AUTOMATIC CLUSTERING AND OPTIMIZED FUZZY LOGICAL RELATIONSHIPS FOR MINIMUM LIVING NEEDS FORECASTING

Forecasting of minimum living needs is useful for companies in financial planning next year. In this study, the firescasting is done using automatic clustering and optimized fuzzy logical relationships. Automatic clustering is used to form a sub-interval time series data. Particle swarm optimization is used to set and optimze interval values in fuzzy logical relationships. The data used as many as 11 years of historical data from 2005-2015. The optimal value of the test results obtained by the p = 4, the number of iterations = 100, the number of particles = 45, a combination of Vmin and Vmax = [-0.6, 0.6], as well as combinations Wmax and Wmin = [0, 4, 0 , 8]. These parameters values produce good forecasting results.


INTRODUCTION
Minimum living needs is set in the regulation of the Minister of Manpower and Transmigration, namely "the need for decent living hereinafter abbreviated KHL is a standard requirement for a single worker or workers can live well physically to the needs of one (1) month".In addition to the articles 6 to 8 also stipulates that the KHM is used as a parameter for determining the minimum wage provinces and cities.From the information on the results of forecasting minimum necessities of life can be used as the design of the company's financial future.
Forecasting is usually done a lot of people to know the events that will occur in the future by looking at the events that have occurred previously (Chen et al, 2016).Such as forecasting temperature, precipitation, stock items, earthquakes, etc. Forecasting traditionally do not pay attention to the previous data and more qualitative not quantitative.On the problem of forecasting minimum life needs no studies when forecasting the minimum living needs will be beneficial for the company.
There are several methods of forecasting that uses quantitative approach, one of them is fuzzy logic (Fatyanosa & Mahmudy, 2016;Wahyuni, Mahmudy & Iriany, 2016).In addition there are other fuzzy model, the model of fuzzy time series Chen et al's more simple also be applied to predict the number of applicants at the University of Alabama (Chen and Tunawijaya, 2010).Forecasting methods developed by Chen et al's or so-called fuzzy logical relationship can produce good forecasting for time series data (Chen and Chen, 2011;Chen and Chen, 2015;Qiu et al, 2015;Cheng et al, 2015).Fuzzy logical relationship get an error lower than in previous studies.From the existing research can be concluded that the fuzzy logical relationship can solve the problems of forecasting.
Use of the method of automatic clustering effectively within the classification of previous data so that it can form a cluster with both (Chen and Tunawijaya, 2011;He and Tan, 2012;Saha and Bandyopadyay, 2013;Hung and Kang, 2014;Askari et al, 2015;Wang and Liu , 2015;Garcia and Flores, 2016).Deemed the use of automatic clustering greatly assist in forecasting to obtain the error value is lower.To improve forecasting results better optimization of the value interval on fuzzy logical relationships can be performed using particle swarm optimization giving an error that the lower (Chen and Kao, 2013;Cheng et al, 2016).
This study is the extension of previous study (Anggodo & Mahmudy, 2016) by adding a mechanism to set and optimze interval values in fuzzy logical relationships..The focus on this study, the first to examine on the basis of fuzzy time series.The second classification data history minimum living needs using automatic clustering.Third optimization using particle swarm optimization interval.Fourth forecasting the minimum living needs using fuzzy logical relationships.Fifth calculate the error value using the Root Mean Squere Error (RMSE) forecasting results with actual data.

FUZZY TIME SERIES
Fuzzy time series is a representation of a fuzzy set.Fuzzy set is built based on the time series data of the KHM.A fuzzy set of data generated from the present into the current state and future year data into the next state.Fuzzy set which has been set used for forecasting the coming year.

Forecast Using Fuzzy Logical Relationships
In this section we will clarify the steps of forecasting methods fuzzy logical relationships by using automatic classification clustering, (Cheng et al, 2016) as follows: Step 1: classifying the data using automatic clustering algorithm and optimize the value of the interval using the PSO.
Step 3: fuzzification every datum of historical data into fuzzy sets.If the datum is ui, where 1 ≤ i ≤ n.So do fuzzification as Ai.
Step 4: building a relationship based on the fuzzy logical fuzzification step 3.If the fuzzification year t and t + 1 is Aj and Ak.So fuzzy logical relationship that is built is Aj → Ak, where Aj called the current state and the next state at the Ak as fuzzy logical relationship.From fuzzy logical relationship be grouped together, in which the same current state included in one group.
Step 5: forecasting using the following principles: Principle 1: if fuzzification year t is Aj and there is a logical relationship in fuzzy fuzzy logical relationship group, with conditions: Aj → Ak, Thus, in forecasting the year t + 1 is mk, where mk is the midpoint of the interval uk and the maximum value of membership of fuzzy sets Ak Uk interval.
Principle 2: If fuzzification year t is Aj and no fuzzy logical ralationship in fuzzy logical relationship group, with conditions: So as to make forecasting year t + 1 using equation 1: , Principle 3: if fuzzification year t is Aj and there is a logical relationship in fuzzy fuzzy logical retlationship group, with conditions: Where the value # is blank.Thus forecasting the year t + 1 is m¬j, where mj is the midpoint of the interval ui and a maximum value of membership of fuzzy sets Aj Uj interval.

