Multi-criteria decision making of turning operation based on PEG, PSI and CURLI methods

. Multi-criteria decision-making ( MCDM ) is the methods identify an alternative that is considered the best among the implemented alternatives. This issue is probably more signi ﬁ cant since each alternative is evaluated based on many criteria that may be contrary. This paper presents the multi-criteria decision-making of a turning process. Turning experiments were carried out with a total of sixteen alternatives. A test material used is SB410 steel. Cutting tools are coated with TiN. The aim of this study is to determine the experiment where the minimum surface roughness and the maximum material removal rate ( MRR) are simultaneously obtained. Three multi-criteria decision-making methods were used include: Pareto-Edgeworth Grierson ( PEG ), Preference Selection Index ( PSI ) and Collaborative Unbiased Rank List Integration ( CURLI ). In each case of the application, it is not necessary to de ﬁ ne weights for the criteria. The stability of ranking the alternatives on the basis of different MCDM methods is also identi ﬁ ed according to the value Gini index. The results demonstrate that the PEG and CURLI methods both determine the best option. The cutting velocity of 1700 rev/min, feed rate 0.192mm/rev and depth of cut of 0.6mm are the options where the surface roughness and MRR are minimum and maximum respectively.


Introduction
Turning is the most common of the cutting machining methods. This method can be used on many types of machines, such as lathes, milling machines, drilling machines and boring machines. In a mechanical workshop, the lathes account for about 40% of the machine and around 25-35% of the mechanical processing volume is composed of the turning workload [1].
To evaluate effectiveness of a machining process in general or a turning process in particular, it is necessary to consider many criteria at the same time, such as surface quality, dimensional accuracy, machining productivity and costs. There are certain expectations for each of these criteria, for example, minimum surface roughness, highest accuracy, highest productivity, minimum machining cost, etc. In fact, however, the expectations are sometimes not satisfied simultaneously. For instance, in turning operation with high speed for improving machining productivity, the tool wear rate is high, reducing the tool life [2]; increasing the feed rate and depth of cut for higher MRR raise the surface roughness [3]; the flow rate and concentration of the cooling fluid increased for reducing tool wear and cutting heat lead to pushing up the costs and affecting environment as well; and in the case of improving the cutting parameters for machining productivity, it also increases the vibration level of the cutting tool, thereby reducing the tool life and increasing surface roughness [4], etc. In this case, the decisions made should ensure that desires are simultaneously satisfied. Many multi-criteria decision-making methods are used during turning processes in many different cases.
The TOPSIS method was used for decision making in the selection of: cutting velocity, feed rate and depth of cut to have the minimum surface roughness and maximum MRR in turning EN8 steel [5]; cutting tool material, cutting velocity, feed rate and depth of cut to obtain both the minimum surface roughness and maximum MRR during turning process of EN25 steel [6]; cutting velocity, feed rate, depth of cut, tool nose radius and negative rake angle to reach the minimum surface roughness and minimum cutting force in the turning operation of AISI 52100 steel [7]; cutting velocity, feed rate and depth of cut to attain the minimum surface roughness (Ra and Rz) and maximum MRR in the experiments of turning EN19 steel [8]; cutting velocity, feed rate and depth of cut in order to acquire simultaneously minimum surface roughness and maximum MRR during turning AISI D2 steel [9]; cutting velocity, feed rate and depth of cut to have the minimum cutting force and surface roughness, maximum tool life and MRR in turning the material Pure Titanium [10], etc.
The VIKOR method was applied to multi-criteria decision-making in turning process in several studies so as to determine: spindle speed, feed rate and depth of cut for minimum surface roughness, minimum three shear force and three vibration components, and maximum MRR when steel EN 10503 workpiece was turned [11]; cutting velocity, feed rate and depth of cut for minimum surface roughness, maximum MRR, and minimum cutting force in turning CP-Titanium Grade 2 material [12]; workpiece speed, feed rate and depth of cut to reach simultaneously minimum surface roughness and tool wear rate, and maximum MRR during a turning process of AISI 316L part [13]; cutting velocity, feed rate, depth of cut and flow rate of cooling fluid to have minimum surface roughness and energy consumption, and maximum MRR in turning mild steel [14]; cutting velocity, feed rate and depth of cut to gain the maximum MRR and minimum surface roughness (Ra, Rq and Rz) turning AA7075 aluminum alloy [15], etc.
The MOORA method was used to multi-criteria decision-making in turning operation in several studies so as to identify: cutting velocity, feed rate, depth of cut and tool nose radius to have the minimum surface roughness, minimum three component cutting forces and maximum MRR in turning steel EN 10503 [16]; tool nose radius, cutting velocity, feed rate and depth of cut for minimum surface roughness and surface hardness, and maximum MRR during the process of turning EN25 steel [17]; cutting velocity, feed rate, depth of cut, positive rake angle, and cutting conditions (Dry and MQL) to achieve all parameters feed force, tangential force, radial force, resultant cutting force, and shape deviations which are minimum in the case of turning Al6026-T9 aluminum alloy [18]; cutting velocity, feed rate and depth of cut for minimum cutting force, surface roughness and tool wear rate in turning Commercially Pure Titanium material [19], etc.
