APPLICATION OF FUZZY ANALYTICAL NETWORK PROCESS IN DETERMINING THE CHOICE OF AREAS OF INTEREST

ABSTRACT

The Untan Statistics Study Program provides a choice of areas of interest that will later be chosen by students.A student's hesitation leads to the need for a decision support system, to help determine what area of interest should be chosen.In the mechanism of determining the field of interest, a method is needed based on considerations between criteria.The method that can be used is the Fuzzy Analytical Network process (FANP) method.FANP is a combination of Fuzzy method and Analytical Network Process (ANP) method.The ANP method can be used in the form of solving with consideration of adjusting the complexity of the problem by deciphering the synthesis along with a priority scale [2].Fuzzy's approach is used to address incomplete data and information and accommodate the vague nature of decision makers in providing judgments that can overcome uncertainty in qualitative criteria [3].The FANP method is a good combination because it allows good dependencies between criteria and alternatives [4].
Research using the ANP method can be applied to decision making by considering various criteria, sub-criteria and alternatives [5].The ANP method aims to consider one criterion with another criterion or one alternative with another alternative.Then a Fuzzy approach is carried out, which aims to overcome the existence of unclear data and accommodate the vague nature of decision makers in providing assessments [6].Therefore, a combination of the Fuzzy and Analytical Network Process (ANP) methods or known as the Fuzzy Analytical Network Process (FANP) method was carried out.The advantage of the FANP method is that it has a level of subjectivity and inaccuracies that occur can be minimized compared to using the ANP method alone [7].
The purpose of this study is to obtain three different decisions, namely based on the opinions of lecturers and students, each of which is obtained using the ANP method.Furthermore, the opinions of lecturers and students were combined which were analyzed using the FANP method.These results are obtained by considering between criteria and sub-criteria.The criteria used in this study are academic criteria, the influence of others, and individual students.Academic criteria have three sub-criteria, namely, job prospects, teaching lecturers, and courses.There are two sub-criteria of the influence of others, namely the sub-criteria of family and friends.While there are two individual sub-criteria for students, namely selfpotential and self-desire of students.The alternatives used are three choices of areas of interest in the Untan Statistics Study Program, namely, the fields of business and finance, social and industrial, and environmental and disaster interests.

Pairwise Comparison Matrix
In this study, data collection was carried out using questionnaires addressed to students and lecturers.In the questionnaire, there is a choice of comparison of each criterion or sub-criterion on a scale of 1-9, with the results getting towards number 9, the criteria or sub-criteria are considered increasingly important.From the results of obtaining the scale, a matrix of pairwise comparison is formed.The pairwise comparison matrix is used to compare all elements in paired form for each sub-system of the hierarchy.The comparison that has been obtained is then transformed in matrix form for numerical analysis presented in Table 1 Pairwise comparison assessments are obtained using the importance levels presented in Table 2.If element i has one of the numbers above When compared element j, then j has the inverse value when compared element i.
The answer to the pairwise comparison matrix using the geometric mean can be calculated using Equation (1).
with   is the geometric mean of pairwise comparisons between i and j,   is the pairwise comparison value for respondents to-k, k=1, 2, …, N, and N is the number of respondents.The geometric mean that has been obtained, the next step is mathematically normalized, it can be written as follows [9]: with   is the geometric mean of pairwise comparisons between i dan j and   is the normalization of the geometric mean value of pairwise comparison between i and j for N respondent.Next, A weighting process is carried out for each criterion that has been determined based on the other criteria.The weighting calculation algorithm starts with paired comparison form data until the weight of each indicator of the criteria and its sub-criteria is obtainedA weighting process is carried out for each criterion that has been determined based on the other criteria.The weighting calculation algorithm starts with paired comparison form data until the weight of each indicator of the criteria and its sub-criteria is obtained [10].

