Pareto–Edgeworth–Grierson (PEG), Preference Selection Index (PSI) and CURLI method in multi criteria decision making for turning process parameters optimization

ABSTRACT

In almost all machining processes there are several constraints associated and the objective functions are in conflict with the another objective function. In these situations, where equal importance is to be given to all constraints, multi criteria decision making is involved to determine the best optimal solution taking into consideration of all the objective functions in the turning process of AISI4140 steel. In this paper, PEG, PSI and CURLI method are employed. The PEG provides effective discrimination among the alternatives and ranking of alternatives is done effectively without any transition. PSI method is used in identifying the suitable alternatives without assigning the subjective weight assignment. In CURLI method, pairwise scoring matrix is obtained by computing the pairwise absolute difference between the values of the each alternative. Gini index is used in this work to quantify the level of disagreement among the PEG, PSI and CURLI ranking results for each alternative. In this work, PEG and CURLI approaches for MCDM for turning process parameters for AISI 4140 steel, the experimental run ‘#A14’ achieved the highest utility value and minimum radial deviation from the ideal solution, resulting combined acceptance of superior productivity in achieving minimum surface roughness and maximum MRR.

Keywords:
Multi criteria decision making; PEG; PSI; CURLI; Turning process; Gini index

1. INTRODUCTION

The common machining method used predominantly used in the manufacturing industries is the turning process and it is found to be consuming maximum mechanical processing volume to an account of more than 50% of the process involved in the industry. This turning process involves several constraints such as the accuracy, geometrical tolerance, quality, productivity, surface roughness and so on. However minimum surface roughness, maximum material removal rate, high productivity, minimum tool wear, minimum cutting force and minimum machining cost are some of the objective functions associated with the turning process. In most of the cases these constraints and the objective functions are in conflict and one objective function could not compromise with another function. In these situations, where equal importance is to be given to all constraints, multi criteria decision making is involved to determine the best optimal solution taking into consideration of all the objective functions in the turning process.

DUC TRUNG [¹] demonstrated the PEG approach for a turning process to determine the optimal decision making involving minimum surface roughness and maximum material removal rate. Sixteen experiments are conducted on SB410 steel with coated TiN as the cutting tool. The ranking of the alternatives are demonstrated using the PEG approach and best option among the alternatives are determined. SELMI et al. [²] compared multi criteria decision making methods through ranking stability index. ELECTREIII, PRMETHEE I and II, TOPSIS, AHP and PEG approaches are compared to determine the similarities and divergence between the several multi criteria decision making techniques. A Gini index is used to quantify ranking dispersion of pareto optima obtained through multi-criteria decision making methods. Results highlighted the importance of PEG approach in MCDM techniques. Researchers discovered the applications of multi criteria decision making methods for the process parameter optimization for a turning process. The best combination of process parameters among the different alternatives are determined and ranked. Also the researchers focused the MCDM application in the manufacturing domain and reviewed MCDM methods such as AHP. TOPSIS, MOORA methods and observed that the MCDM method are the more efficient method in solving multi criteria problems for turning process. A novel approach namely Additive ratio assessment method is used to determine the optimum process parameters while turning AISI 4340 steel [³, ⁴]. KHAN and KALIPADA [⁵] explored MCDM methodology in the determination of optimum process parameters during turning of commercially pure titanium grade 2. TOPSIS method is used for determining optimal parameters involving minimum cutting force, minimum surface reference, minimum machining temperature and maximum material removal rate. L9 Orthogonal array is used for conducting the experiments and MCDM approach is used to determine the optimal turning parameters using the TOPSIS method. This methodology is found to be used by many industrialists, researchers and decision makers to optimize multi objective problems more effectively and efficiently. MAJUMDER and SAHA [⁶] discovered the capability of solving complex optimization problems in production process by multi criteria decision making approaches. MOORA coupled with PCA is used to determine the optimal combination of input parameters to give minimum power consumption, minimum surface roughness and minimum vibration. L27 orthogonal array is used to conduct the experiments for turning ASTM A588 mild steel. MOORA-PCA and TOPSIS-PCA are used to determine the multi performance characteristics during the turning process. The comparison between MOORA-PCA and TOPSIS-PCA shows that MOORA methodology is more effective than TOPSIS methodology and the optimal process parameters are determined for turning ASTM A588 and it is reported that the application problems for dealing multi objective optimization problems the MDCM approaches are more effective.

SHAIK et al. [⁷] used MCDM approach for multi response optimization for machining EN8 steel for sustainable manufacturing. NGUYEN [⁸] introduced an improved curly method is used for multi criteria decision making considering different criteria. MCDM technique is demonstrated for choosing the best grinding wheel and the best service supplier. The ranking of the alternatives are also compared and sensitivity analysis is conducted to examine ability of the ranking results. This paper demonstrates the CURLI method for solving a MCDM problem and it is applicable for making interest in various fields. TRUNG et al. [⁹] used CURLI Aggregator method is a novel aggregation technique is developed to solve multiple criteria decision making problems. This method is used to rank the previously determined ranks by the CURLI method. CURLIA method is found to be the effective method in ranking the alternatives and it is demonstrated through three case studies by different application. TRUNG et al. [¹⁰] compared PSI and CURLI method for applying multi objective optimization problem involving 16 existing alternatives to minimize surface roughness, flank wear and maximize material removal rate. In this study, it is concluded that the CURLI method is the best method and the most suitable for solving multi objective optimization problems in turning process.