Classification Of Data Using Automatic Clustering
Automatic clustering algorithm is used to classify numerical data based on the interval (Wand and Liu, 2015).Interval is the distance, so that the numerical data classified by the shortest distance.The smaller the distance between the two elements of the numerical data, the higher the similarity (Qiu et al, 2015).In Figure 1 is shown the stages of automatic clustering.Step 1: The first sort ascending numerical data, assuming no similar data.d 1 , d 2 , d 3 ,., , , d i ., , ,d n .
Then calculate avarage_diff using equation 2: avarage_diff which is the average of the data numberik and d 1 , d 1 , ...,d n . is the numerical data that has been sorted.
Step 2: Take the first numerical data (ie the smallest datum) to be placed to the current cluster or need to create a new cluster based on the following principles: Principle 1: assume the current cluster is the first cluster and there is only one datum that d1 and d2 is considered that datum adjacent to d1, shown as follows: (3) cluster_diff which is the average of the current cluster and c 1 , c 2 , ... c n is the data in the current cluster.
Step 3: based on the clarification step 2, according to the contents corresponding cluster following principles: Principle 1: if the cluster there are more than two datum, then maintain the smallest and largest datum and datum remove the others.Principle 2: If the cluster there are two datum, then maintain it all.Principle 3: If the cluster has only one datum dq, then add the datum to the value d q -avarage_diff and d q + avarage_diff into clusters.But also must adjust to the following situations: Situation 1: if the first cluster, then remove d q -avarage_diff and maintain d q .
Situation 2: if the cluster Last post, then remove avarage_diff + d q and maintain d q .
Situation 3: if d q -avarage_diff smaller than the smallest value in the antecedent cluster datum, then the third principle does not apply.
Step 4: assume the results of step 3 as follows: Step 5: results of step 4 for the interval into sub-intervals p, where p ≥ 1.

Interval Optimization Using PSO
The concept of PSO algorithm is quite simple and effective in for finding solutions of complex problems (Novitasari, Cholissodin & Mahmudy, 2016; Mahmudy 2014), PSO algorithm model the best solution search by activities of particles moving in the search space, the position of the particle is a representation of the solution represented by the cost.Cost value obtained from the calculation error forecasting results using the RMSE (Cheng et al, 2016).PSO main concept is every particle has a speed which is calculated based pbest and gbest and coefficient values was raised at random.Each to shift the position of each particle must update the value of pbest, gbest, as well as the speed of each particle.
The process of the PSO algorithm in the optimization objective function in accordance with the problems.The first initializes particles presenting the solution of problems.Both do the calculation of the value of cost for each particle.The third did the best position value updates of each particle or particles or pbest and overall gbest.Fourth calculate the speed of each particle, the particle velocity will determine the direction of movement of the particle's position.The fifth did displacement particle positions and do repair to sort in ascending value of the particle, the first iteration randomly generated for the next iteration obtained by equation 4.
which v i shows the particle velocity i, t is the iteration time, w is the weight of inertia, c i is the coefficient of particles (cognitive = 1, social = 2), r i is a random value in the interval [0,1], x i the value of the position of the particle i, g b t value the best solution on the particle i and iteration t, and the best overall solution value gbt particle at iteration t.Once the updated value of the speed, the next step is to change the position of each particle using the equation 5.
Each iteration changes inertia weight value shown in equation 6.
t max is the maximum iteration value has diinsialisasi beginning before PSO do, t is an ongoing iteration.w max and w min a minimum and maximum weight diinsialisasi previously.
Updates the value of w in equation 6 usually called time varying Inertia Weight (TVIW).
In the PSO algorithm implementation is sometimes found fast moving particles, the particles have a tendency to come out as a result of the search space limit.Hence, to control the exploitation of the particles need to be limits on the minimum and maximum speed or so-called velocity clamping (Marini and Walczak, 2015).The calculation of the speed limit is shown in equation 7.
Where v max shows the value of the maximum speed, k generated at random intervals (0, 1], whereas x max and x min respectively the smallest and largest value of minimum living needs.Limitation of speed or threshold that is used as follows:

EXPERIMENTAL RESULT
Tests were conducted to evaluate the value of a parameter in the automatic clustering and particle swarm optimization solve the problems of forecasting the minimum living needs.For testing the PSO performed 10 times.Use of this because stotastic PSO algorithm, the best result of the average value.

Testing The Value of P
The first will be tested on automatic clustering p values shown in Figure 2.

