Application of Fuzzy Algorithms and Analytical Hierarchy Process Modification in Decision Support Systems for Lazis Scholarship UNNES

Lazis scholarship is a scholarship given to underprivileged students and does not yet have a system that supports the decisions to be taken. AHP is one of the most popular decision making methods in solving problems. But, AHP has several weaknesses. So that it will be modified based on previous research and the addition of fuzzy algorithms to get a better decision support system method. The results of this research were A009 students with the final result priority index value of 0.004176516 getting the first position. And the addition and modification in in this research is better than the standard decision support system. Fuzzy c-means produce scores that are more variable than manual grouping. Using sorting and ranking will produce a pairwise comparison matrix that is definitely consistent and has an average faster processing time is 0.028396 seconds, whereas with the standard method is 0.284415 seconds. Modification of alternative priorities also have a relatively faster average implementation time of 0.3165 seconds than the standard calculation with 2.6003 seconds. And modifications to the FPIV, if taking the top 25 ranking in the standard FPIV produces 3 the same value while in the modified FPIV there is 1 same value.


INTRODUCTION
Lazis UNNES scholarship is a scholarship given to underprivileged Muslim students of UNNES from semester 1 to semester 8. In 2019, Rumah Lazis UNNES as the scholarship provider opened a number of quota scholarship recipients and submitted the selection process to each department respectively. However, because the selection is done by the provisions of each department, this can allow intentional or unintentional mistakes, so that it becomes less optimal and can result in recipient selection not being objective. In 2018, actually Rumah Lazis UNNES in determining the recipients of their scholarships has conducted an open recruitment process for each student who wishes to apply for a scholarship. However, the selection process is fairly simple, namely by providing an assessment based on scoring guidelines without differentiating the importance. Of the two ways above, there are weaknesses in providing scholarships that are right on target. Terry states that one of the basics of decision making is rational, where the resulting decision must be objective, logical, more transparent, consistent to maximize results or values within certain constraints so that it can be said to be close to the truth or according to what is desired [1]. While research conducted by Rivai suggested one of the stages of decision making is allocating weights to the criteria to choose the best alternative [2].
Based on the opinion above, we need a decision-making system for the Lazis UNNES scholarship. Analytical Hierarchy Process or AHP is one of the most popular analytical techniques in the MCDM method for complex decision making problems. AHP has several advantages to be used as a decision-making tool including interdependence where AHP can be used on elements of a system that is mutually free, AHP considers the relative priority of factors in the system so that people are able to choose the best alternative based on their goals, and do not require a relationship linear and there is a calculation process to get priority values [3].
However, the AHP method has several weaknesses. First, in determining the priority value of criteria there is a weakness in the difficulty of determining consistency in the pairwise comparison matrix of AHP [4]. Secondly, in determining the priority value of each alternative in each criterion it is necessary to make a pairwise comparison matrix and also the criteria value matrix of a number of existing criteria, the process itself is quite long. Finally, in determining the final priority index value to determine the ranking order of each alternative often produces the same final index value, even though the parameter values of the two test data are different [5]. So that it will be modified on the AHP method based on previous research.
To maximize this decision support system, data conversion will use data grouping with the fuzzy c-means algorithm. Using a grouping with fuzzy logic is better than the classical method, because in fuzzy logic the degree of membership is known to have a range of values 0 (zero) to 1 (one), which has a value of blurring or blurring (fuzziness) between true or false [6]. In the data that will be used in this research, there are criteria data in the form of range data, this makes the data cannot be included in the fuzzy cmeans clustering process, so that the data needs to be processed using fuzzy tsukamoto algorithm.

METHODS
This research will implement the fuzzy algorithm and modification of the analytical hierarchy process to determine the recipient of the Lazis scholarship UNNES. Fuzzy cmeans algorithm is used to convert values. Fuzzy tsukamoto algorithm is used to convert range values into nominal values. While the AHP modification is done at the stage of determining criteria priorities, determining alternative priorities, and determining value of the final priority index.

Fuzzy C-Means Algorithm
Fuzzy c-means is data grouping technique (fuzzy clustering) in which the existence of each data point in a cluster is determined by the level of membership. Fuzzy c-means is a supervised grouping algorithm, because in the fuzzy c-means algorithm the number of clusters to be formed needs to be known first [7].

Fuzzy Tsukamoto Algorithm
Fuzzy tsukamoto is an extension of a monotonous reasoning, which has the characteristic that every result of the IF-THEN form must be represented by a fuzzy set with a monotonous membership function. So as a result, the output of inference results from each rule is given explicitly (crisp) based on α-predicate [9].
Fuzzy tsukamoto algorithm is used to get nominal data from the father's income and mother's income criteria data which were originally in the form of range data, where the steps are as follows: 1) Determine the minimum and maximum values of related data.
2) Determine the applicable fuzzy rules. Where: Rule 1 = if UKT is big then income is big Rule 2 = if UKT is small then income is small 3) Calculates membership value from UKT data.
= Alternative data from known data = Maximum data = Minimum data 4) Make the implication function of income data for each group.
Where: = Alternative data from sought data in rule 5) Find the z value for each rule.
Where: = Alternative data from sought data

Determining Criteria Priorities
The modification stage is done by changing the pairing matrix with a scale of importance being a method of sorting and ranking, where the steps are as follows: 1) Sort criteria based on the importance of each criteria, then give values based on 2) Make a pairwise comparison matrix using the formula below. (20) Where: = Unit of pairwise comparison matrix = Element value comparator = Element value compared 3) Considerations of the pairwise comparisons were synthesized to obtain overall priorities with a criterion value matrix.

Determining Alternative Priorities
In generating alternative priority values, where initially using the pairwise comparison matrix and the alternative value matrix was changed using the priority formula in Eq. 22.
Where: = Priority value = Element value to-i

Determining Final Priority Index Value
Modification at this stage is to change the formula slightly in the calculation of the Final Priority Index Value (FPIV), with the aim of minimizing the same NIPA value even though the parameter values of the two test data are different [5].
Where: = Priority value = Element value to-i EVs-t = Eigenvector sub criteria (in sub criteria with the largest eigenvector) EVs-n = Eigenvector sub criteria 1 ...

RESULT AND DISCUSSION
Based on 810 student data that has been entered into the system with the criteria used are father's work, mother's work, father's income, father's income, UKT, GPA and student condition (orphan or not), resulting in 10 Lazis scholarship recipients based on this decision support system, can seen in Table 2.

Fuzzy C-Means Algorithm
In the system in this research, fuzzy c-means is used to convert the initial data into data that will be processed by the decision-making method. If taken in a range of adjacent values, a comparison of scores with a manual process is shown in Table 3 and Figure  1.

Figure 1. Charts Scoring with C-Means and Manuals
Based on the graph above it can be seen that manual calculations for GPA of 3.41 to 3.5 produce the same score of 3, while the fuzzy c-means calculation produces scores that vary more between 2 to 5, although the initial data is not too much different.

Fuzzy Tsukamoto Algorithm
Fuzzy tsukamoto algorithm in this research can be used to get unit data from the initial income criteria in the form of a range data, father's income can be seen in Table 4.

Determining Criteria Priorities
The modification phase is done by changing the pairing comparison matrix with a scale of importance that is considered difficult in determining consistency, so consistency checking must be done using a consistency index calculation, with the sorting and ranking method so that it is not necessary to check the consistency of the paired comparison matrix made. Assessment process with sorting and ranking as in Table 5. Determining the importance of each criterion on a scale of importance is more difficult when compared to ranking. And it is not yet known also that the importance scale can make a consistent pairwise comparison matrix or not, so there is a need to check consistency with the consistency index calculation. In contrast to determining interests by using rating, where there is no need to check for consistency because the resulting pairwise comparison matrix is definitely consistent, this has been confirmed in previous research.
If you take Faisol's research that discusses the comparison of FAHP and AHP [10], the time needed for weighting the criteria to have a faster execution time is shown in Table  6 and Figure 2. This is because in the priority criteria process in the modified AHP there is no need to check the consistency of the pairwise comparison matrix.

Determining Alternative Priorities
Modification to the alternative priority calculation process. just using a simpler calculation formula but the calculation process that is executed is basically not too changed. this can be seen from Figure 3 where the results obtained are exactly the same as the calculation alternative priority standard process. If taking the execution time needed in an alternative weighting in Faisol's research [10].
Although there is no difference in the final result. which is somewhat faster. can be seen in Figure 4. This is because. the alternative priority process in the AHP modification uses a simpler formula.

Determining Final Priority Index Value
Comparison of calculation results using the initial FPIV formula and the modified NIPA formula. if we take from the top 25 can be seen in Table 7.
Based on Figure 5. it can be known that the initial FPIV calculation process contains 3 equal value data. namely rank 6. 18. and 23. While the calculation of FPIV modification is 1. namely in rank 8.
This modification only affects if the parameter values in two different test data are still within the same criteria range. not if the parameter values are the same. And in the modified FPIV formula there is an alternative initial value variable. so this FPIV modification will be more maximal if it is used in a system that uses data with all initial data in the form of numbers such as income. IPK. and UKT data.

CONCLUSION
The application of the fuzzy algorithm and the modification of the AHP method to the recipients of the SPK Lazis scholarship in 2018 at UNNES. which involved the use of 810 student registrant data obtained results in which the first position was occupied by A009 students with a final priority index value of 0.004176516 and ten ratings Top recipients of Lazis scholarships are shown in Table 2. Using the calculation process in the decision support system in this research is better than the standard decision support system. this was shown in the previous discussion. Such as the use of fuzzy Tsukamoto can be used to change the value of the range into unit values. Fuzzy c-means produce a more variable score. but the more data and the more varied the spread of data. The better if the number of clusters is determined too. In modifying the determination of the importance of each criterion. Using sorting and ranking will produce a pairwise comparison matrix that is certainly consistent and has a faster processing time than using an interesting scale. But is less suitable for solving unstructured problems. In the alternative priority. modification has a relatively faster execution time than standard calculations. But it is also not suitable to solve unstructured problems. And modifications to the FPIV can be minimized to produce the same final value. But more leverage if used on a system that uses data with all initial data in the form of all numbers.