THINH et al. [¹¹] applied multi criteria decision making method for selection of best cutting oil. Seven different alternatives are selected and optimal oil is selected by using PIV method and CURLI method. It is observed that the ranking of the alternatives is effectively performed and criteria weights are determined for the each criteria. it is concluded that the same best oil selected in both PIV and CURLI method and it is also reported that the weighted criteria are not required for these methods. TOUGGUI et al. [¹²] demonstrated the dry turning optimization of stainless steel 316L based on TOPSIS process. This research found that the flank wear, tangential cutting force, surface roughness and material removal rate are conflicting responses, which require multi criteria decision making. In this case, the optimal cutting process parameter for turning operation for achieving minimum surface roughness, minimum cutting force and maximum material remove rate are determined using the TOPSIS approach. Material selection for the tool holder for milling operation is carried out using MCDM technique [¹³]. MARCOS technique is used in the investigation of EDM based on MCDM techniques [¹⁴,¹⁵,¹⁶].

A multi-criteria decision making technique is proposed to determine the optimal turning process parameters facilitating minimum cutting forces and maximum material removal rate. Several MCDM methods viz., SAW, WASPAS, TOPSIS, VIKOR, MOORA, COPRAS, PIV, PSI, MAIRCA, EAMR methods are used for this multi criteria decision making process. The weight of the criteria are determined by equal weight method, ROC weight and Entropy method [¹⁷,¹⁸,¹⁹]. The ranking of the alternatives in MCDM approach becomes crucial and hence researchers proposed CURLIA method, which aggregates ranking previously determined by several MCDM methods [²⁰]. A review of the performance of the PSI application in MCDM problems based on PRISMA is presented. It is observed that PSI is an effective straight forward application with low computational effort and received wider attention for complex decisions [²¹].

Several researchers have focused on single objective optimization for machining parameters for surface roughness or material removal rate. However in practical machining environment, the performance characteristics are conflicting and interdependent. Limited research are carried out in optimizing multi objective optimization using these novel MCDM techniques such as PEG, PSI and CURLI methods. This work uses these techniques to determine optimal parameters during turning process. The previous researchers emphasized laboratory-scale evaluation, while this study considers parameters relevant to practical machining conditions. The proposed approach provides a comprehensive evaluation of machining parameters through integrated analysis and offers a more reliable and best solution for selecting optimal parameters in the turning process. Turning process plays a vital role in manufacturing industries and highly influences the surface quality and productivity. Due to conflicting parameters such as tool life, surface roughness, material removal rate and so on, the determination of optimal parameters is often a big challenge. Industries require an effective approach to determine the optimal parameters with the given considerations and this research is motivated to develop a reliable multi criteria optimization approach for selecting the best turning process parameters.

2. EXPERIMENTAL METHODOLOGY

The multi objective optimization problems are more common in any machining process with conflicting objectives such as minimization of surface roughness and maximization of material removal rate. It is evident to determine the optimal machining conditions for higher productivity and surface quality during the turning process. This works demonstrates the Pareto–Edgeworth–Grierson (PEG) method as a multi-criteria decision- making (MCDM) tool to determine the optimal turning parameters for turning of AISI 4140 steel using a single point cutting tool coated with TiN. The turning parameters are conducted on a CNC turning centre as shown in Figure 1. AISI 4140 is selected as the work material since it is widely used ow alloy steel with high toughness, strength, wear resistance and good machinability making suitable for industrial components. TiN coated cutting tools are used since it significantly reduces tool wear and cutting force and improves the tool life and productivity of the turning process [²²]. MCDM techniques are used by the researchers for a better rank-sensitive improvement and critical review of applications, integrations and future direction in several industries [²³, ²⁴].

Figure 1
CNC turning centre.

In this work, surface roughness and material removal rate are considered as the primary evaluation criteria. Surface roughness affects the dimensional accuracy, functional performance, wear resistance and service life of the machined components. Surface roughness is measured using Mitutoyo surface roughness tester. Three readings are recorded for each experiment and the average of these values are recorded in the experimental data. Material removal rate is the key measure of machining productivity and highly influences the manufacturing time and production cost. Since surface roughness and MRR influences on both machining quality and productivity, they are considered as the vital evaluation criteria in this work when compared to the other criteria’s. The process parameters and its levels are shown in Table 1. The experimental matrix as shown in Table 2. is designed as proposed by Taguchi and L16 orthogonal array is used to conduct sixteen experiments. Three factors with four levels for each factor is designed allowing proper evaluation of parameter effects with balanced combination and improved resolution of factor influence. L16 array reduces the experimental effort when compared to full factorial design and it is highly reliable and produces experimental accuracy and statistical validity. Material removal rate is measured using weigh loss method by calculating the weight of the workpiece before and after machining. This method provides higher accuracy and commonly used by several researchers. The formula used to calculate the MRR is given in equation (1).

Table 1
Process parameters and its levels.

CUTTING PARAMETERS	LEVEL 1	LEVEL 2	LEVEL 3	LEVEL 4
Cutting speed (vc), m/min	550	850	1150	1450
Feed rate (f), mm/rev	0.1	0.2	0.3	0.4
Depth of cut (d), mm	0.3	0.5	0.7	0.9

Table 2
Experimental data.

