycn .
c1 )/yc1 U yuNyaycn .
cycy )/ycycy yaycn = yuNyaycn .
c1 )/yc1 U yuNyaycn .
cycy )/ycycy With yuNyaycn .
cyc ) is the derivative of ycycn ke yaycn along with yuNyaycn .
cyc )yun.
dan 1 O yc O ycy .
is the number of classe.
The derivative value of yuNyaycn .
cyc ) determined according to the following Rule 1 : If the actual data of ycUyc is included in ycyc , then the derivative value of ycyc is 1 , and ycyc 1 is 0.
5 , and if it is not ycyc , and ycyc 1 , it is considered as 0.
Rule 2 : If the actual data of ycUyc ycUyc is included inycycn , 1 O yc O ycy then the derivative value ycyc is 1, whereas ycycOe1 and ycyc 1 are 0.
5, and if it is not ycyc , ycycOe1 and ycyc 1 it is considered Cheng's Fuzzy Time Series MethodA n 16 ADI International Conference Series Vol 4 January 2022 Rule 3 p-ISSN : 2774-9576 e-ISSN : 2747-2981 : If the actual data of ycUyc ycUyc is included inycyc , then the derivative value ycyc is 1, whereas ycycOe1 is 0.
5 , and if it is not ycyc and ycycOe1 it is considered as 0 .
3 Fuzzy Time Series Cheng The FTS Cheng method has a different method from Chen's in making intervals, using a Fuzzy Logical Relationship (FLR) which connects several data and then gives weights if the FLRs are equal.
FTS Cheng's steps are as the following:
Determining the universal set and then divide it into several intervals whose range or distance are the same.
ycO = .
yaycoycaycu ]a .
Interval width formation Calculating the range using the following formula:
ycI = yaycoycaycu Oeyaycoycnycu a .
R is range, yaycoycaycu is the largest data, yaycoycnycu is the least.
For the next step, the universal set is broken down and further divided into several intervals that have the same width.
In determining this interval distance, the Struges formula is applicable.
ya = 1 3.
322 ycoycuyci .
n is the sum of all historical data used.
From these results, several linguistic values will be formed which are used to describe fuzzy sets, that is intervals from the universal set.
(U).
ycO = .
c1 , yc1 .
A , ycya }a .
Determining the width of the interval ycycaycuyciyce .
cI) yco= a .
ycuycycoycayceycyc ycuyce ycaycoycaycyc ycnycuycyceycycycaycoyc.
Calculating the midpoint .
coycuycyceyc ycoycnycoycnyc ycycyycyyceyc ycoycnycoycny.
AA .
With ycn is a Fuzzy set.
From the calculations, the partition of the universal set according to the length of the interval is obtained.
ycycn = .
yaycoycnycu yc.
yc2 = .
aycoycnycu yco.
yaycoycnycu 2yc.
yc3 = .
aycoycnycu 2yco.
yaycoycnycu 3yc.
U ycyco = .
co Oe .
yaycoycnycu ycoyc.
A .
ycoycn = Calculating the Fuzzy set aims to see the number of frequencies that are not the same, with its largest frequency being divided by h equal intervals.
Moreover, the second largest is divided into h-1 intervals that have similarities, and the third one is divided into h-2 which are the same, and so on until it can no longer be divided, and that is the last frequency.
Performing the Fuzzification Supposing that ya1 , ya2 .
A , yaycy is a Fuzzy set whose linguistics value is obtained from the linguictics variable.
, the set is calculated as Fuzzy ya1 , ya2 .
A , yaycy whereas the universal set ycO is as the following :
ya1 = .
/yc1 0.
5/yc2 0/yc3 U 0/ycycy } ya2 = .
5/yc1 1/yc2 0.
5/yc3 U 0/ycycy } ya3 = .
/yc1 0.
5/yc2 1/yc3 U 0/ycycy } U yaycy = .
/yc1 0/yc2 0/yc3 0/yc4 U 0.
5/ycycyOe1 1/ycycy }AA .
Cheng's Fuzzy Time Series MethodA n 17 ADI International Conference Series Vol 4 January 2022 p-ISSN : 2774-9576 e-ISSN : 2747-2981 With ycyc .
cn = 1,2.
A , yc.
is a universal set .
cO) and the symbol "/" is the derivation of yuNyaycn .
cyc ) upon yaycn .
cn = 1,2.
A , yc.
whose value is 0, 0.
5 or 1.
Formig the Fuzzy Logic Relationships (FLR) and Fuzzy Logic Relationships Group (FLRG).
Finding out the correlation between FLR with a historical data.
After the data is Fuzzified, if it uses order one, then the two data are sequential as in yaycn .
c Oe .
and yaycn .
then FLR yaycn Ie yayc .
Relationships are identified based on the results of the fuzzyfication of time series If the variable of time series ycn = ya.
c Oe .
is a fuzzyfication asyayco and ya.
is the result of fuzzification asyayco , then yayco and yayco can be denoted asyayco Ie yayco , with yayco is a current state historical data and yayco is a next state historical data.
If the FLR is forming as ya1 Ie ya3 , ya1 Ie ya4 , ya1 Ie ya5 , accordingly, the FLRG from the previously mentioned FLR is ya1 Ie ya3 , ya4 , ya5 .
Assigning the scale to the same group of Fuzzy Logic relations.
Determining the scale of the FLR relationship into FLRG is by grouping those that have similarity and then give the scale.
FLRs with the same current state .
are grouped and given the scale, then transfer it to the scaled matrix.
The formula is as follows:
ycO = .
c11 yc12 U yc1ycy yc21 yc22 U yc1ycy U yc ycy1 U yc ycy2 ycycnyc
U U
Where (?) is the weighting matrix and is the weight of the matrix in row-ycn and in- yc column with ycn = 1,2.
U , ycy .
yc = 1,2.
U , ycy.
Sending the FLRG weights to a standardized weighting matrix is next, which has the following equation:
ycO O= .
c11 O yc12 O U yc1ycy O yc21 O yc22 O U yc1ycy O U yc ycy1 O U yc ycy2 O ycycnyc O
U U
ycycyycy O .
Where the weighting matrix is standardized with the following formula:
ycycnyc ycycnyc O= Ocycy a .
yc=1 ycycnyc Looking out for defuzzification in case one want to produce a predictive value , the standardized matrix ycO O is multiplied with ycoycn .
coycn is the middle value of the Fuzzy se.
The calculation in the prediction is as follows:
yaycn = ycycn1 O .
co1 ) ycycn2 O .
co2 ) U ycycnycy O .
coycy )a .
With yaycn is the result ofprediction, with the equation of 22.
If the fuzzification from the - ycn period is yaycn , and yaycn is naught from FLR as well as FLRG, it then could be written down as yayc Ie OI, where the maximum value is at ycycn , then the value of the prediction.
aycn )is the middle value ycycn , or can be defined by ycoycn .
4 MAPE Predicting Accuracy MAPE is a relative measure that is widely used to see the percentage of deviations or errors from prediction or forecasting results, the MAPE equation can be seen as follows:
ycAyaycEya = Ocycuycn=1 .
cEyaycn .
ycu With ycEyaycn is the error percentage with the following formula:
ycU Oeya ycEyaycn = yc yc ycu100%a .
ycUyc With ycUyc is actual data or original data on research yayc and is the predicted data or the forecasting data result .
Findings Descriptive Analysis of the Data The data that the researchers use is data on daily positive cases of Covid-19 in Indonesia, from September 1, 2020 to October 30, 2020, which was obtained from the official website of the Indonesian government Covid19.
The amount of data used is 60 data from data on daily positive cases of Covid-19.
Figure 1 shows a graph of the number of positive Covid-19 cases that occurred in Indonesia from September 1, 2020 to October 30, 2020.
Based on the data within the two months, it can be seen that the least positive case of Covid was September 1, 2020, amounting to 2775.
And the most is in October 8, 2020, which is 4850.
The trend of the graph tends to be Cheng's Fuzzy Time Series MethodA n 18 ADI International Conference Series Vol 4 January 2022 p-ISSN : 2774-9576 e-ISSN : 2747-2981 Figure 1.
Illustration of the number of positive cases of Covid-19 in Indonesia 2 ChengAos Fuzzy Time Series Method 1 Formation of the Universal Set The formation of the universal set using historical data, by definingyaycoycnycu .
yaycoycaycu , which are the lowest and highest data.
It can be concluded:
ycO = .
yaycoycaycu ] ycO = .
2 Formation of Interval Length Calculating the Range ycI = .
aycoycaycu Oe yaycoycnycu ] ycI = 4850 Oe 2775 ycI = 2075 Calculating the Amount of the Interval Cases In calculating the number of interval classes, the Struges formula is used, where n is the number of historical data:
ya = 1 3,322 ycoycuyci ycoycuyci ycu ya = 1 3,322 ycoycuyci ycoycuyci 60 ya = 6,907018454 ya=7 Calculating the Inerval Width The width of the interval resulting from the division between the Range and the number of interval classes is as follows:
ycI yco= ya yco= yco = 296,4285714 3 Fuzzy Set Formation Fuzzy sets are made by looking at frequencies that are not the same or different.
The results of the density frequency calculation can be shown in table 1.
Interval
Lower
Limit
Upper Limit
Total
Data
Total Sub Interval
Sub Interval Width
148,2143
3071,42
3367,85
3664,28
3071,42857
3367,85714
3664,28571
3960,71428
98,80952
74,10714
98,80952
Cheng's Fuzzy Time Series MethodA
ADI International Conference Series Vol 4 January 2022
3960,71
4257,14
4553,57
4257,14285
4553,57142
Total
Frequency p-ISSN : 2774-9576
e-ISSN : 2747-2981
49,40476
59,28571
296,4286
15, 13, 11, 7, 4, 3
Table 1.
Density Frequency Next is to assume that ya1 , ya2 .
A , yayco as a fuzzy set of linguistic values of linguistic variables.
The total number of sub intervals is 24, then creating a fuzzy interval with frequency density can be seen in table 2.
Sub
Lower Limit
Upper Limit
Median Sub
Interval
Width
2923,2142
2849,1071
148,21428
2923,2142
3071,4285
2997,3214
148,21428
4494,2857
4553,5714
4523,9285
59,285714
4553,5714
4701,7857
296,42857
ya24 Table 2.
Fuzzy Interval with Density Frequency Determining the new limit of each interval according to the width of the sub interval in each sub interval and the number of sub intervals according to the number of sub intervals.
Then, determining the middle value by adding the lower and upper limits and then dividing them by 2.
4 Performing the Fuzzification Fuzzyfication results can be seen in table 3.
Date 01Sep20 02Sep20 15Sep20 16Sep20 29Sep20 Positi Case Fuzzi Date Positi Case Fuzzif 02Oct-20 15Oct-20 16Oct-20 29Oct-20 ya8 Cheng's Fuzzy Time Series MethodA 01Oct-20 n 20 ADI International Conference Series Vol 4 January 2022 30Sep20 p-ISSN : 2774-9576 e-ISSN : 2747-2981 ya19 30Oct-20 ya1 Table 3.
Fuzzification of Historical Data The formation of fuzzyfication on historical data is carried out by looking at the latest fuzzy Fuzzyfication is done by defining the data into appropriate intervals, that is the historical data that falls into a range at certain intervals.
5 Classifying Fuzzy Logic Relationship (FLR) FLR is formed based upon the current historical dataya.
c Oe .
or the current state with future historical dataya.
or the next state.
The results of the formation of the FLR are formed from the results of the previous fuzzification.
The following results from the first order FLR can be seen in table 4.
Date
01-Sep20
02-Sep20
15-Sep20
16-Sep20
29-Sep20
30-Sep20
FLR
Date
01-Oct-20
FLR
ya19 Ie ya17 ya1 Ie ya3 02-Oct-20 ya17 Ie ya20 ya3 Ie ya7 15-Oct-20 ya16 Ie ya31 ya7 Ie ya13 16-Oct-20 ya21 Ie ya19 ya7 Ie ya13 29-Oct-20 ya14 Ie ya8 ya13 Ie ya19 30-Oct-20 ya8 Ie ya1 Table 4.
Hasil FLR 6 Classifying Fuzzy Logic Relationship Group (FLRG) The FLRG builds on the previous FLR.
Fuzzy set predicts more than one set, so right hand side can be combined into one group.
Fuzzy Logic Relationship Group (FLRG) can be seen in FLRG
G22
G23
Current state Next state ya1 Ie ya3 , ya2 ya2 Ie ya22 Ie ya24 , ya4 ya23 Ie ya24 , ya22 , ya15 Table 5.
FLRG Result 7 Scaling The scaling is done by observing on how many relations are the same in the FLRG.
The following scaling result is illustrated in Table 6.
FLRG
Current state
Next state
ya1 Ie
ya3 , ya2
ya2 Ie
G22
ya22 Ie
ya24 , ya4
G23
ya23 Ie ya24 , ya22 , ya15 Table 6.
Scaling Result 8 Fuzzy Time Series Cheng Prediction Result Cheng's Fuzzy Time Series MethodA n 21 ADI International Conference Series Vol 4 January 2022 p-ISSN : 2774-9576 e-ISSN : 2747-2981 Determining the prediction results is based on the FLRG that has been formed.
The following prediction results based on FLRG is illustrated in Table 7.
Curr
Next
Predicti Integerate Prediction 3059,07 3059
ya3 , ya2 2
3318,45 3318
G2 ya22
3960,71 3961
ya24 , ya4 2 Ie G2 ya23 ya24 , ya22 , ya315 4416,88 4417 Ie Table 7.
Prediction Results Built Upon the FLRG To obtain the prediction results, defuzzification is carried out by multiplying the mean value of the sub interval.
Since there is some scaling in the Cheng method, it is included in the After that, the prediction results based on FLRG are entered into historical data after being grouped by FLRG.
The following results from the predictions can be seen in Table Date
01-Sep20
02-Sep20
30-Sep20
01-Oct-20
29-Oct-20
30-Oct-20
Positiv
e Case
FLR
FLRG
Predi
ya1 Ie ya3
ya13 Ie ya19
G13
ya19 Ie ya17
ya14 Ie ya8
ya8 Ie ya1
G18
G14
Table 8.
Prediction Result 3 MAPE Calculation The accuracy of the prediction results with MAPE.
The following MAPE results can be seen in Table 9.
Date
Positiv
e Case
Predictio
MAPE
01-Sep20
02-Sep20
30-Sep20
01-Oct-20
29-Oct-20
0,520325203
7,983193277
2,946813608
13,29593268
Cheng's Fuzzy Time Series MethodA
ADI International Conference Series Vol 4 January 2022
p-ISSN : 2774-9576
e-ISSN : 2747-2981
30-Oct-20
18,81256472
Total
411,6663101
Average MAPE
6,977395086
Table 9.
MAPE Result The average MAPE is 6.
This means that the Cheng Fuzzy Time Series method produces a MAPE error of 6.
977395086% or rounded to 7% so it is considered splendid.
4 Number of Covid-19 Positive Case Prediction Predicting by using the FTS Cheng method is calculated by observing at the latest data.
history, the latest data is seen on October 30, 2020, thus predictions on the next date is carried out per October 31, 2020.
Looking next at the fuzzyfication of the previous data, prediction is calculated per October 31, 2020 using the fuzzyfication of October 30, 2020, that is the A_1.
Accordingly, the calculation is as follows:
31 October 2020 has the ya1 fuzzyfication.
Therefore.
FLR ya1 Ie ya1 from fuzzification on 30 October 2020 to 31 October 2020 and entered into FLRG G1, because its current state is ya1 and inside G1 has next state ya3 , ya2 then adding up next state from 31 October 2020 data to ya3 , ya2 , ya1 and the total is 3, then the prediction calculation is as follows:
yaycn = ycycn1 O .
co1 ) ycycn2 O .
co2 ) U ycycnycy O .
coycy ) ya.
= yc3 O .
co3 ) yc2 O .
co2 ) yc1 O .
co1 ) = [ ] O .
0,833.
[ ] O .
7,321.
[ ] O .
9,107.
= 1040,27777 999,107133 949, 702372
= 2989,087302
= 2989
It can be concluded that the predicted number of positive cases of Covid-19 in Indonesia in October 31, 2020 using the Cheng Fuzzy Time Series method was 2989.
Then the graph of historical data and predictive data can be seen in Figure 2.
Figure 2.
Graph of Historical and Prediction Data Throughout the research, the actual data on the number of positive Covid-19 cases on October 31, 2020 is already existed, as many as 3143.
Therefore, the MAPE errors based on the prediction results on October 31, 2020 is obtained as many as 2989 result with the following Ocycuycn |.
cUyc Oe yayc )/ycUyc .
cu100% ycAyaycEya = ycu .
3 Oe 2.
/3143 .
cu100% = 4,899777283% Cheng's Fuzzy Time Series MethodA n 23 ADI International Conference Series Vol 4 January 2022 p-ISSN : 2774-9576 e-ISSN : 2747-2981 All in all, the prediction results using the FTS Cheng method on October 31, 2020 had a MAPE error of 4.
899777283% or 5%, meaning that it had very good accuracy.
Conclusion The FTS Cheng method predicts the number of positive cases of Covid-19 in Indonesia using 60 data from September 1, 2020 to October 30, 2020 gives an average MAPE error of7% stating that the FTS Cheng method has a very good performance since the MAPE error is lower than 10%.
The results of the prediction of the number of positive cases of Covid-19 that occured in Indonesia on October 31,2020 with the FTS Cheng Series method of 2989 producing as much as 5% MAPE error by 95%.
The FTS Cheng method can be implemented to predict the the number of positive cases of Covid-19 that occured in Indonesia seeing that the MAPE error is lower than 10%.
2 Suggestion For further research, it is recommended to conduct research with other forecasting methods to predict the number of positive cases of Covid-19 in Indonesia.
Then it is recommended to make a program to simplify the calculations.
References