The COPRAS method was used to define the spindle speed, feed rate and depth of cut to ensure that the cutting capacity, tool vibration and surface roughness were simultaneously minimized when in turning steel ASTM A36 [20]; cutting velocity, feed rate and depth of cut for minimum surface roughness and maximum MRR when SCM440 steel was turned [21]; cutting velocity, feed rate, depth of cut, cutting tool and machining environment (dry or wet) to reach the minimum surface roughness, machining time, tool wear rate, and maximum MRR during turning process of SU304 stainless steel [22], etc.
The use of multiple methods for multi-criteria decisionmaking was also carried out in a number of studies: The MOORA and WASPAS methods were applied so as to determine the cutting velocity, feed rate, depth of cut and percentage of TiC (additive) in order to have minimum cutting force and surface roughness and the largest MRR during the turning process of aluminum alloy Al 6063 [23]; the TOPSIS and MOORA were used to find the value of spindle speed, feed rate and depth of cut in order to ensure that all three parameters of cutting capacity, surface roughness and vibration frequency of the tool are smallest in the case of turning steel ASTM A558 [24]; the TOPSIS and SAW were applied to identify the cutting velocity, feed rate and depth of cut for the minimum surface roughness, tool wear rate, cutting heat and cutting force in turning steel Ti-6Al-4V [25]; the TOPSIS and PIV were blended to define the cooling fluid concentration and flow rate, tool nose radius, cutting velocity, feed rate and depth of cut to gain minimum surface roughness, tool wear rate and roundness error during the process of turning 9XC steel [26]; another study applied eight methods TOPSIS, VIKOR, MOORA, COPRAS, SAW, WASPAS, PIV and PSI to determine spindle speed, feed rate, depth of cut and tool nose radius to have the minimum three component cutting forces have and highest MRR in turning operation of 150Cr14 steel [27], etc.
The importance of applying multi-criteria decisionmaking methods in turning processes is likely confirmed by the numerous studies related to this topic, some of which are mentioned above. However, it is necessary to define the weights of the criteria for application. This determination is relatively difficult for decision makers because of the fact that there are many dissimilar methods of weight determination and the weight of each criterion is different in each method. The number of criteria is also not the same. Since the weights of the criteria are different, the ranking of the alternatives is distinct as well [28]. Thus, if an application of a certain multicriteria decision-making method does not require determining the weights of the criteria, this obstacle will be eliminated.
Pareto-Edgeworth Grierson (PEG) [29], Preference selection index (PSI) [30], and Collaborative Unbiased Rank List Integration (CURLI) [31] are known as multicriteria decision making methods that do not need to define the weights of criteria. These three methods have been applied to multi-criteria decision making in several studies.
The PEG method was used for multi-criteria decisionmaking in several studies such as: polyethylene pipe design [32]; Flexural plate design, and in Seismic structural retrofitting. In both of these cases, the best option is the same as cases using the methods ELECTRE III, PROM-ETHEE I and II, and AHP [33]. The PEG is also applied in the design of building [34] and machine [35], the estimation of construction costs [36], etc. However, it can be confirmed that there has not been a study using the PEG to make multi-criteria decisions in the turning process to date.
Some researchers applied the PSI method in multicriteria decision making: in the design of production systems [37]; in the selection of computer software for human resource management [38]; in finding a business location [39], etc. However, the application of this method to multi-criteria decision making during the turning processes is still limited.
The CURLI method was proposed in 2016 [31]. Apart from the application in the study itself, so far, this method has not been found to be used in any research in any area for some unknown reason. Perhaps, specific steps for implementation are not presented, leading to the lack of attention. This issue is further clarified in the next section of this article.
The two methods PEG and CURLI have never been applied to make multi-criteria decisions on the turning processes, while the PSI has only been used for multicriteria decision making in the turning processes in several studies. It can be said that applying all three of these methods at the same time to multi-criteria decision-making in the turning process has never been done before. This is the reason that motivates this study.
A turning test process took place in this research with the sixteen experiments. These were designed according to the Taguchi method. At each trial, the cutting velocity, feed rate and depth of cut were varied. They are parameters that can be easily changed by the operator of the machine [40]. The surface roughness and MRR were calculated. The reason these two parameters are chosen as output parameters is the surface roughness has a direct influence on the workability and lifetime of the product, while the MRR is an important measure to evaluate the productivity of the machining [41,42]. Three methods PEG, PSI and CURLI were used to solve the multi-objective decision problem. The aim of this study is to determine the experiment where the minimum surface roughness and the maximum MRR are simultaneously obtained.
2 Several methods of multi-criteria decision making