EXPT. RUN	CUTTING SPEED	FEED RATE	DEPTH OF CUT	SURFACE ROUGHNESS	MRR
1	550	0.1	0.3	0.364	1589.254
2	550	0.2	0.5	0.614	3876.762
3	550	0.3	0.7	0.822	6147.047
4	550	0.4	0.9	0.986	7895.325
5	850	0.1	0.5	0.349	2580.472
6	850	0.2	0.3	0.569	2860.478
7	850	0.3	0.9	0.894	9856.214
8	850	0.4	0.7	0.989	9257.328
9	1150	0.1	0.7	0.683	4065.235
10	1150	0.2	0.9	0.563	9989.369
11	1150	0.3	0.3	0.526	6181.768
12	1150	0.4	0.5	0.778	9785.327
13	1450	0.1	0.9	0.423	10994.258
14	1450	0.2	0.7	0.587	16397.155
15	1450	0.3	0.5	0.422	10254.217
16	1450	0.4	0.3	0.632	8977.662

(1) $$MRR=\frac{\left(w_b-w_a\right)}{\rho *t}$$

Where (w_b - w_a) is difference in the mass of the material removed, ‘ρ’ is the density of the material and ‘t’ is the machining time. PEG is a distance based approach that evaluates each alternative based on its proximity to an ideal reference point in a normalized decision space. After this, a mean based shift normalization is employed to all alternative to obtain high stability in ranking of the alternatives. PEG approach provides geometric interpretation of multi-criteria performance, reduced sensitivity to extreme values, simplified computation and strong discrimination capability.

3. MULTI CRITERIA DECISION MAKING

This work incorporates conflicting objectives such as minimum surface roughness and maximum material removal rate. The application of MCDM becomes inevitable since improving one performance characteristics will affect another function and making the multi objective optimization insufficient. MCDM method enables simultaneous evaluation of multiple response parameters and thereby improving the dimensional accuracy. Here, three MCDM techniques viz., PEG, PSI and CURLI methods are used for determining the optimal turning process parameters. MCDM are used to combine multiple performance indicators into a single decision framework and determine the optimal machining parameters.

3.1. Pareto–Edgewort–Grierson (PEG) approach

Pareto–Edgeworth–Grierson (PEG) is a multi-criteria decision making method which do not need to define the weight of the criteria. PEG approach is used for making multi-criteria decision making in several applications such as Polyethylene pipe design [¹], flexural plate design and seismic structural retrofitting. PEG method is best suited for the optimization problems involving conflicting objectives. A distance based aggregation mechanism is used to evaluate the alternatives in a normalized space design. All conventional ranking techniques such as TOPSIS, AHP, VIKOR relies upon weighted summation, whereas PEG approach emphasis on proximity to an ideal solution using radial distance measures. A dimensionless comparable value are generated and shifts them toward a balanced reference coordinate and thereby improving discrimination among the closely performing alternatives. Weigh assignment to the criteria are not required and it enhances the robustness and stability of the approach. PEG is used in several industrial applications because of its excellent computational efficiency and balance compromise philosophy. PEG is emerging as a novel method as a reliable decision making technique in multi-objective optimization studies. Several steps implemented for PEG approach for multi-criteria decision making process is given in Figure 2.

Figure 2
Steps in PEG method.

3.2. Preference Selection Index (PSI) approach

The preference selection method is a technique used in Multi-Criteria decision making to evaluate and rank the different alternatives involving multi criteria problems. A best alternative is successfully chosen among the alternatives with the creation of decision matrix, where the alternatives are evaluated among different criterion. The data is then normalized and preference values are calculated and preference selection index is obtained for each alternative. The highest the PSI value, it indicates the best choice of the alternative. Simple mathematical procedure, initial assignment of weights to the criteria, ranking of the alternatives are the salient features of PSI method.

Normalization of decision matrix for minimization problems is given by the equation

(2) $$N_{ij}=x_{ij}/\max \left(x_{ij}\right)$$

Normalization of decision matrix for maximization problems is given by the equation

(3) $$N_{ij}=\left(\max \left(x_{ij}\right)\right)/x_{ij}$$

Where x_ij is the original value of alternative and N_ij is the normalized value.

3.3. Collaborative Unbiased Rank List Integration (CURLI) approach

CURLI method is applicable in making the decision which involves many conflicting criteria in organizing the decision criteria and logical evaluation of the alternatives. This method identifies the relevant criteria that affect the decision and analyse the influence of each criteria and their alternatives. The ranking of the criteria are also performed according to the importance of each alternative. Logical comparison and analysis is used for evaluating the alternatives and the best alternative is selected. The final score of the alternative is given by the equation

(4) $$S_i={\sum }_{j=1}^n\left(w_j*r_{ij}\right)$$

Where w_ij is weight of the criterion, r_ij is the ranking of the alternative under each criterion, n is the number of criteria.

4. RESULT AND DISCUSSION

4.1. Pareto–Edgewort–Grierson (PEG) approach

The sixteen alternatives are evaluated using PEG method for evaluating minimum surface roughness and maximum material removal rate. Both the criteria were normalized to transform them into a comparable maximization framework with surface roughness values are normalized using inverse transformation and material removal rate with direct normalization techniques. The shift constants are considered as the mean of the normalized surface roughness and material removal rate. The shifted coordinates are computed to reposition all alternatives within a positively scaled decision space. The discrimination among the closely performing alternatives are improved and dispersion bias are highly reduced because of this transformation. Euclidean radian distance (∆r) from the ideal reference coordinate are calculated to evaluate the performance of the each alternative. The PEG utility index is then derived using linear transformation of radial distances. The smaller ∆r values corresponds to higher utility indices and provides the best overall ranking.