Testing Consistency
Consistency tests on weight values are performed on each comparison matrix.As for some things that can be done when measuring the level of consistency as followsConsistency tests on weight values are performed on each comparison matrix.As for some things that can be done when measuring the level of consistency as follows: For some orders of the matrix, an average value is obtained Random Index (RI) presented in Table 3 [11].
Average rating RI can be used to determine Consistency Ratio a matrix using Equation (7).If the value has been converted into a TFN matrix, the value of fuzzy synthetic extent (Si) synthesis is then calculated.The purpose of obtaining the fuzzy synthetic extent value is to assess the weight of each criterion against the main purpose of the hierarchy [13].The formula is given as follows: To obtain , fuzzy use of m value in Equation (8).
with V is a vector value, M is a fuzzy synthesis value matrix, so that an ordinate value is obtained (d')' () =   (  ≥ Sc), (12) with Sp is the fuzzy synthesis value of one, Sc is another fuzzy synthesis value.Then a vector value is obtained ′ = (′( 1 ), ′( 2 ), . . ., ′(  ))  , (13) with Ai (i=1, 2, …, n) are n decision elements and d' (Ai) is a value that describes the relative choice of each decision attribute [15].Normalization of vector weight values is obtained by Equation ( 14) [16].
So that the fuzzy vector weight normalization value is obtained as follows: = (( 1 ), ( 2 ), . . ., (  )  . ( with W is a non fuzzy number.The calculation of the final weight of priority and the ranking of the final weight of priority are used to determine the order of each element [17].

RESULTS AND DISCUSSION
The data used in this study were primary data obtained by distributing questionnaires.There were 18 respondents with details of 6 people from the class of 2019, and 7 people from the class of 2020 who had chosen the field of interest, as well as several lecturers who supervised the field of interest in the Statistics Study Program.The data obtained is then formed into a pairwise comparison matrix for each criterion and sub-criteria.
One example of a paired comparison matrix at the criterion level for the 1st respondent in lecturers can be seen in Table 5.After obtaining a pairwise comparison matrix at the level of criteria and sub-criteria from all respondents to the lecturer, then weighting is carried out with the geometric average using Equation (1).
12 = (7 × 9 × 8 × 6 × 7) After weighting with the geometric average, a matrix of paired levels of lecturer respondent criteria was obtained which is presented in Table 6.The next step is to normalize the weighting value of the lecturer respondent criteria level matrix using Equation (2).
1,776 = 0,563.This is done on each weight value, so that the results of the normalization of the pairwise comparison matrix for the level of criteria for lecturer respondents are presented in Table 7.The calculation is carried out in the same way in the assessment results according to students, so that the normalization of paired comparison matrices at the level of criteria and sub-criteria is obtained.The results of the comparison between the weights of lecturers and students can be seen in Table 8.The weighted values obtained from the normalization of paired comparison matrices, must be tested for consistency first before being set as a priority.This is done using Equation (3).If n = 3, in Table 3 obtained the value of RI = 0.58, Then the consistency ratio value is obtained as follows: Value CR 0,046 ≤0,1000, with a CR value of 4.6%.Since the value is less than 10%, it can be said that respondents' assessment of the questionnaire is consistent and the weight obtained can be used for prioritization.Table 9 presents a comparison of CI and CR scores for lecturer and student questionnaires as follows: After obtaining the local weighting value on each criterion or sub-criterion, then an overall comparison is carried out to obtain the global weight value.Criteria and alternatives that are taken into consideration in determining the field of interest.Calculations with the help of Support Decision software obtained the results given in Table 10.After comparison of alternative choices of areas of interest by taking into account the relationship between sub criteria and criteria, overall results were obtained in Table 11.Based on Table 11, it was found that the field of industrial social interest is the best alternative for students because it has the highest weight of 44.1%, while lecturers in the field of business and finance interest are the best alternative with the highest weight value of 44.9%.
The data used for the measurement of priority interests were obtained by combining student and lecturer questionnaires.The data obtained is then formed into a pairwise comparison matrix for each criterion.One example of a pairwise comparison matrix at the criterion level can be seen in Table 12.The determination of paired comparison matrix elements in Table 12 was carried out by means of geometric averages from the combination of student and lecturer questionnaires with the ANP method.The CR value in the combined lecturer and student questionnaire was obtained at -0.189 which means less than 0.1000.Thus, it can be said that respondents' assessment of the questionnaire is consistent.
A consistent comparison matrix can be used for conversion to a Triangular Fuzzy Number (TFN) matrix.The matrix values in Table 12 are converted to TFN matrices which can be seen in Table 13.After obtaining the value of fuzzy synthesis in the first criterion, namely academic criteria, then it is carried out as well as other criteria.The calculation of the fuzzy synthesis value obtained is given in Table 14.Based on the ordinate value there is a minimum value of each  1 ,  2 ,   3 , fuzzy synthesis criterion, so that the vector weight value can be determined as follows: ′ = (1; 0,571; dan 0,815) The normalized vector weight value will be 1, with the normalized value as follows: W  = (0,419; 0,239, 0,342)  ⏟ ∑   =1 Thus, the weight of the (local) criteria obtained is 0.419; 0.239 and 0.342.Thus, it can be concluded that the top priority with the highest weight is found in academic criteria with a score of 41.9%, with the second highest priority being individual student criteria at 34.2%, and 23.9% for other people's influence criteria.
The ranking of each alternative is obtained by taking into account the relationship between sub-criteria and criteria.The calculation process is carried out using the help of Support Decision software.The results obtained can be seen in Table 16.Based on the use of FANP in determining the selection of areas of interest according to the opinions of students and lecturers who have been combined, it was found that the fields of business and finance became the first priority in the selection of areas of interest with the highest weight of 44.5%.The second priority is the social industry sector with a weight of 37.5% and the environment and disaster sector occupies the last position with the lowest weight value of 18%.