PEG method
The steps for implementation of multi-criteria decision making according to the PEG approach are as follows [29]: Step 1: Determination of criteria vectors.
where function (1) is used for the criterion as high as possible, function (2) is used for the criterion as low as possible, i = 1,…, n; j = 1,…, m.
Step 2: Arrangement of the criteria vector values in ascending order.
Step 3: Determination of aggregate vectors for each criterion.
Step 4: Arrangement of the aggregate vector values in descending order.
Step 5: Calculation of shifted vectors.
Step 8: Calculation of the mean square error (MSE) for each alternative.
Step 9: Ranking the alternatives according to the rule that the alternative with the highest is considered the best

PSI method
The steps for implementation of multi-criteria decision making according to the PSI approach are as follows [30]: Step 1: Formation of decision matrix.
where: function (12) is used for the criterion as high as possible, function (13) is used for the criterion as low as possible.
Step 3: Calculation of mean values of normalized data.
Step 4: Identification of preference value from the mean value.
Step 5: Identification of deviation in the preference value.
Step 6: Determination of the overall preference value for the attributes.
Step 7: Calculation of preference selection index for each alternative.
Step 8: Ranking the alternatives. The best alternative is the one with maximum value of u i .

CURLI method
The CURLI method was first proposed in 2016 [31]. In that study, the authors selected candidates for a school of medicine. The candidates' abilities were in turn commented on by the interviewers. Instead of scoring the candidates in the traditional way, the interviewers only assessed whether a candidate is better or worse than another based on a certain criterion. However, in that study, they applied directly to the case of using four interviewers to evaluate four candidates without presenting the general steps. This may be explained that some of the candidates were interviewed by all the interviewers and some of them were not. As a result, formulating the generalized steps for implementation may be difficult for the authors of that study. Regarding machining processes in general and turning processes in particular, however, the results of each test (surface roughness, flatness error, dimensional accuracy, etc.) are all numbers that need to be measured during the experiment. Therefore, the values of all those parameters must be examined equally. In other words, if each experimental alternative is considered as a candidate, then all those candidates must be considered by experiment analysts. Hence, it is necessary to develop a specific sequence of steps to rank the alternatives according to the CURLI method. In this study, the implementation steps are generalized to make multi-criteria decisions based on the CURLI method.
The steps are presented as follows: Step 1: Building a matrix with m rows and n columns, where m is the number of alternatives, n is the number of criteria. The matrix is called the decision matrix, as shown in Table 1. In which, the criteria can be opposite, namely, some criteria should be as small as possible and some criteria should be as high as possible. The goal of building the matrix is to determine the alternative Ai (i = 1…m) to be considered the best.
Step 2: For each criterion, a square matrix of order m (with m rows and m columns) is established, as shown in Table 2. Scoring is carried out in each cell of the matrix in the following way, for example: scoring 1 at the cell of column 1 and row 2 if the value of C j of A 1 is better than of A 2 ; scoring À1 at the cell of column 2 and row 1 if the value of C j of A 2 is worse than of A 1 ; scoring 0 at the cell of column 2 and row m if the value of C j of A 2 is equal to of A m ; no scoring at the cells that their order of the columns and rows are the same (the cells on the main diagonal of the matrix). This matrix is called the scoring matrix for each criterion. In short, there is n scoring matrices corresponding to n criteria.