In this work, the ranking of alternatives are done and presented in Table 3. It is observed that in the ranking of alternatives, the absence of ranking tie indicates strong discriminative capability of the method. In this work, A14 achieved the highest utility value and minimum radial deviation from the ideal solution, resulting combined acceptance of superior productivity in achieving minimum surface roughness and maximum material removal rate. Alternatives A13 and A15 also exhibited high MRR values along with reasonably controlled Ra values. Their radial distances were only marginally higher than A14, indicating near-optimal compromise behavior. Alternatives A8, A1, and A4 occupy the lowest ranks and these alternatives exhibit significant imbalance. The PEG approach, thereby provides a reliable decision support mechanism for multi objective machining optimization. The main effects plots for means for surface roughness and material removal rate are plotted as shown in Figure 3(a, b). It is observed from the main effects plots for means for surface roughness, the surface roughness decreases with increasing the cutting speed and increases with increase in feed rate. Also form the main effects plots for means for MRR, it is observed that the MRR increases with increase in cutting speed with improved productivity. MRR also increases with increase in feed rate.

Table 3
PEG parameters and ranking of the alternatives.

RUN	x i		y i		x*		y*		ΔR	F0	MSE	RANK
	Ra	MRR	Ra	MRR	Ra	MRR	Ra	MRR
A1	0.9773	0	0.9773	0	0.9849	0.2998	0.9849	0.2998	0.7002	0.372	0.0359	15
A2	0.5859	0.1554	0.5859	0.1554	0.7234	0.4098	0.7234	0.4098	0.5927	0.52	0.0009	8
A3	0.261	0.3098	0.261	0.3098	0.5073	0.5181	0.5073	0.5181	0.6669	0.419	0.0205	13
A4	0.0047	0.4223	0.0047	0.4223	0.3367	0.5964	0.3367	0.5964	0.8036	0	0.1576	16
A5	1	0.0669	1	0.0669	1	0.3479	1	0.3479	0.6521	0.44	0.0147	9
A6	0.6563	0.0858	0.6563	0.0858	0.7709	0.361	0.7709	0.361	0.639	0.457	0.0109	11
A7	0.1484	0.5574	0.1484	0.5574	0.4327	0.6902	0.4327	0.6902	0.6213	0.483	0.0031	7
A8	0	0.5166	0	0.5166	0.3339	0.6623	0.3339	0.6623	0.7448	0.314	0.061	14
A9	0.4781	0.1667	0.4781	0.1667	0.6526	0.417	0.6526	0.417	0.6731	0.41	0.0228	12
A10	0.6656	0.5694	0.6656	0.5694	0.7773	0.6986	0.7773	0.6986	0.3364	0.868	0.0943	4
A11	0.411	0.3093	0.411	0.3093	0.6077	0.5178	0.6077	0.5178	0.5846	0.532	0.0004	10
A12	0.3297	0.5539	0.3297	0.5539	0.5532	0.688	0.5532	0.688	0.5068	0.636	0.0028	5
A13	0.8844	0.6353	0.8844	0.6353	0.9231	0.7453	0.9231	0.7453	0.2484	0.996	0.188	2
A14	0.6297	1	0.6297	1	0.7527	1	0.7527	1	0.2473	1	0.1924	1
A15	0.8859	0.5853	0.8859	0.5853	0.9241	0.7099	0.9241	0.7099	0.2745	0.949	0.1495	3
A16	0.5586	0.4855	0.5586	0.4855	0.7056	0.6427	0.7056	0.6427	0.472	0.684	0.0075	6

Figure 3
(a) Main effects plot for means for surface roughness; (b) main effects plot for means for material removal rate.

It is observed from the main effect plots for surface roughness as shown in Figure 3(a), feed rate has the greater influence of surface roughness followed by depth of cut and cutting speed. Surface roughness increases with increasing feed rate, resulting in poor surface finish at higher feed rates. The surface roughness also decreases with increase in cutting speed. The main effect plots for material removal rate as shown in Figure 3(b) reveals cutting speed has the most significant influence and with higher the feed rate, the material removal rate is also higher. Also with increase in depth of cut, the material removal rate also increases considerably. The calculation of Mean Square Error (MSE) in PEG analysis is significant because it measures the variation of experimental results from the predicted or average performance values. A lower MSE indicates better consistency, accuracy, and reliability of an alternative, whereas a higher MSE reflects greater deviation and instability in performance. In multi-response optimization, MSE helps identify the alternative with minimum error and improved process performance.

4.2. Preference Selection Index (PSI) approach

In this work, Preference Selection Index method is employed to rank the alternatives involving two functions namely minimization of surface roughness and maximization of material removal rate. The experimental data are normalized using approximate normalization to ensure that the experimental data were transformed into dimensionless values and most suitable for comparison. The mean values of the normalized decision matrix are then calculated and it found that mean normalized values for surface roughness and material removal rate are 0.6064 and 0.4601 respectively. The preference variation values are computed using these mean value and it is found that the preference variation value for surface roughness is 0.6255 and for material removal rate is 0.8571. The next step in PSI method is to compute the deviation values and it is found that the deviation value for surface roughness is 0.3745 and for material removal rate is 0.1429. These deviation values will provide the relative importance of the criteria using PSI method and it is found that the computed weight for surface roughness is 0.724 and weight for the material removal rate is 0.276, which shows the weightage of surface roughness is highly influencing in turning process optimization of AISI4140steel when compared to the material removal rate. PSI values for all the alternatives are calculated as shown in Table 4 and it is found, alternative A13 achieved the highest PSI Value of 0.783 indicating the best overall performance among the sixteen alternatives. It is also found that the alternative A4 obtained the lowest PSI value, indicating least favorable performance among the given alternatives. The ranking of the alternatives demonstrates the effectiveness of the PSI method in identifying the suitable alternatives without assigning the subjective weight assignment.

