# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022061
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## A novel BWM integrated MABAC decision-making approach to optimize the wear parameter of CrN/TiAlSiN coating

 1 Department of Mechanical Engineering, National Institute of Technology Silchar, Assam- 788 010, Inida 2 School of Mechanical Engineering, Sathyabama Institute of Science and Technology (Deemed to be University), Chennai - 600119, Tamil Nadu, India

*Corresponding author: Saikat Ranjan Maity

Received  November 2021 Revised  March 2022 Early access April 2022

Using a multi-criteria decision-making (MCDM) method combined with a Taguchi ($L_{16}$) design of experiment, the wear parameter for CrN/TiAlSiN coated hardened DAC-10 tool steel is optimized. Temperature, sliding velocity, applied load, and sliding distance together forms the wear parameter. Wear rate, friction coefficient, surface roughness, wear depth, and worn surface hardness were all tested to see how it affected by the wear parameters. The criteria weight was derived using the best-worst method (BWM) and combined with the Multi-Attributive Border Approximation area Comparison (MABAC) approach to rank the alternatives. The obtained data were then subjected to sensitivity testing using three-phase techniques. The suggested MCDM technique was validated through all phases of sensitivity analysis, with alternative ${WP}_6$ (T = 100 $^{\circ}$C, Sv = 0.05 m/s, L = 5 N, and Sd = 2000 m) showing as the best alternative. Furthermore, the proposed method BWM-MABAC was tested on previously published outcomes, and the results showed an excellent correlation between present and past studies, with a rank correlation coefficient value of greater than 0.99.