Step 3: Adding all the scoring matrices for each criterion together for a new matrix, which is called the processing scoring matrix.
Step 4: Restructuring the processing scoring matrix by changing the positions of the rows and columns so as to form a matrix where the upper area of the main diagonal has no cells with a positive score (the highest is zero). The ideal case is that all negative scores are above the main diagonal of the matrix. After restructuring, the alternative ranked in row 1 is considered the best.
x m2 x mj x mn Table 2. Example of scoring matrix for each criterion. Solution The turning tests were implemented on a conventional lathe ECOCA (Fig. 1). SB410 steel (conforming to JIS À Japanese standard) was used in the experiments. This steel has good machinability, low cost and is the most popular steel for manufacturing common machining parts made of silver, shafts, gears, levers. The cutting tool is coated with TiN. This type of cutting tool has high hardness, high oxidation resistance and is widely used in cutting technology [43,44].
Before the experiment, the specimens were roughly turned. The length and diameter of the test specimens were 320 mm and 28 mm, respectively. Three parameters were changed at each trial, including cutting velocity, feed rate and depth of cut. The values of the cutting parameters were chosen according to the machine's ability, workpiece material, and some studies [45,46], as shown in Table 3. Sixteen tests were performed as shown in Table 4.
MRR is defined as (19): Where n w is the cutting velocity (rev/min), d is the diameter of the workpiece, f d is the feed rate (mm/rev), and a p is the depth of cut (mm).
Surface roughness is measured by SJ-201 (Mitutoyo À Japan) machine. During the measurement, the part is mounted on two V-blocks, the measuring head of the machine moves parallel to the center shaft of the part, in other words, perpendicular to the cutting velocity vector. Each steel specimen was measured at least three times, the surface roughness at each test was calculated as the average of successive measurements. The surface roughness and MRR results are also included in Table 4.
The Minitab software was used to analyze the experimental results. With the significance level to be 0.05 [47], the Pareto chart represents the influence of the cutting parameters on the surface roughness, shown in Figure 2. The Pareto software found a limit that a certain parameter is considered affecting the surface roughness to be 2.18. The gray rectangles representing the cutting parameters all show that this limit is exceeded, as a consequence, all three cutting parameters have a great influence on the surface roughness. In which, the feed rate is the most influential, followed by the cutting velocity and the depth of cut. These results are consistent with many published studies [3,48]. Figure 3 is another type of graph showing the impact of the cutting parameters on the surface roughness. Accordingly, the surface roughness decreases rapidly if the cutting velocity increases, while the surface roughness increases quickly if the feed rate and depth of cut both increase. This result is also consistent with the conclusions from some research [3,48]. It can be said that: in order to have a small surface roughness, it is necessary to choose a high cutting velocity and the low feed rate and depth of cut. However, the low feed rate and depth of cut lead to the low MRR as well (based on formula (19)). Thus, it is probably difficult   9 (2022) to find the value of the cutting parameters for the small surface roughness and high MRR if only the graphs in Figures 2 and 3 are observed. On the other hand, the data in Table 4 shows that the minimum surface roughness is in A 13 , while the maximum MRR is in A 10 . Therefore, it is likely difficult to see which alternative is the best for obtaining the minimum surface roughness and maximum MRR at the same time. So as to cope with this issue, multicriteria decision making should be considered. It is further clarified in the next section of this article.