Table 4
PSI parameters and its ranking.

ALT	C1	C2	PSI, Ѳ	RANKING
A1	0.959	0.097	0.721	4
A2	0.568	0.237	0.476	11
A3	0.424	0.375	0.411	15
A4	0.354	0.481	0.389	16
A5	1	0.157	0.768	3
A6	0.613	0.174	0.492	9
A7	0.39	0.601	0.449	12
A8	0.353	0.565	0.412	14
A9	0.511	0.248	0.438	13
A10	0.62	0.609	0.617	6
A11	0.663	0.377	0.584	7
A12	0.449	0.597	0.49	10
A13	0.825	0.67	0.783	1
A14	0.595	1	0.707	5
A15	0.827	0.625	0.771	2
A16	0.552	0.548	0.551	8

4.3. Collaborative Unbiased Rank List Integration (CURLI) approach

CURLI method is employed to rank the sixteen alternatives based on minimization of surface roughness and maximization of material removal rate. The processing scoring matrices for surface roughness and material rate are constructed and presented in Tables 5 and 6 respectively. Pairwise scoring matrix is obtained by computing the pairwise absolute difference between the values of the each alternative. The dispersion values are obtained from the processing matrices and it indicates the discrimination capability of each criterion. A higher total processing score indicates the greater ability of the criterion to distinguish between the alternatives. It is observed that the processing score for surface roughness is higher when compared to the material removal rate. To determine the final ranking, the normalized values of each criterion are multiplied with their weights to obtain the preference value, which reflect the combined influence of both criteria and rank the alternatives effectively. The CURLI parameters and its ranking are shown in Table 7 and it observed that alternative A14 is ranked ‘1’ and it provides the best optimal turning parameters among the given alternatives.

Table 5
Processing scoring matrix for surface roughness.

	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12	A13	A14	A15	A16
A1	0	0.25	0.458	0.622	0.015	0.205	0.53	0.625	0.319	0.199	0.162	0.414	0.059	0.223	0.058	0.268
A2	0.25	0	0.208	0.372	0.265	0.045	0.28	0.375	0.069	0.051	0.088	0.164	0.191	0.027	0.192	0.018
A3	0.458	0.208	0	0.164	0.473	0.253	0.072	0.167	0.139	0.259	0.296	0.044	0.399	0.235	0.4	0.19
A4	0.622	0.372	0.164	0	0.637	0.417	0.092	0.003	0.303	0.423	0.46	0.208	0.563	0.399	0.564	0.354
A5	0.015	0.265	0.473	0.637	0	0.22	0.545	0.64	0.334	0.214	0.177	0.429	0.074	0.238	0.073	0.283
A6	0.205	0.045	0.253	0.417	0.22	0	0.325	0.42	0.114	0.006	0.043	0.209	0.146	0.018	0.147	0.063
A7	0.53	0.28	0.072	0.092	0.545	0.325	0	0.095	0.211	0.331	0.368	0.116	0.471	0.307	0.472	0.262
A8	0.625	0.375	0.167	0.003	0.64	0.42	0.095	0	0.306	0.426	0.463	0.211	0.566	0.402	0.567	0.357
A9	0.319	0.069	0.139	0.303	0.334	0.114	0.211	0.306	0	0.12	0.157	0.095	0.26	0.096	0.261	0.051
A10	0.199	0.051	0.259	0.423	0.214	0.006	0.331	0.426	0.12	0	0.037	0.215	0.14	0.024	0.141	0.069
A11	0.162	0.088	0.296	0.46	0.177	0.043	0.368	0.463	0.157	0.037	0	0.252	0.103	0.061	0.104	0.106
A12	0.414	0.164	0.044	0.208	0.429	0.209	0.116	0.211	0.095	0.215	0.252	0	0.355	0.191	0.356	0.146
A13	0.059	0.191	0.399	0.563	0.074	0.146	0.471	0.566	0.26	0.14	0.103	0.355	0	0.164	0.001	0.209
A14	0.223	0.027	0.235	0.399	0.238	0.018	0.307	0.402	0.096	0.024	0.061	0.191	0.164	0	0.165	0.045
A15	0.058	0.192	0.4	0.564	0.073	0.147	0.472	0.567	0.261	0.141	0.104	0.356	0.001	0.165	0	0.21
A16	0.268	0.018	0.19	0.354	0.283	0.063	0.262	0.357	0.051	0.069	0.106	0.146	0.209	0.045	0.21	0

Table 6
Processing scoring matrix for material removal rate.

	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12	A13	A14	A15	A16
A1	0	2287.508	4557.793	6306.071	991.218	1271.224	8266.96	7668.074	2475.981	8400.115	4592.514	8196.073	9405.004	14807.9	8664.963	7388.408
A2	2287.508	0	2270.285	4018.563	1296.29	1016.284	5979.452	5380.566	188.473	6112.607	2305.006	5908.565	7117.496	12520.39	6377.455	5100.9
A3	4557.793	2270.285	0	1748.278	3566.575	3286.569	3709.167	3110.281	2081.812	3842.322	34.721	3638.28	4847.211	10250.11	4107.17	2830.615
A4	6306.071	4018.563	1748.278	0	5314.853	5034.847	1960.889	1362.003	3830.09	2094.044	1713.557	1890.002	3098.933	8501.83	2358.892	1082.337
A5	991.218	1296.29	3566.575	5314.853	0	280.006	7275.742	6676.856	1484.763	7408.897	3601.296	7204.855	8413.786	13816.68	7673.745	6397.19
A6	1271.224	1016.284	3286.569	5034.847	280.006	0	6995.736	6396.85	1204.757	7128.891	3321.29	6924.849	8133.78	13536.68	7393.739	6117.184
A7	8266.96	5979.452	3709.167	1960.889	7275.742	6995.736	0	598.886	5790.979	133.155	3674.446	70.887	1138.044	6540.941	398.003	878.552
A8	7668.074	5380.566	3110.281	1362.003	6676.856	6396.85	598.886	0	5192.093	732.041	3075.56	527.999	1736.93	7139.827	996.889	279.666
A9	2475.981	188.473	2081.812	3830.09	1484.763	1204.757	5790.979	5192.093	0	5924.134	2116.533	5720.092	6929.023	12331.92	6188.982	4912.427
A10	8400.115	6112.607	3842.322	2094.044	7408.897	7128.891	133.155	732.041	5924.134	0	3807.601	204.042	1004.889	6407.786	264.848	1011.707
A11	4592.514	2305.006	34.721	1713.557	3601.296	3321.29	3674.446	3075.56	2116.533	3807.601	0	3603.559	4812.49	10215.39	4072.449	2795.894
A12	8196.073	5908.565	3638.28	1890.002	7204.855	6924.849	70.887	527.999	5720.092	204.042	3603.559	0	1208.931	6611.828	468.89	807.665
A13	9405.004	7117.496	4847.211	3098.933	8413.786	8133.78	1138.044	1736.93	6929.023	1004.889	4812.49	1208.931	0	5402.897	740.041	2016.596
A14	14807.9	12520.39	10250.11	8501.83	13816.68	13536.68	6540.941	7139.827	12331.92	6407.786	10215.39	6611.828	5402.897	0	6142.938	7419.493
A15	8664.963	6377.455	4107.17	2358.892	7673.745	7393.739	398.003	996.889	6188.982	264.848	4072.449	468.89	740.041	6142.938	0	1276.555
A16	7388.408	5100.9	2830.615	1082.337	6397.19	6117.184	878.552	279.666	4912.427	1011.707	2795.894	807.665	2016.596	7419.493	1276.555	0

Table 7
CURLI parameters and its ranking.

ALTERNATIVE	NORMALIZED VALUES		PREFERENCE VALUE	RANK
	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE
A1	0.023438	0	1.26807E-06	16
A2	0.414063	0.154479	0.154492927	13
A3	0.739063	0.307795	0.307818003	11
A4	0.995313	0.425859	0.425889343	9
A5	0	0.066938	0.066934832	15
A6	0.34375	0.085848	0.085861637	14
A7	0.851563	0.55828	0.558296207	5
A8	1	0.517837	0.517862747	7
A9	0.521875	0.167207	0.167225939	12
A10	0.334375	0.567272	0.567259898	4
A11	0.276563	0.310139	0.310137615	10
A12	0.670313	0.553493	0.553499554	6
A13	0.115625	0.635134	0.635106068	2
A14	0.371875	1	0.999966016	1
A15	0.114063	0.585158	0.585132597	3
A16	0.442188	0.49895	0.49894732	8

Based on the computed preference values, the raking of the alternatives are done. It is observed that the alternative A14 achieves the highest preference values and it indicates the best overall performance among all the alternatives. The alternative A1 obtains the lowest preference value and suggesting a weaker performance among the alternatives. CURLI method demonstrates the effectiveness of the ranking of the alternatives by considering the relative importance and dispersion of the criteria. Multi-criteria decision making by the CURLI method is found to more efficient to achieve better results among the alternatives.

4.4. Comparison of PEG, PSI and curli methods in MCDM – Gini index

Gini index is used in this work to quantify the level of disagreement among the PEG, PSI and CURLI ranking results for each alternative. Gini index provides an effective and objective method for determining the relative importance of performance criteria without relying on the subjective criteria. The Gini index measures the degree of dispersion among the experimental data and assigns weights based on inequality in criterion performance. Higher the Gini coefficient, larger disagreement between the methods and lower the Gini coefficient, consistency in ranking between the methods is noticed as shown in Table 8. It is observed that most of the alternatives exhibit relatively low Gini coefficients indicating a high degree of consistency among the three MCDM techniques used in this work, viz., PEG, PSI and CURLI method. The alternatives A9 and A16 exhibit low Gini values, indicating strong agreement among the MCDM methods, PEG, PSI and CURLI methods employed in this work. The alternatives A14 and A5 exhibits higher Gini values, indicating larger disagreement in the ranking of the alternatives among the three methods.

Table 8
Gini index value.

ALTERNATIVE	RANKING RESULTS OF THE ALTERNATIVE			GINI INDEX
	PEG	PSI	CURLI
A1	15	4	16	0.2286
A2	8	11	13	0.1042
A3	13	15	11	0.0684
A4	16	16	9	0.1138
A5	9	3	15	0.2963
A6	11	9	14	0.098
A7	7	12	5	0.1944
A8	14	14	7	0.1333
A9	12	13	12	0.018
A10	4	6	4	0.0952
A11	10	7	10	0.0741
A12	5	10	6	0.1587
A13	2	1	2	0.1333
A14	1	5	1	0.381
A15	3	2	3	0.0833
A16	6	8	8	0.0606

Sensitivity analysis examines how the input parameters and the criteria weights affect the decision making model. Sensitivity analysis confirms the consistency and reliability of the obtained optimal machining parameters [²²,²³,²⁴]. Sensitivity analysis is carried out to compare the rankings obtained by PEG, PSI and CURLI methods to check the consistency and robustness of the optimal solutions. The alternative A14 is ranked 1st in PEG and CURLI method and proves to be more dominant when compared to the other alternatives. A13 and A15 consistently ranks second and third position and the results are found to be more stable and redundant. The significance of the optimized solutions helps industries to select optimal cutting conditions that will improve the tool life, reduce the material wastage and improves the process efficiency. The trial and error methods are omitted and cutting conditions are selected with higher amount of accuracy and precision.