Citation: Sunil Kumar, Saikat Ranjan Maity, Lokeswar Patnaik. A novel BWM integrated MABAC decision-making approach to optimize the wear parameter of CrN/TiAlSiN coating. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022061
##### References:
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##### References:
 [1] P. Achuthamenon Sylajakumari, R. Ramakrishnasamy and G. Palaniappan, Taguchi grey relational analysis for multi-response optimization of wear in co-continuous composite, Materials, 11 (2018), 1743. [2] I. K. Aliyu, M. U. Azam, D. U. Lawal and M. A. Samad, Optimization of SiC Concentration and Process Parameters for a Wear-Resistant UHMWPE Nancocomposite, Arabian J. Sci. Eng., 45 (2020), 849-860. [3] X. Bai, J. Li and L. Zhu, Structure and properties of TiSiN/Cu multilayer coatings deposited on Ti6Al4V prepared by arc ion plating, Surf. Coat. Technol., 372 (2019), 16-25. [4] A. Baradeswaran, A. Elayaperumal and R. F. Issac, A statistical analysis of optimization of wear behaviour of Al-Al2O3 composites using Taguchi technique, Proceed. Eng., 64 (2013), 973-982. [5] A. Baradeswaran, S. C. Vettivel, A. E. Perumal, N. Selvakumar and R. F. Issac, Experimental investigation on mechanical behaviour, modelling and optimization of wear parameters of B4C and graphite reinforced aluminium hybrid composites, Mater. Des., 63 (2014), 620-632. [6] F. Behroozi, S. M. H. Hosseini and S. S. Sana, Teaching-learning-based genetic algorithm (TLBGA): An improved solution method for continuous optimization problems, Int. J. Sys. Assur. Eng. Manag., 12 (2021), 1362-1384. [7] A. K. Birjandi, F. Akhyani, R. Sheikh and S. S. Sana, Evaluation and selecting the contractor in bidding with incomplete information using MCGDM method, Soft Compt., 23 (2019), 10569-10585. [8] V. Bramaramba and S. Sen, Optimization study on sliding wear characteristics and heat-treatment conditions of different grades of ferritic ductile cast iron, Trans. Indian Inst. Metal, 73 (2020), 1131-1146. [9] W. K. Brauers and E. K. Zavadskas, The MOORA method and its application to privatization in a transition economy, Control Cybern., 35 (2006), 445-469. [10] S. Chakraborty, S. S. Dandge and S. Agarwal, Non-traditional machining processes selection and evaluation: A rough multi-attributive border approximation area comparison approach, Comput. Indus. Eng., 64 (2020), 106201. [11] B. P. Chang, H. Akil, R. B. Nasir and A. Khan, Optimization on wear performance of UHMWPE composites using response surface methodology, Tribol. Int., 88 (2015), 525-262. [12] C. Dang, Y. Yao, T. Olugbade, J. Li and L. Wang, Effect of multi-interfacial structure on fracture resistance of composite TiSiN/Ag/TiSiN multilayer coating, Thin Solid Films, 653 (2018), 107-112. [13] G. G. Fuentes, E. Almandoz, R. Pierrugues, R. Martínez, R. J. Rodríguez, J. Caro and M. Vilaseca, High temperature tribological characterisation of TiAlSiN coatings produced by cathodic arc evaporation, Surf. Coat. Technol., 205 (2010), 1368-1373. [14] K. Gajalakshmi, N. Senthilkumar and B. Prabu, Multi-response optimization of dry sliding wear parameters of AA6026 using hybrid gray relational analysis coupled with response surface method, Measur. Control, 52 (2019), 540-553. [15] B. M. Girish, B. M. Satish and S. Sarapure, Optimization of wear behavior of magnesium alloy AZ91 hybrid composites using taguchi experimental design, Metall. Mater. Trans. A, 47 (2016), 3193-3200. [16] W. J. Gong, Q. Li, L. Yin and H. C. Liu, Undergraduate teaching audit and evaluation using an extended MABAC method under q-rung orthopair fuzzy environment, Int. J. Intell. Sys., 35 (2020), 1912-1933. [17] J. Gu, L. Li, M. Ai, Y. Xu, Y. Xu, G. Li and P. Zhang, Improvement of solid particle erosion and corrosion resistance using TiAlSiN/Cr multilayer coatings, Surf. Coat. Technol., 402 (2020), 126270. [18] G. Haseli, R. Sheikh and S. S. Sana, Base-criterion on multi-criteria decision-making method and its applications, Int. J. Manag. Sci. Eng. Manag., 15 (2020), 79-88. [19] J. Huang, Z. S. Li and H. C. Liu, New approach for failure mode and effect analysis using linguistic distribution assessments and TODIM method, Reliab. Eng. Syst. Saf., 167 (2017), 302-309. [20] C. L. Hwang and K. Yoon, Multiple attribute decision making: A state of the art survey, Lect. Notes Econ.Mat. Syst., 186 (1981). [21] N. Kaushik and S. Singhal, Hybrid combination of Taguchi-GRA-PCA for optimization of wear behavior in AA6063/SiCp matrix composite, Produc. Manuf. Res., 6 (2020), 171-189. [22] S. K. Khatkar, R. Verma, S. S. Kharb, A. Thakur and R. Sharma, Optimization and effect of reinforcements on the sliding wear behavior of self-lubricating AZ91D-SiC-Gr Hybrid composites, Silicon, 13 (2021), 1461-1473. [23] S. Kumar, S. R. Maity and L. Patnaik, Wear assessment of Cr2O3-/TiAlN-coated DAC-10 tool steel against steel and Al2O3 counterbodies, Int.J.Appl. Ceram. Technol., (2021). [24] S. Kumar, S. R. Maity and L. 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(a) Cross-sectional FE-SEM micrograph and (b) corresponding line EDS of CrN/TiAlSiN coating
Representation of $G_-$, G and $G_+$
Algorithm of the proposed methodology
Sensitivity analysis of BWM-MABAC method using criteria weight change
Effect of dynamic matrices on the ranking of MABAC method
Comparison between proposed MABAC and other developed MCDM methods
Literature review
 Author (Year) Materials Optimization Technique Process parameter Wear responses Kaushik et al. (2018)[21] AA6063/SiCp composites Taguchi integrated GRA-PCA Applied Load, Sliding distance and Weight percentage of SiC Wear rate, Frictional force and specific wear rate Stalin et al. (2018) [65] AA6063-Si3N4 composite Taguchi Load, Weight percentage of reinforcement, Sliding velosity and distance Wear rate Singh et al. (2018) [63] Phyllanthus Emblica seeds oilbased lubricants Response surface methodology (RSM) Blend ratio, Load and Sliding velosity Specific wear rate and CoF Singh et al. (2018) [62] AA6082-T6/ TiB2 composites RSM Reinforcement, Sliding speed, Load and Sliding distance Wear Prakash et al. (2018) [51] (413/B4C) composites Integrated Taguchi with Gray relational analysis Reinforcement, Sliding speed, Load and Sliding distance Specific wear rate and CoF Aliyu et al. (2020) [2] UHMWPE composites Taguchi SiC loading, Consolidation pressure and Holding time Specific wear rate Suresha et al. (2019) [66] Polyaryletherketone composites Taguchi Noramal load, Filler content and Sliding velosity and distance Specific wear rate and CoF Stalin et al. (2019) [64] Aluminium composites ANN integrated teaching learningbased optimization algorithm Reinforcement, Sliding speed, Load and Sliding distance Wear rate Gajalakshmi et al. (2019) [14] Aluminium alloy (AA6026) hybrid GRA with a RSM Load, Speed of pin and Track diameter Wear, CoF and Frictional force
