JUSIKOM PRIMA (Jurnal Sistem Informasi dan Ilmu Komputer Prim.
Vol.
6 No.
Agustus 2022
E-ISSN : 2580-2879
Analysis of Application of Fuzzy Grid Partition on Mamdani Method Fuzzy Inference System Murni Marbun1.
Sandhuri2.
Aishwarya3
1,2,3
STMIK Pelita Nusantara Jl.
Iskandar Muda No.
1 Medan.
Sumatera Utara.
Indonesia E-mail : dimpleflorence@yahoo.
ABSTRACT- The Mamdani method has been widely used for various control devices, which is the beginning of fuzzy technology and has the advantage of being able to express concepts that are difficult to formulate and the use of fuzzy membership functions in making objective observations of subjective values, making it easier to make decisions that are full of uncertainty.
The Mamdani method has also been widely used for various optimization This study produces new findings on the analysis of the application of fuzzy grid partition on the fuzzy inference system of the Mamdani method for the issue of optimizing the amount of production of a food product.
The research stage begins with determining the number of partitions that will form a grid structure.
The grid formed from the combination of relations between each partition will have the potential to develop rules.
Based on the results of the analysis, determining the amount of production using the Mamdani method produces a smaller amount of production but produces stock output that is not within the specified stock limit, while the application of fuzzy grid partition in the Mamdani method has a higher and correct amount of product because it produces stock output that is at the specified stock limit.
Keywords : Mamdani Method.
Fuzzy Grid Partition.
Stock Limit
INTRODUCTION
Some methods used in making decisions that are full of uncertainty in fuzzy logic are the Mamdani method, the Tsukamoto method, and the Sugeno The fuzzy inference system includes three methods used for various optimization problems .
Applications of fuzzy inference methods can be found in various aspects of the production or manufacturing industry .
Fuzzy inference systems can be an efficient tool to help make decisions about manufacturing re-engineering, optimize process parameters for process drilling, realize better batch process scheduling or design process-optimized injection moulded parts .
All these applications have in common that they all need to consider several factors together before reaching the final result.
The relationship between inputs and outputs and the relationship between each input factor is quite complicated, and it is difficult to formulate an interactive or indirect relationship.
Therefore, the advantages of fuzzy inference systems stand out because the If-then rule-based inference mechanism can be defined directly by practice experience.
Although the most optimal results from accurate mathematical expressions are difficult to obtain, fuzzy inference dramatically simplifies and speeds up the computational process and produces results that are good enough for reference.
The application of Fuzzy Grid Partition has been tested to optimize the fuzzy inference system of the Tsukamoto method.
The test uses labels linked to variables built by Fuzzy Grid Partition to correct the limitations of the Tsukamoto Fuzzy Inference System.
Fuzzy Inference System using Fuzzy Grid Partition to get a fair optimal solution for the Fuzzy Tsukamoto problem.
The new membership function as a result of the fuzzy grid partition can improve the limits of the fuzzy inference system of the Tsukamoto method, where the fuzzy grid partition can determine the number of fuzzy rules .
This study analyses the application of fuzzy grid partition in generating rules that can be used as labels that can be linked from variables to optimize the output of the Mamdani method.
The Mamdani type inference output expects membership events to become fuzzy sets to be carried out after the aggregation process.
Fuzzy set for each output defuzzification needs to be done.
It is efficient, and sometimes a single spike is used as an output function rather than a distributed fuzzy set.
single output function can be thought of as a predefuzzified fuzzy set.
This can increase the efficiency of the defuzzification process because it greatly simplifies the calculations required by the more general Mamdani method, which finds the centre of mass of a two-dimensional function.
The Mamdani type integrates all two-dimensional functions to find the centre of mass, the weighted average of several data points .
The fuzzy grid-partition approach can be used in the design of fuzzy systems because it is easier to Several studies have applied the fuzzy grid partition approach, among others, generating several JUSIKOM PRIMA (Jurnal Sistem Informasi dan Ilmu Komputer Prim.