4.5. Limitations

There are several limitations associated with interpreting these results. The experiments are conducted by selecting the process parameters as cutting speed, feed and depth of cut. The other influencing parameters such as vibration effects, cutting environment, tool geometry were not included. The optimization is based only on surface roughness and MRR, whereas the additional performance measures like tool wear, cutting force are neglected in this work. This study employed MCDM approaches and the ranking of the alternatives may vary when applied with alternation optimization methods.

5. CONCLUSION

Multi Criteria Decision Making is best suited for multi objective problems as presented in this work. Turning of AISI 4140 steel using coated TiN is performed on a CNC lathe with cutting speed, feed rate and depth of cut as the cutting process parameters. The objective of the work is minimization of surface roughness and maximization of material removal rate. In most cases, these objectives are conflicting and PEG approach in MCDM is applied to determine the optimal turning process parameters. The PEG (Pareto–Edgeworth–Grierson) method is applied to evaluate sixteen alternatives employing mean-based shift normalization followed by radial distance computation from the ideal reference coordinate. It is observed A14 is providing highest utility index and minimum radial deviation. The corresponding process parameters are; cutting speed 1450 m/min, feed rate 0.3 mm/rev and depth of cut 0.5 mm. The experiments are validated and the percentage of error is found to be less than 5% and it is highly accepted. This ensures a best compromise between the minimum surface roughness and maximum material removal rate providing high surface quality and productivity.

6. DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

7. BIBLIOGRAPHY

• ^[1] DUC TRUNG, D., “Multi-criteria decision making of turning operation based on PEG, PSI and CURLI methods”, Manufacturing Review, v. 9, pp. 9, 2022. doi: https://doi.org/10.1051/mfreview/2022007.
  » https://doi.org/10.1051/mfreview/2022007
• ^[2] SELMI, M., KORMI, T., ALI, N.B.H., “Comparison of multi-criteria decision methods through a ranking stability index.”, International Journal of Operations Research, v. 27, n. 1-2, pp. 165-183, 2016. doi: https://doi.org/10.1504/IJOR.2016.078462.
  » https://doi.org/10.1504/IJOR.2016.078462
• ^[3] DIVYA, C.H., SUVARNA RAJU, L., SINGARAVEL, B., “Application of MCDM methods for process parameter optimization in turning process—a review”, In: Recent Trends in Mechanical Engineering: Select Proceedings of ICIME 2020, pp. 199–207, 2020. doi: https://doi.org/10.1007/978-981-15-7557-0_18.
  » https://doi.org/10.1007/978-981-15-7557-0_18
• ^[4] SINGARAVEL, B., PRABHU SHANKAR, D., PRASANNA, L., “Application of MCDM method for the selection of optimum process parameters in turning process”, Materials Today: Proceedings, v. 5, n. 5, pp. 13464–13471, 2018. doi: https://doi.org/10.1016/j.matpr.2018.02.341.
  » https://doi.org/10.1016/j.matpr.2018.02.341
• ^[5] KHAN, A., KALIPADA, M., “Application of MCDM-based TOPSIS method for the selection of optimal process parameter in turning of pure titanium”, Benchmarking, v. 24, n. 7, pp. 2009–2021, 2017. doi: https://doi.org/10.1108/BIJ-01-2016-0004.
  » https://doi.org/10.1108/BIJ-01-2016-0004
• ^[6] MAJUMDER, H., SAHA, A., “Application of MCDM based hybrid optimization tool during turning of ASTM A588.”, Decision Science Letters, v. 7, n. 2, pp. 143–156, 2018. doi: https://doi.org/10.5267/j.dsl.2017.6.003.
  » https://doi.org/10.5267/j.dsl.2017.6.003
• ^[7] SHAIKH, M.B.N., ALI, M., KHAN, Z.A., et al., “An MCDM approach for multi-response optimisation of machining parameters in turning of EN8 steel (AISI-1040) for sustainable manufacturing.”, International Journal on Interactive Design and Manufacturing, v. 17, n. 6, pp. 3159-3176, 2023. doi: https://doi.org/10.1007/s12008-023-01368-8.
  » https://doi.org/10.1007/s12008-023-01368-8
• ^[8] NGUYEN, A.T., “The improved CURLI method for multi-criteria decision making”, Engineering Technology and Applied Science Research, v. 13, n. 1, pp. 10121–10127, 2023. doi: https://doi.org/10.48084/etasr.5538.
  » https://doi.org/10.48084/etasr.5538
• ^[9] TRUNG, D., TRANG, B., ÖZÇALICI, M., et a., “CURLIA: A streamlined aggregation method that elevates ranking accuracy in complex MCDM problems”, Yugoslav Journal of Operations Research, v. 40, n. 00, pp. 40, 2025. doi: https://doi.org/10.2298/YJOR250815040T.
  » https://doi.org/10.2298/YJOR250815040T
• ^[10] TRUNG, D.D., PHUONG GIANG, N.T., SON, N.H., “Comparision of both methods psi and curli: applied in solving multi-objective optimization problem of turning process”, EUREKA: Physics and Engineering, v. 1, n. 1, pp. 167–179, 2024. doi: https://doi.org/10.21303/2461-4262.2024.003071.
  » https://doi.org/10.21303/2461-4262.2024.003071
• ^[11] THINH, H.X., MAI, N.T., GIANG, N.T., et al., “Applying multi-criteria decision making methods for cutting oil selection”, Eastern-European Journal of Enterprise Technologies, v. 123, n. 1, pp. 52–58, 2023. https://doi.org/10.15587/1729-4061.2023.275717.
• ^[12] TOUGGUI, Y., SALIM, B., TAREK, M., et al., “Dry turning optimization of austenitic stainless steel 316L based on Taguchi and TOPSIS approaches.”, Matériaux & Techniques, v. 108, n. 4, pp. 401, 2020. doi: https://doi.org/10.1051/mattech/2020034.
  » https://doi.org/10.1051/mattech/2020034
• ^[13] ÇALIŞKAN, H., KURŞUNCU, B., KURBANOĞLU, C., et al., “BILAL KURŞUNCU., CAHIT KURBANOĞLU., ŞEVKI YILMAZ GÜVEN., “Material selection for the tool holder working under hard milling conditions using different multi criteria decision making methods”, Materials & Design, v. 45, pp. 473–479, 2013. doi: https://doi.org/10.1016/j.matdes.2012.09.042.
  » https://doi.org/10.1016/j.matdes.2012.09.042
• ^[14] KAMILLA, B.S., SAHOO, B.B., BARUA, A., et al., “Parametric optimization of resistance spot welded dissimilar metals utilizing advanced hybrid Taguchi-MARCOS method”, In International Conference on Recent Advances in Mechanical Engineering Research and Development, pp. 135–142, Singapore, 2022.
• ^[15] BISWAL, S., SAHOO, B.B., JEET, S., et al., “ Experimental investigation based on CDM optimization of electrical discharge machined Al-WC-B4C hybrid composite using Taguchi-MARCOS method”, Materials Today: Proceedings, v. 74, pp. 587–594, 2023. doi: https://doi.org/10.1016/j.matpr.2022.09.522.
  » https://doi.org/10.1016/j.matpr.2022.09.522
• ^[16] DUC TRUNG, D., “Multi-criteria decision making under the MARCOS method and the weighting methods: applied to milling, grinding and turning processes”, Manufacturing Review, v. 9, pp. 3, 2022. doi: https://doi.org/10.1051/mfreview/2022003.
  » https://doi.org/10.1051/mfreview/2022003
• ^[17] DUC TRUNG, D.O., “A combination method for multi-criteria decision making problem in turning process”, Manufacturing Review, v. 8, pp. 26, 2021. doi: https://doi.org/10.1051/mfreview/2021024.
  » https://doi.org/10.1051/mfreview/2021024
• ^[18] TRUNG, D., THINH, H.X., “A multi-criteria decision-making in turning process using the MAIRCA, EAMR, MARCOS and TOPSIS methods: a comparative study”, Advances in Production Engineering & Management, v. 16, n. 4, pp. 443–456, 2021. doi: https://doi.org/10.14743/apem2021.4.412.
  » https://doi.org/10.14743/apem2021.4.412
• ^[19] TRUNG, D.D., “Application of TOPSIS and PIV methods for multi-criteria decision making in hard turning process”, Journal of Machine Engineering, v. 21, n. 4, pp. 57–71, 2021. doi: https://doi.org/10.36897/jme/142599.
  » https://doi.org/10.36897/jme/142599
• ^[20] TRUNG, D.D., TRANG, B.T.T., ÖZÇALICI, M., et al., “CURLIA: A streamlined aggregation method that elevates ranking accuracy in complex MCDM problems.”, Yugoslav Journal of Operations Research, v. 40, 2025. doi: https://doi.org/10.2298/YJOR250815040T.
  » https://doi.org/10.2298/YJOR250815040T
• ^[21] LIM, C.Y.H., LIM, S.C., LEE, K.S., “The performance of TiN-coated high speed steel tool inserts in turning”, Tribology International, v. 32, n. 7, pp. 393–398, 1999. doi: https://doi.org/10.1016/S0301-679X(99)00066-3.
  » https://doi.org/10.1016/S0301-679X(99)00066-3
• ^[22] TRUNG, D.D., DUDIĆ, B., DUC, D.V., et al., “Comparison of MCDM methods effectiveness in the selection of plastic injection molding machines”, Teknomekanik, v. 7, n. 1, pp. 1–19, 2024. doi: https://doi.org/10.24036/teknomekanik.v7i1.29272.
  » https://doi.org/10.24036/teknomekanik.v7i1.29272
• ^[23] TRUNG, D.D., ÖZÇALICI, M., ERSOY, N., et al., “SIWEC-R: A rank-sensitive improvement to SIWEC methodology”, Teknomekanik, v. 8, n. 2, pp. 183–210, 2025. doi: https://doi.org/10.24036/teknomekanik.v8i2.40172.
  » https://doi.org/10.24036/teknomekanik.v8i2.40172
• ^[24] OBEIDAT, M.S., AL SLITI, H., OBEIDAT, A., “The Preference Selection Index (PSI) in multi-criteria decision-making: a systematic and critical review of applications, integrations, and future directions”, Mathematical & Computational Applications, v. 30, n. 6, pp. 124, 2025. doi: https://doi.org/10.3390/mca30060124.
  » https://doi.org/10.3390/mca30060124

Publication Dates

• Publication in this collection
  03 Aug 2026
• Date of issue
  2026

History

• Received
  11 Mar 2026
• Accepted
  29 May 2026