Testing of Iterations
Testing iteration aims to see the value of the best iterations on this issue.These initial conditions include a parameter p = 4, the number of particles = 5, Wmax = 0.9, Wmin = 0.1, c 1 = 1, c 2 = 1. Figure 3 shows the results of testing the number of iterations.
Figure 3 shows the number of iterations of 100 had a value of cost (RMSE) from the bottom at 22065.574096827.Can be seen in the increasing number of iterations does not mean the lower the cost is because the PSO algorithm is an algorithm stotastic or random nature.

Testing the Number of Particle
Testing the numberof particles aimed to look at the value of the number of particles the best on this issue.These initial conditions include a parameter p = 4, the number of iterations = 100, Wmax = 0.9, Wmin = 0.1, c 1 = 1, c 2 = 1. Figure 4 shows the results of testing the number of particles.Figure 4 shows the number of particles 45 provides a value that is equal to the lowest cost 22036.208233097.On the number of particles after 45 value higher cost, so that on this issue the best particle number is 45.

Testing Percentage of Speed
Testing the percentage of speed or Vmin and Vmax aims to know the value of a percentage of the dynamic range of the velocity of particles in PSO resulting combination with interval fuzzy logical relationships are optimal.These initial conditions include a parameter p = 4, the number of iterations = 100, the number of particles = 45, Wmax = 0.9, Wmin = 0.1, c 1 = 1, c 2 = 1. Figure 5 shows the percentage of the speed test results.

Testing Value of Wmin and Wmax
Testing the value of Wmin and Wmax to get the best combination.These initial conditions include a parameter p = 4, the number of iterations = 100, the number of particles = 45, Vmin = -0.6,Vmax = 0.6, c 1 = 1, c 2 = 1. Figure 6 shows the results of testing the value Wmin and Wmax.
Figure 6 shows the best combination of value Wmin and Wmax is [0.4,0.8] for 22006.341736784.

Testing using the Best Parameter
This section will compare the results of forecasting the results of forecasting using automatic clustering, fuzzy logical relationships (ACFLR) with p = 4 while the forecasting results using automatic clustering, particle swarm optimization, and fuzzy logical relationships with the parameter value p = 4, the number of iterations = 100, the number of particles = 45, the percentage of Vmax = 0.6, the percentage of Vmin = -0.6,Wmin = 0.4, Wmax = 0.8, c 1 = 1 and c 2 = 1 shown in Figure 7.

CONCLUSION
Fuzzy logical Relatioships Particle swarm optimization is very helpful to optimize the value of the interval on fuzzy logical relationships that get results RMSE values were lower.Automatic clustering in classifying time series data to establish the interval.The best parameter values so as to produce the optimal value, among others, p = 4, the number of iterations = 100, the number of particles = 45, the percentage of speed = [-0.6,0.6], the value Wmin and Wmax = [0.4,0.8 ].
Further research can be applied this method for forecasting other data are more numerous and optimizing the parameters of fuzzy logical relationships resulting in smaller RMSE values.

Figure 2 .
Figure 2. Testing the value of p Figure 2 shows the value of p = 4 RMSE worth 23404,944 and when the value of p = 5 RMSE values increase.Based on this it does not conduct further testing of the p value for a value of more than 5.

Figure 4 .
Figure 4. Testing the number of particles

Figure 3 .
Figure 3. Testing the number of iterations

Figure 7 .
Figure 7. Compare the result of forecasting Figure 7 shows the results of data comparison between the actual with ACPSOFLR and ACFLR, where ACPSOFLR forecasting results closer to the actual data with RMSE value of 22006.34154while ACFLR has RMSE value of 23404.9442.

Figure 6 .
Figure 6.Testing the value Wmin and Wmax {d 1 }, d 2 d 3 , ..., d i , ..., d n.If avarage_diff ≤ d2-d1, d2 then input into the current cluster consisting d 1 , if it does not create a new cluster consisting d 2 .Principle 2: assume that the current cluster is not the first cluster and d j is the datum only in the current cluster.Assume d k is adjacent to the datum datum datum d j and is the largest in the antecedent of a cluster, shown as follows:{d 1 }, . . ., {...,d i },{d j }, d k , . . ., dn.If the dk-dj ≤ avarage_diff and d k -d j ≤ d jd i , then input to a cluster owned d k d j , if it does not create a new cluster consisting d k .Principle 3: assume that the current cluster is not the first cluster and assume that in a datum the current cluster.Assume that datum adadalah dj nearest to.If d j -d i ≤ avarage_diff and d j -d i ≤ cluster_diff, then d j input into clusters consisting d i .If it does not create a new cluster for d j .Cluster_diff calculation shown in equation 3.
k , d l } to the interval [d k , d l ) and create a new interval [d j , d k ) on the interval [d i , d j ) and [d k , d l ).Now [d k , d l ) P-ISSN:2356-3109 E-ISSN: 2356-3117