CONCLUSIONS
This study has discussed the use of Fuzzy Analytical Network Process in determining areas of interest in the Statistics study program FMIPA Tanjungpura University.Based on the results and discussions that have been explained, the decision was obtained, namely, the merger of lecturers and students' opinions obtained a global value weight in the fields of business and finance with the highest weight value of 44.5%, the social and industrial sector with a weight of 37.5%, and the field of interest in the disaster environment occupied the last position with the lowest weight of 18%.So that a decision was obtained that the field of business and financial interest is the main priority alternative in determining the choice of field of interest in the UNTAN Statistics Study Program.
a. Multiplication of the initial matrix of each criterion or subcriterion by a weight value, ∑ ∑     , the values of each row on the matrix then divide by their weight values,  by using Equation (5),   used for calculations Consistency Index (CI), As for the calculation of value CI presented on Equation (6).A matrix is generated from comparisons made randomly with a comparison scale 1-9.

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The next step is to divide the consistency value for the criterion level by each of its weight values which can be done using Equation (The result of dividing the consistency value by the weight value of each criterion so that the average value obtained is the maximum eigenvalue.After getting the grade   , The next step is to calculate the consistency index value

1. INTRODUCTION Tanjungpura
University (Untan) is one of the State Universities in West Kalimantan.One of the Study Programs offered is the Statistics Study Program.Untan Statistics Study Program has shown its existence.This can be seen from the large interest of students who want to enter the Untan Statistics Study Program, as evidenced by the results of the announcement of the Higher Education Entrance Test Institute that the interest in the Untan Statistics Study Program increases every year [1].

Table 3 . Average rating Random Index (RI)
[11]re committing to FANP calculations, the hierarchical structure of the problem is solved first by calculating the ANP to find the consistency of its comparison matrix values.A comparison matrix is said to be consistent when the values CR≤ 0,1[11].If eligible, the consistently converted comparison matrix values to a scale Triangular Fuzzy Number (TFN), to increase objectivity, effectiveness, and evaluate the value of trust in a criterion.The values of the ANP pairwise comparison matrix are then converted into the TFN scale, which is presented in

Table 13 . Triangular Fuzzy Number Matrix Conversion
The predefined Triangular Fuzzy Number matrix value is used to find the fuzzy synthesis value (Si) on each criterion (  ) based on Equation (8) as follows: