DEVELOPMENT OF A NEW MULTI-CRITERIA DECISION-MAKING METHOD

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Introduction
Currently, there are many different multi-criteria decision-making methods (MCDMs), and choosing which one to use is a challenge for decision makers. It can be said that because the ranking results of the alternatives may not be the same when using different MCDM methods. MCDM methods can be divided into four groups. The first group includes methods that both require normalization of the data and require the determination of weights for the criteria. The second group consists of methods that do not require normalization of the data but require the determination of weights for the criteria. The third group are methods that do not require weighting for the criteria but require normalization of the data. The remaining group (the fourth group) is composed of methods that do not require normalization of the data nor do they require the determination of weights for the criteria. Thus, it can be seen that when using the method of group four, the decision maker will eliminate the difficulties in data normalization as well as determining the weights for the criteria. In group four, there is only one method, the CURLI method. This method is gaining popularity in recent times. However, when using the CURLI method, it will be difficult to rank the alternatives if the number of options to be ranked is large. Thus, improving the CURLI method so that it can be easily used will assist decision makers in multi-criteria decision making. Therefore, research devoted to new MCDM method is relevant.

Literature review and problem statement
Many investigations have been carried out to determine the appropriateness of data normalization methods when combined with multi-criteria decision-making methods. In [1], the CODAS method was used to combine with five different data normalization methods in ranking smartphone categories. This study has shown that rank inversion occurs when different data normalization methods are used. In [2], the VIKOR method was combined with four different data normalization methods to rank the products of a supermarket. The results of this study show that only one of the four data normalization methods is suitable to combine with the VIKOR method. In [3], the SAW method was used in combination with four different data normalization methods to evaluate candidates for graduate study. This study showed that only one of the four data normalization methods used were found to be suitable for incorporation with the SAW method. In [4], three methods of data normalization have been used in conjunction with the PIV method in the financial ranking of firms. This study showed that only one of the three data normalization methods used were found to be suitable for incorporation with the PIV method. In [5], the ROV method was used to combine with eight different data normalization methods to rank the financial performance of companies. The results showed that only one of the eight methods of data normalization were determined to be suitable to be combined with the ROV method. In [6], the TOPSIS method was combined with six different metric normalization methods to rank drone-landing options. This study has shown that only one out of six methods of data normalization were determined to be suitable to be combined with the TOPSIS method. In [7], the AHP method was used in combination with five different data normalization methods to rank smart parking locations. This study has shown that only one out of five data normalization methods is suitable to be combined with the AHP method. In [8], the WSPAS method was combined with six different data normalization methods to rank robots. This study concluded that only one of the six data normalization methods was determined to be suitable to be combined with the WSPAS method.
Thus it is possible to see the complexity of data normali zation in multi-criteria decision making. Meanwhile, all MCDM methods mentioned above when applied need to standardize the data. Using a multi-criteria decision-making method without the need to normalize the data would eliminate this complexity. CURLI is the method that meets this requirement [9]. In addition, if it is necessary to determine the weight for the criteria when making a multi-criteria decision, it is also a difficulty for the decision maker. This is also considered a limitation of all the MCDM methods mentioned above. A wrong decision can be made if the selection of the weighting method is incorrect. These difficulties will also be eliminated if a decision-making method is used that does not require weighting of the criteria. CURLI is also the method to meet this requirement [9]. However, the application of the CURLI method will face certain difficulties if the number of options to be ranked is large. This is the impetus to develop the CURLI method into a new method so that it is more convenient to use.

The aim and objectives of the study
The aim of this study is to develop the CURLI method into a new multi-criteria decision making method.
To achieve this aim, the following objectives are accomplished: -to discover the limitation of the CURLI method and propose a solution to overcome it; -to rank alternatives using a new multi-criteria decisionmaking method.

Materials and methods
This study carried out the development of a new method based on the CURLI method. Therefore, it is necessary to have an overview of the CURLI method first. The steps for implementation of multi-criteria decision-making according to the CURLI method are as follows [9]: Step 1. Build a decision matrix with m alternatives and n criteria (Table 1), where x ij is the value of criterion C j of alternative A i , with i = 1 ÷ m, j = 1 ÷ n. Table 1 Decision matrix Step 2. Create n square matrix of level m as shown in Table 2. Microsoft Excel software is the tool used to perform this task. Each square matrix is the score of a criterion. The scoring rules are as follows, example for a certain criterion C j : -if in the cell corresponding to row 2 and column 1, x 2j is worse than x 1j , then that cell will score 1; -if in the cell correspoding to row 1 and column 2, x 1j is better than x 2j , then that cell will score -1; -if in the cell correspoding to row 2 and column m, x 2j equals x mj , then that cell will score 0; -in the cells where the number of rows matches the number of columns, score 0.
Let's call this matrix the scoring matrix for each criterion. Table 2 Example of the scoring matrix for C j criterion Step 3. Combining all the scored square matrix for n criterion according to formula (1). This task was also performed using microsoft Excel software. There is a matrix called the process scoring matrix, denoted by PA the matrix. This is content that has been improved over its original version: Step 4. Rank the alternatives according to the principle that the best solution is the one with the smallest value of S i , and vice versa. This is also the difference in the performance rating of the alternatives of the proposed method (CURLI2 method) compared to the original version (CURLI method).

1. Limitations of the CURLI method and how to overcome it
The implementation of step 4 of CURLI method is a very difficult task, take the decision makers a lot of effort. This task is even more difficult if the number of alternatives that need to be ranked is large. This is also a confirmation of a recently published study [10]. A recent study had to create a complex computer program in Java language when applying this method [11]. This work is clearly complicated and sometimes it causes difficulties for the decision makers who are not good at information technology. It further shows the inadequacy of decision-making in urgent cases. This is considered the first limitation of the CURLI method.
To remove these limitations of CURLI method, a method is proposed and named CURLI2. The steps for implementation of multi-criteria decision-making according to CURLI2 method include: -the first three steps are the same as CURLI method; -Step 4. Add the cells in each row of PA matrix according to (2). The alternative with the lowest score (S) is the best alternative, and vice versa: Obiviously, it is much more convenient to add up the scores of cells of each alternative to rank the alternatives according to the scores than rearrange the rows and columns as in step 4 of CURLI method.

2.
Multi-criteria decision making using the proposed method 5. 2. 1. Example 1 In this example, five material types to create car protective cover are ranked. Each type of material is evaluated by six criteria ( Table 3). The meaning of each criterion is presented in the top row of Table 3. Table 3 Material types to create car protective cover [12][13][14] No. Where, four criteria C1-C4 are the larger the better. In contrast, C5 and C6 are the smaller the better [12][13][14]. Choosing an alternative which simutaneously ensures all the criteria C1-C4 are considered the largest and C5, C6 are considered the smallest is the task for multi-criteria decision-making. Some MCDM methods were used to complete this task include CURLI [12], PROMETHEE [13], and EDAS [14]. The result of ranking the alternative done by these method will be used to compare to the ranking result done by CURLI2 method.
Ranking the alternatives according to CURLI2 method is done as follows: Step 1. Build a multi-criteria decision-making matrix. This matrix is the data of the material types (Table 3).
Step 2. Scoring six criteria, let's obtain the results Tables 4-9. Table 4 Scoring matrix for criterion C1 (example 1) No. Table 5 Scoring matrix for criterion C2 (example 1) Table 6 Scoring matrix for criterion C3 (example 1) Table 7 Scoring matrix for criterion C4 (example 1) Table 8 Scoring matrix for criterion C 5 (example 1) Table 9 Scoring matrix for criterion C 6 (example 1) Step 3. Add the scoring matrix for each criterion (from Tables 4-9) according to formula (1) let's obtain PA matrix as in Table 10. Table 10 PA Matrix (example 1) Step 4. The score S of each alternative is calculated according to (2), the results are presented in Table 11. The results of ranking the alternatives according to score S are also summarized in Table 11. Besides, the ranking results of CURLI method, PROMETHEE method and EDAS method are also summarized in Table 11. Table 11 Ranking the alternatives according to different MCDM methods (example 1) No.
CURLI-2 (Proposed method) CURLI [12] PRO-METHEE [13] EDAS [14] S Rank It can be seen from the data in Table 11 that the result of ranking the alternatives according to CURLI2 method is not the same as the ranking results according to other methods. Howerver, all the methods show that A 4 is the best alternative, which means the task of finding the best alternative is equivalent using all four different methods. Besides, the second-ranked alternative (alternative A 3 ) and the fifthranked alternative (alternative A 1 ) are exactly the same when using these four methods. In other words, in this example, using CURLI2 method gives the same effectiveness compared to other MCDM methods.
Where C1 is the smaller the better, the other four criteria are the larger the better. Finding out an alternative which simultaneously ensures that C1 is considered to be the smallest and the other four criteria are considered the largest is the task for multi-criteria decision-making. This task is also done when using different methods, include CURLI [12], EDAS [14], TOPSIS [15], and EXPROM2 [16]. The results of ranking the alternatives done by using these MCDM methods will also be used to compare to the ranking result done by using CURLI2 method. Table 12 Material types to create gear [12,[14][15][16] No. Ranking the alternatives using CURLI2 method according to the steps in example 1. The result of ranking the alternatives using CURLI2 method has been summarized in Table 13. In addition, the ranking results using the other MCDM methods are also summarized in Table 13. Table 13 Ranking the alternatives using different MCDM methods (example 2) No.

