Improved hybridization of Fuzzy Analytic Hierarchy Process (FAHP) algorithm with Fuzzy Multiple Attribute Decision Making - Simple Additive Weighting (FMADM-SAW)

In this research, the improvement of hybridization algorithm of Fuzzy Analytic Hierarchy Process (FAHP) with Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) in selecting the best bank chief inspector based on several qualitative and quantitative criteria with various priorities. To improve the performance of the above research, FAHP algorithm hybridization with Fuzzy Multiple Attribute Decision Making - Simple Additive Weighting (FMADM-SAW) algorithm was adopted, which applied FAHP algorithm to the weighting process and SAW for the ranking process to determine the promotion of employee at a government institution. The result of improvement of the average value of Efficiency Rate (ER) is 85.24%, which means that this research has succeeded in improving the previous research that is equal to 77.82%. Keywords: Ranking and Selection, Fuzzy AHP, Fuzzy TOPSIS, FMADM-SAW.


Introduction
In the research [1] hybridization algorithm of Fuzzy Analytic Hierarchy Process (FAHP) with Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) was conducted. Hybridization is done by weighting with FAHP algorithm and ranking with FTOPSIS algorithm. The result of this research is the average value of Efficiency Rate (ER) of 77.82% which is still felt too low. The conclusion of this research suggest that in this method developed again by hybridization of FAHP algorithm with Multiple Attribute Decision Making (FMADM).

Study of Literature
Decision Support System (DSS) is an interactive computer-based system that helps decision makers utilize data and models to solve a problem. There are several methods including Analytical Hierarchy Process (AHP) and Technique For Order Preference by Similarity to Ideal Solution (TOPSIS) [2]. AHP is a method in a decision-making system that uses several variables with a multilevel analysis process [3]. The analysis is done by giving the priority value of each variable, then do the pairwise comparison of the variables and alternative. TOPSIS is a method based on the concept that the best-chosen alternative not only has the shortest distance from the ideal solution, but also has the longest distance from the ideal solution.
In [1]  the weight of criteria and the FTOPSIS method is applied to prioritize the optimal alternative according to the criteria.

Flowchart Research
The Flowchart hybridization algorithm Fuzzy Analytic Hierarchy Process (FAHP) with Fuzzy Multiple-Attribute Decision Making -Simple Additive Weighting (FMADM-SAW) can be seen as in Figure 1.

Figure 1. Flowchart Research
In the flowchart above, the input data in the form of SKP value and the value of Work Behavior taken 2 years. Furthermore, the data is processed by using FAHP, FMADM-SAW and hybridization algorithm is a combination of FAHP-FMADM-SAW algorithm. The result of the process is the Work Performance Value of each algorithm and validation value which is the determination of whether or not an employee is given promotion.

Data used
The data used comes from Aparatur Sipil Negara (ASN) at Badan Kepegawaian Daerah dan Pengembangan Sumber Daya Manusia of Medan City (BKDPSDM) which is calculated according to the provisions of Badan Kepegawaian Negara as in Table 1

FAHP algorithm
The calculation steps of the FAHP algorithm are as in Table 3.

Structure of hierarchy
The hierarchical structure of the selection problem of promotion can be seen in Figure 2.

FMADM-SAW algorithm
Step c. Rating for each decision criterion Ratings for each decision criterion can be seen as in Table 4.

Implementation of Hybridization Algorithm (FAHP-FMADW-SAW)
Hybridization algorithm is the application of FAHP algorithm on weighting and FMADM-SAW for ranking based on input from FAHP to determine promotion of ASN with the case study of BKDPSDM. Ways of weighting and consistency ratio with FAHP algorithm and ranking with the FMADM-SAW algorithm can be seen as Chapter 3.3 and 3.4 above. In Table 5 we can see the weighting results for each criterion (SKP or Work Behavior). In Table 6 shows the ranking for each employee (alternative) Furthermore, the weight obtained with FAHP algorithm is calculated by the FMADM-SAW algorithm to step rank for determination of promotion in the employee. Flowchart Hybridization algorithm can be seen as in Figure 3.  In this form look the data input alternative the employee biodata that will be processed ranking for determination promotion. In this form seen the ranking process of each alternative that can be seen the result on the bottom right.

Conclusion
There is an improvement of Dooki, A.E., Bolhasani, P. & Fallah, M. (2017) research, where the average value of Efficiency Rate (ER) is only 77.82% which is still too low. In Dooki, Bolhasani and Fallah's research, hybridization of Fuzzy Analytic Hierarchy Process (FAHP) algorithm was adopted by Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) to select the best bank chief inspector based on several qualitative and quantitative criteria with various priorities. The AHP and TOPSIS Fuzzy Methods are used to determine the criteria and ranking weight of each of the selected inspectors. In this research, we made an improvement of Dooki and Bolhasani and Fallah research by improving the FAHP algorithm with Simple Additive Weighting (SAW), which is done by applying FAHP Algorithm to the weighting process and SAW for the ranking process to determine the promotion of the employee. The result of improvement is the average value of ER is 85.24%, which means that this research has succeeded in improving Dooki and Bolhasani and Fallah research by 7.42%.