Vol.
6 No.
Agustus 2022
E-ISSN : 2580-2879
, combine texture approach .
, choose features .
, partition feature space .
This study aims to analyze the application of fuzzy grid partition in the Mamdani method to produce optimal output in making conclusions or decisions with several stages, namely determining the number of partitions (K), forming fuzzy sets with grid composition of rules.
and defuzzification.
FUZZY
GRID PARTITION
MAMDANI METHOD
The fuzzy inference system of the Mamdani method is often also known as the min Ae max method which was introduced by Ebrahim Mamdani in 1975 .
The stages of the mamdani method to get the output consist of .
Determination of the number of partitions (K) Fuzzy set generate Input variables and output variables are divided into one or more fuzzy sets.
Input variables and output variables are divided into partitions to form a grid structure, the grid formed from the combination of relations between each partition will have the potential to develop rules, as illustrated in Fig.
1 in the following two attributes.
Where:
Usf .
i ] = fuzzy solution membership value up to the i-th rule Ukf .
i ] = fuzzy consequent membership value of rule Ae i Defuzzification The defuzzification method on the composition rule is the Centroid (Composite Momen.
In this method, the crisp solution is obtained by taking the centre point of the fuzzy region.
Generally formulated:
yca ycs0 = Oyca ycs yuN.
yccyc yca Oyca yuN.
yccyc yceycuyc ycaycuycuycycnycuycycuycyc a.
Z = i-th domain value AA.
= the degree of membership of the point Z0 = defuzzification result value RESEARCH METHODS To complete this research, it is necessary to have a clear framework for the stages.
The stages of the analytical research framework for applying Fuzzy Grid Partition on the Mamdani method can be seen in Fig.
2 below.
Figure 1.
Grid Partition Implication function The implication function used is Min.
The rules formed are derived from the rules for applying fuzzy grid partition with the number of partitions Composition Rules If the system consists of several rules, then the inference is obtained from combining the rules.
The method used in performing fuzzy system inference is the max.
The max method is a fuzzy set solution obtained by taking the maximum value of the rule, then using it to modify the fuzzy set area, and applying it to the output using the OR .
If all propositions have been evaluated, then the result will contain a fuzzy set that reflects the contribution of each proposition.
In general, it can be written:
Usf .
i ] = max (Usf .
i ].
Ukf .
i ])a.
Figure 2.
Research Framework
RESULTS AND DISCUSSION
1 Result Suppose Company A wants to produce ABC type of food.
It is known that the data from the last month are as follows, the greatest demand is 6500 packages/day, and the smallest demand is 2300 packages/day.
The largest stock in the warehouse is 590 packages/day, and the smallest stock is 120 packages/day.
With these limitations, company A can only produce 7150 packages/day, and the smallest JUSIKOM PRIMA (Jurnal Sistem Informasi dan Ilmu Komputer Prim.
Vol.
6 No.
Agustus 2022
E-ISSN : 2580-2879
production efficiency is 2000 packages/day.
If the production process uses four rules:
If demand decreases and stock is large, then production decreases.
If the demand decreases and the stock is low, then production will decrease If demand increases and there is a lot of stock, then production increases If demand increases and stock is low, then production increases The problem must be solved how many food products must be produced if there is a demand for 3900 packages and the stock in the warehouse is 310 The research stages are as follows:
Mamdani Method Demand with domain 0 Ae 6500 consisting of Demand Decrease and Demand Increase.
Figure Variable demands as follows:
Figure 4.
Stock Variable Stock variable membership function as follows:yuNycIycycuycayco ycIycoycnyciEaycycoyc .
= , yc O 120 590Oeyc , 120 O yc O 590 , yc Ou 590 yuNycIycycuycayco ycAycaycuyc .
, yc O 120
yc Oe 120
= {
, 120 O yc O 590 , yc Ou 590 If the stock in the warehouse is 310 packages, 590 Oe 310 = 0.
yuNycIycycuycayco ycIycoycnyciEaycycoyc .
= Figure 3.
Demand Variables The membership function of the Request variable is as follows:
yuNyayceycoycaycuyccyc yayceycaycyceycaycyce .
, ycu O 2300
6500 Oe ycu
= {
, 2300 O ycu O 6500 , ycu Ou 6500 yuNyayceycoycaycuyccyc yaycuycaycyceycaycyce .
, ycu O 2300
ycu Oe 2300
= {
, 2300 O ycu O 6500 , ycu Ou 6500 yuNycIycycuycayco ycAycaycuyc .
310 Oe 120 = 0.
Production with a domain of 0 Ae 7150 consists of decreased and increased production.
The image of the production variable is as follows:
If there is a request for 3900 packages, then:
yuNyayceycoycaycuyccyc yayceycaycyceycaycyce .
= 6500 Oe 3900 = 0.
yuNyayceycoycaycuyccyc yaycuycaycyceycaycyce .
= 3900 Oe 2300 = 0.
Stock with domain 0 Ae 590 which consists of little stock and large stock.
Picture of stock variables as follows::
Figure 5.
Production Variable The membership function of the Production variable is as follows:
yuNycEycycuyccycycaycycnycuycu yayceycaycyceycaycyce .
, yc O 2000
7150 Oe yc
= {
, 2000 O yc O 7150 , yc Ou 7150 JUSIKOM PRIMA (Jurnal Sistem Informasi dan Ilmu Komputer Prim.
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E-ISSN : 2580-2879
yuNycEycycuyccycycaycycnycuycu yaycuycaycyceycaycyce .
, yc O 2000
yc Oe 2000
= {
, 2000 O yc O 7150 , yc Ou 7150 5193 Oe yc yuN.
= { , yc O 4060 , 4060 O yc O 5193 , yc Ou 5193 Defuzzification Formation of Variable Fuzzy Set Request 3900 yuNyayceycoycaycuyccyc yayceycaycyceycaycyce .
= 0.
yuNyayceycoycaycuyccyc yaycuycaycyceycaycyce .
= 0.
Formation of Stock Variable Fuzzy Set 310 yuNycIycycuycayco ycIycoycnyciEaycycoyc .
= 0.
yuNycIycycuycayco ycAycaycuyc .
= 0.
Implication Function There are four implication function rules in the Fuzzy Mamdani Method, namely:
Figure 6.
Defuzzification Function R.
If the demand is reduced and there is a lot of stock, the production will decrease.
yu Oe ycyycyceyccycnycoycayc1 = yuNyayceycoycaycuyccyc yayceycaycyceycaycyce O yuNycIycycuycayco ycIycoycnyciEaycycoyc = ycAycnycu ( 0.
62,0.
= 0.
The defuzzification process uses the centroid method to determine the crisp z value.
It is carried out by dividing the area into three parts, namely 1, 2, and 3, with the respective regions of A1.
A2, and A3, and the moment to the membership value are M1.
M2, and M3.
If the demand is reduced and the stock is low, the production will decrease.
yu Oe ycyycyceyccycnycoycayc2 = yuNyayceycoycaycuyccyc yayceycaycyceycaycyce O yuNycIycycuycayco ycIycoycnyciEaycycoyc = ycAycnycu ( 0.
62,0.
= 0.
If demand increases and there is a lot of stock then production increases yu Oe ycyycyceyccycnycoycayc3 = yuNyayceycoycaycuyccyc yaycuycaycyceycaycyce O yuNycIycycuycayco ycoycaycuyc = ycAycnycu ( 0.
38,0.
= 0.
If demand increases and stock is low then production increases yu Oe ycyycyceyccycnycoycayc4 = yuNyayceycoycaycuyccyc yaycuycaycyceycaycyce O yuNycIycycuycayco ycIycoycnyciEaycycoyc = ycAycnycu ( 0.
38,0.
= 0.
Composition Rules yuNycyce .