CURLI-2 (Proposed method)
CUR-LI [12] EDAS [14] TOP-SIS [15] EX-PROM2 [15] The data in Table 13 have shown that the results of ranking the alternatives are not the same when using different methods. However, all five used methods have showed that A 7 is the best alternative and A 1 is the worst alternaitve. In other words, the task to find out the best alternative (A 7 ) has been successfully completed when using five different MCDM methods. Which means, in this example, using CURLI2 method is equally as effective as using other MCDM methods.

2. 3. Example 3
In this example, seven different types of robot are ranked. Each robot type is described by five criteria (Table 14) [17,18].
Where, criteria C1, C2, C4 and C5 are the larger the better. In contrast, C3 is the smaller the better. The task of multi-criteria decision-making is to find out an alternative, which simultaneously ensures that C3 is the smallest, and the other criteria are the largest. R and CURLI methods [17], CODAS method [18] are used to complete this task. Table 14 Different robot types [17,18] No. Ranking the alternatives using CURLI2 is done in the same way as in example 1. Table 15 showed the results of ranking the alternatives using different methods. The data in Table 15 has showed that the result of ranking the alternatives using CURLI2 has a high degree of similarity compared to when using other MCDM methods. The fifth, sixth and seventh-ranked alternatives are exactly the same when using three methods CURLI2, R and CURLI. Specially, all four used methods showed that A 2 is the best alternative. In other words, CURLI2 method has successfully completed its role when it is used to make multi-criteria decision in this example.

Discussion of the results of multi-criteria decision making using the CURLI-2 method
From the data in Tables 11, 13, 15, it is shown that the best solution determined using the CURLI-2 method always coincides with the best alternative determined using other MCDM methods. That shows that the proposed me-thod (CURLI-2 method) is completely reliable when used for multi-criteria decision making. It means that it is correct to detect the limitation in step 4 of the CURLI method as well as to suggest a solution to overcome it. The difference between the CURLI-2 method and the CURLI method is in the way step 4 is performed. Although the implementation is different when using these two methods, they always show the same best solution when ranking alternatives.
The procedure in step number four is the difference between the CURLI-2 method and the CURLI method. Despite this difference, in all the examples performed, both methods identified the same best alternative (in Tables 11,13,14).
The limitation of the proposed method (CURLI-2 method) is that the scoring for options is based on dry numbers only. For a given criterion, if the difference in its value among the alternatives is very large, which scoring seems difficult to interpret.
The disadvantage of the CURLI-2 method is that it does not consider the weight of the criteria. That means the decision maker's opinion on the priority of the criteria against each other will not be taken into account. This is also the disadvantage of the CURLI method.
The work to be done in the future is applying CURLI2 method to rank the alternatives when the number of alternatives changes, which means after ranking the alternatives, there will be alternatives added or removed from the list of alternatives. Thereby, it is possible to make necessary improvements (if necessary) to further improve the CURLI2 method.

Conclusions
1. The development of the CURLI method has developed a new MCDM method. The new method is called CURLI-2. Using the CURLI-2 method will be simpler than using the current MCDM methods.
2. In all cases examined, the best alternative determined using the CURLI-2 method was consistent with that of the other MCDM methods.

Conflict of interest
The authors declare that they have no conflict of interest in relation to this research, whether financial, personal, authorship or otherwise, that could affect the research and its results presented in this paper.

Financing
The study was performed without financial support.

Data availability
The manuscript has data included as electronic supplementary material.