Multi-criteria decision making of turning operation 4.1 Application of PEG method
Formulas (1) and (2) are applied to calculate X i,j . Formula (3) is used to define x i ; Y i,j are calculated based on formula (4) and y i are computed according to the formula (5). x*, y* are identified on the basis of the formulas (6) and (7), respectively; Formula (8) is used for Dr i determination. f i 0 are calculated based on formula (9). Table 5 presents the values of some parameters in PEG and rank of the alternatives.

Application of PSI method
Formation of decision matrix. It consists of the last two columns in Table 4.
The normalized values of the attributes are defined according to the formulas (12), (13). The result is presented in Table 6.
The mean of the normalized value is calculated according to formula (14). Accordingly, the mean of the normalization of the surface roughness and the MRR correspondingly 0.527 and 0.407.
Determination of the overall preference value for the attributes is according to (17): w Ra = 0.240; w MRR = 0.760.   The preference selection index u for each alternative is defined as (18), shown in Table 6.
The alternatives are ranked based on the value of u i . The result is also presented in Table 6.

Application of CURLI method
The steps under the CURLI method are applied for multicriteria decision making.
Building a decision matrix. It consists of the last two columns in Table 4.
Scoring the alternatives for each criterion. Scoring results for the Ra and MRR are presented in Tables 7 and 8, respectively.
The processing scoring matrix is determined and the results are as shown in Table 9.
The rows and columns are repositioned in the way that the cells in the upper part of the main diagonal no longer have a positive score. This process can be executed manually or under programming methods with a computer. In this study, it was done manually. The results of sorting  P1  P2  P3  P4  P5  P6  P7  P8  P9  P10  P11  P12  P13  P14  P15  P16 A1  Duc Trung: Manufacturing Rev. 9, 9 (2022) for the processing scoring matrix are presented in Table 10.
According to the data in Table 10, A 14 is the best alternative and A 1 is the worst. The ranking results of the alternative under three approaches are shown in Table 11.
The data in Table 11 revealed that: -All three methods found that A 1 is the worst alternative.
The data in Table 4 show that the MRR at A 1 is considerably smaller than other fifteen alternatives. Consequently, A 1 to be the worst is reasonable.
-The PEG and CURLI both found A 14 to be the best alternative, while the PSI identified A 10 as the best option. The best and second best alternatives were opposite when using the PEG and PSI method. At the moment, this difference is not explained yet. However, due to this difference, the data in Table 4 should be looked at again. At A 10 , the MRR was highest among all sixteen alternatives, while the surface roughness was ranked at number 10. Meanwhile, MRR was ranked at number two, and surface roughness was ranked at Table 9. Processing scoring matrix. Table 10. Processing scoring matrix arrangement.
Under this circumstance, the decision maker must consider whether A 10 or A 14 is the best alternative. In this research, the calculation of the value Gini index was executed for reaching this task.
The value Gini index is used to determine the stability of ranking criteria when using different multi-criteria decision-making methods [49].
The value Gini index is defined according to the following formula [49].
where m is the number of alternatives, z is the number of multi-criteria decision-making methods used, R h and R l are the ranking values of the alternatives of the decisionmaking method h and l. D(R) ∊ [0,1]. D(R) = 0 means that the rank of an alternative is exactly the same under different methods. In contrast, D(R) = 1 means that the rank of the alternatives are the most different under the distinct MCDM methods. Upon comparing two alternatives, the one with the smaller value Gini index is the better. Formula (20) was applied to calculate the values Gini index in Table 11 and the results are presented in Table 12.
The alternatives of A 1 and A 5 have the same ranking results under all three MCDM methods, hence, their values Gini index are equal to 0. A 16 has the highest value Gini index, equal to 0.435363, its stability is lowest when using the three MDCM methods. Namely, A 16 was ranked No.5 when using the PEG method, No.9 when using the PSI method and No.6 when using the CURLI method. Comparison of A 10 and A 14 shows that: A 10 has a value Gini index of 0.186584 and A 14 has a value Gini index of 0.124389. Thus, the ranking stability of A 14 is smaller than A 10 . Hence, this proves that A 14 is better than A 10 , and at the same time A 14 is the best alternative among sixteen options. This result also demonstrates that the PSI method is not as good as the PEG and CURLI in determining the best alternative. A nearest published study indicated the same: the PSI method is not as good as the TOPSIS, VIKOR, MOORA, COPRAS, SAW, WASPAS, và PIV [27].

Conclusion
In this paper, the experiments of turning SB410 steel with a TiN-coated cutting tool are performed. Three parameters were changed at each trial, including cutting velocity, feed rate and depth of cut. The surface roughness and MRR were identified in each test. Three multi-criteria decision making methods including PEG, PSI and CURLI were applied for selecting the solution so as to reach the minimum surface roughness and maximum MRR. Some conclusions are drawn as follows: -For the first time, the two methods PEG and CURLI are used for multi-criteria decision making. These methods have the common feature that both do not need to determine the weights of the criteria when making multicriteria decisions. Fortunately, both of these methods identified the same best and worst solution. -The PSI are also known as multi-criteria decision making methods that do not need to define the weights of criteria. The worst alternative was pointed out when applying this method and it is similar to the PEG and CURLI. -The stability of ranking the alternatives using the different MCDM methods is determined through the value Gini index and on the basis of it, the best solution is identified. -The PEG and CURLI methods are likely better than the PSI in finding the best alternative. -The use of multi-criteria decision-making methods without determining the weights of the criteria may be easier in decision-making. In which, PEG and CURLI methods are recommended to be used. Especially, while applying, most of the multi-criteria decision making methods (such as: TOPSIS, VIKOR, MOORA, etc.) require the value of the criteria to be a quantitative criterion, the CURLI method can rank the solutions with the criteria values in both qualitative and quantitative forms. Table 11. Ranking results of the alternatives based on the three methods. A2  A3  A4  A5  A6  A7  A8  A9  A10  A11  A12  A13  A14  A15  A16   PEG  16  13  10  6  15  14  9  8  11  2  12  3  7  1  4  5  PSI  16  13  10  5  15  14  7  6  11  1  12  3  8  2  4  9  CURLI  16  14  12  9  15  13  7  4  10  3  11  2  8  1  5 6 -To obtain the "minimum" surface roughness and "maximum" MRR at the same time, it is necessary to select the cutting velocity, feed rate and depth of cut respectivel are 1700 rev/min, 0.192 mm/rev, and 0.6 mm.