= ycAycaycu .
uNycEycycuyccycycaycycnycuycu yayceycaycyceycaycyce , yuNycEycycuyccycycaycycnycuycu yaycuycaycyceycaycyce ) = max .
At the time yuNycEycycuyccycycaycycnycuycu yayceycaycyceycaycyce .
= 0.
6 then value z = 4060 At the time yuNycEycycuyccycycaycycnycuycu yaycuycaycyceycaycyce .
= 0.
38 then value z =5193 Thus the membership function for the composition result is :
ycA1 = O 6 yc yccyc = 0.
3 yc 2 | = 4945080 5193 Oe yc ycA2 = O yc yccyc 58 yc Oe 0.
000883yc 2 yccyc
= O
= 2.
29 yc 2 Oe 0.
000294yc 3 .
3 = 2511008,841 ycA3 = O 38 yc yccyc = 0.
19 yc 2 | 7150
= 4589498
area as follows:
ya1 = 4060 O 0.
6 = 2436
6 Oe 0.
O .
3 Oe 4.
ya2 = = 124.
ya3 = .
0 Oe 5.
O 0.
38 = 743.
Based on these calculations, the central point of the fuzzy area is obtained, namely:
4945080 25511008,841 4589498
yc = 3645.
yc= JUSIKOM PRIMA (Jurnal Sistem Informasi dan Ilmu Komputer Prim.
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Application of Fuzzy Grid Partition on Mamdani Method Determination of the number of partitions (K) Formation of Demand Variable Function (D) Figure 10.
Multiple stock function 590 Oe ycu = 0.
ycu Oe 120 yuNycIycA22 = = 0.
yuNycIycA12 = Figure 7.
Reduced demand function yuNycEya12 = 6500Oeycu = 0.
ycuOe0 yuNycEya22 = = 0.
Implication Function There are 16 implication function rules in the Fuzzy Mamdani Method with the application of Grid Partition, namely:
If demand ya12 and Stock ycA12 then production is reduced yu1 = min.
= 0.
[R.
If demand ya12 and Stock ycA22 then production is reduced yu2 = min.
= 0.
[R.
If demand ya12 and Stock ycA12 then production is reduced yu3 = min.
= 0.
[R.
If demand ya12 and Stock ycA22 then production is reduced yu4 = min.
= 0.
[R.
If demand ya12 and Stock ycI12 then production is reduced yu5 = min.
= 0.
[R.
If demand ya12 and Stock ycI22 then production is reduced yu6 = min.
= 0.
[R.
If demand ya12 and Stock ycI12 then production is reduced yu7 = min.
= 0.
[R.
If demand ya12 and Stock ycI22 then production is reduced yu8 = min.
= 0.
[R.
If demand ya12 and Stock ycA12 then production increases yu9 = min.
= 0.
[R.
If demand ya12 and Stock ycA22 then production increases yu10 = min.
= 0.
[R.
If demand ya12 and Stock ycA12 then production increases yu11 = min.
= 0.
[R.
If demand ya12 and Stock ycA22 then production increases yu12 = min.
= 0.
[R.
If demand ya12 and Stock ycI12 then production yu13 = min.
= 0.
[R.
Figure 8.
Demand function increases 6500 Oe ycu = 0.
ycu Oe 2300 yuNycEya22 = = 0.
yuNycEya12 = Fungsi Variabel Stok (S) Figure 9.
Few stock functions 590 Oe ycu = 0.
ycuOe0 yuNycIycI22 = = 0.
yuNycIycI12 = JUSIKOM PRIMA (Jurnal Sistem Informasi dan Ilmu Komputer Prim.
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[R.
If demand ya12 and Stock ycI22 then production yu14 = min.
= 0.
[R.
If demand ya12 and Stock ycI12 then production yu15 = min.
= 0.
[R.
If demand ya12 and Stock ycI22 then production yu16 = min.
= 0.
The defuzzification process uses the centroid method to determine the crisp z value.
It is done by dividing the area into four parts, namely 1, 2, 3 and 4, with the respective regions of A1.
A2.
A3, and A4, as well as the moment of the membership -respectively M1.
M2.
M3, and M4.
ycA1 = O0 6 yc yccyc = 0.
3 yc 2 | 4060
= 4945080
4575 4575Oeyc Composition Rules yuNycyce .
= ycAycaycu .
uNycEycycuyccycycaycycnycuycu yayceycaycyceycaycyce , yuNycEycycuyccycycaycycnycuycu yaycuycaycyceycaycyc.
= max .
When yuNycEycycuyccycycaycycnycuycu yayceycaycyceycaycyce .
= 0.
then the value of z as follows:
ycA2 = O4060 5193 ycOe4575 ycA3 = O4575 7150Oeyc2 ycA4 = O yc2 = 4575 62 yc yccyc = 0.
31 yc 2 | When yuNycEycycuyccycycaycycnycuycu yaycuycaycyceycaycyce .
= 0.
62 then the value of z as follows:
= 0.
yc3 = 5193 Thus the membership composition result is:
= 1569029.
yc yccyc = 0.
00054yc 3 Oe 3.
7014yc 2 | 7150Oeyc yc3 Oe2000 yc yccyc = 4.
407 yc Oe 0.
000642yc 3 .
5 = 1081256.
6 = 5150 1
yc1 = 4060 6 yc O 4060 4575 Oe yc 4060 O yc O 4575 yuN.
= yc Oe 4575 4575 O yc O 5193 62 yc Ou 5193 = 7488127.
Area as follows:
ya1 = 4060 O 0.
6 = 2436
6 Oe 0.
O .
5 Oe 4.
ya2 = = 25.
62 Oe 0.
O .
3 Oe 4.
ya3 = = 37.
ya4 = .
0 Oe 5.
O 0.
= 1213.
Based on these calculations, the central point of the fuzzy area is obtained, namely:
yc= 4945080 1081256.
Defuzzification yc = 4063.
Figure 11.
The Defuzzification Function of the Partititon Grid method Discussion 1 Mamdani Method Analysis Based on the calculation of the central point value .
, the number of food products that must be produced if there is a demand for 3900 packages and stock in the warehouse for 310 packages is 3645.
Based on the analysis of the Mamdani method, it can be seen that the remaining stock for the next period in the warehouse is .
Ae 3900 = 55 packages.
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It is known that the minimum stock allowed in the warehouse is 120, and the maximum stock is 590 The application of the Mamdani method with a total production of 3645 packages is incorrect because it does not meet the minimum limit of the number of stocks.
2 Analysis of the Application of Fuzzy Grid Partition on the Mamdani Method Based on the calculation of the centre point value .
, the number of food products produced if there is a demand for 3900 packages and stock in the warehouse for 310 packages is 4063.
Based on the analysis of the application of fuzzy grid partition in the Mamdani method, it can be seen that the remaining stock for the following stock in the warehouse is .
Ae 3900 = 473 packages.
It is known that the minimum stock allowed in the warehouse is 120, and the maximum stock is 590 The application of fuzzy grid partition in the Mamdani method with a total production of 4063 packages is correct because it meets the maximum limit of the allowable stock.
CONCLUSION
The application of fuzzy grid partition to the fuzzy inference system of the Mamdani method produces correct and optimal output.
The application of the Mamdani method in determining the amount of production resulted in a stock output that did not meet the minimum limit of 55 packages.
While the application of fuzzy grid partition in the Mamdani method produces stock output with the number of stocks at the maximum limit of 473 packages.
The amount of food production using the Mamdani method for the demand for 3900 packages with a stock of 310 is 3645 packages, while the amount of output using the application of fuzzy grid partition in the Mamdani method is 4063 packages.
The application of the Mamdani method resulted in a smaller amount of production compared to the application of the fuzzy grid partition in the Mamdani Still, applying the fuzzy grid partition in the Mamdani method resulted in the correct stock output, namely 473 packages, which were still in the range of 120 - 590 packages.
REFERENCES