 Author (Year) Materials Optimization Technique Process parameter Wear responses Kaushik et al. (2018)[21] AA6063/SiCp composites Taguchi integrated GRA-PCA Applied Load, Sliding distance and Weight percentage of SiC Wear rate, Frictional force and specific wear rate Stalin et al. (2018) [65] AA6063-Si3N4 composite Taguchi Load, Weight percentage of reinforcement, Sliding velosity and distance Wear rate Singh et al. (2018) [63] Phyllanthus Emblica seeds oilbased lubricants Response surface methodology (RSM) Blend ratio, Load and Sliding velosity Specific wear rate and CoF Singh et al. (2018) [62] AA6082-T6/ TiB2 composites RSM Reinforcement, Sliding speed, Load and Sliding distance Wear Prakash et al. (2018) [51] (413/B4C) composites Integrated Taguchi with Gray relational analysis Reinforcement, Sliding speed, Load and Sliding distance Specific wear rate and CoF Aliyu et al. (2020) [2] UHMWPE composites Taguchi SiC loading, Consolidation pressure and Holding time Specific wear rate Suresha et al. (2019) [66] Polyaryletherketone composites Taguchi Noramal load, Filler content and Sliding velosity and distance Specific wear rate and CoF Stalin et al. (2019) [64] Aluminium composites ANN integrated teaching learningbased optimization algorithm Reinforcement, Sliding speed, Load and Sliding distance Wear rate Gajalakshmi et al. (2019) [14] Aluminium alloy (AA6026) hybrid GRA with a RSM Load, Speed of pin and Track diameter Wear, CoF and Frictional force
Literature review (continue)
 Author (Year) Materials Optimization Technique Process parameter Wear responses Ming-Der et al. (2020) [37] Zr doped DLC coating The GAANFIS method Bias, Pulse frequency, CH4, Sputtering distance and C/Ze current Wear rate Sahoo (2009) [57] Ni-P coating Taguchi Bath temperature, Concentration of reducuing agent, Concentration of rource of nickel and Annealing temperature Wear depth Baradeswaran et al. (2013) [4] Al-Al2O3 composites Taguchi integrated with RSM Applied load and Sliding distnace Wear mass loss and CoF Rana et al. (2014) [53] AA5083/10 Wt. Sicp composite Taguchi Load, Sliding speed and distance Wear rate Baradeswaran et al. (2014) [5] Aluminium and B4C composites RSM Load, Sliding speed and distance Wear mass loss Chang et al. (2015) [11] UHMWPE composites RSM Filler loading, Applied load and Sliding speed Wear rate and CoF Saravanan et al. (2015) [60] TiN coating RSM Load, Sliding velosity and distance Wear mass loss and CoF Saravanan et al. (2016) [59] TiN coating RSM Load, Sliding velosity and distance Wear mass loss, CoF, Ra, Wear depth and Hardness
 Author (Year) Materials Optimization Technique Process parameter Wear responses Ming-Der et al. (2020) [37] Zr doped DLC coating The GAANFIS method Bias, Pulse frequency, CH4, Sputtering distance and C/Ze current Wear rate Sahoo (2009) [57] Ni-P coating Taguchi Bath temperature, Concentration of reducuing agent, Concentration of rource of nickel and Annealing temperature Wear depth Baradeswaran et al. (2013) [4] Al-Al2O3 composites Taguchi integrated with RSM Applied load and Sliding distnace Wear mass loss and CoF Rana et al. (2014) [53] AA5083/10 Wt. Sicp composite Taguchi Load, Sliding speed and distance Wear rate Baradeswaran et al. (2014) [5] Aluminium and B4C composites RSM Load, Sliding speed and distance Wear mass loss Chang et al. (2015) [11] UHMWPE composites RSM Filler loading, Applied load and Sliding speed Wear rate and CoF Saravanan et al. (2015) [60] TiN coating RSM Load, Sliding velosity and distance Wear mass loss and CoF Saravanan et al. (2016) [59] TiN coating RSM Load, Sliding velosity and distance Wear mass loss, CoF, Ra, Wear depth and Hardness
Literature review (continue)
 Author (Year) Materials Optimization Technique Process parameter Wear responses Saravanan et al. (2016) [58] ${\gamma}$-irradiated Ti alloy against TiN coating RSM Load, Sliding velosity and distance Wear mass loss of TiN coating and counterbody Girish et al. (2016) [15] Hybrid metal matrix composite (Magnesium alloyAZ91) Taguchi Composition, Sliding velosity and distance Wear rate Achuthamenon Sylajakumari et al. (2018) [1] AA6063/ SiC composites Taguchi Load, Sliding speed and distance CoF and Wear rate Natrayan et al. (2020) [38] AA6061/ Al2O3/ SiC composite Taguchi Load, Sliding speed and distance Wear rate and CoF Sathish et al. (2019) [61] Mg-(5.6Ti +3Al)2.5B4C composites Taguchi Load, Sliding velosity and distance Wear rate Bramaramba et al. (2020) [8] Ferritic ductile cast iron Taguchi Load, Time, Grade and Heat treatment Wear mass loss and Hardness Premnath (2020) [50] Al-SiC nanocomposites Desirability approach Number of passes, Rotationa a nd Transverse speed Tensile strength, Microhardness and Wear loss Rajmohan et al. (2020) [52] Magnesiumsilicon composites Grey-Fuzzy algorithm integrated with Taguchi Load, Speed, Distance and Weight of SiC Wear rate and CoF
 Author (Year) Materials Optimization Technique Process parameter Wear responses Saravanan et al. (2016) [58] ${\gamma}$-irradiated Ti alloy against TiN coating RSM Load, Sliding velosity and distance Wear mass loss of TiN coating and counterbody Girish et al. (2016) [15] Hybrid metal matrix composite (Magnesium alloyAZ91) Taguchi Composition, Sliding velosity and distance Wear rate Achuthamenon Sylajakumari et al. (2018) [1] AA6063/ SiC composites Taguchi Load, Sliding speed and distance CoF and Wear rate Natrayan et al. (2020) [38] AA6061/ Al2O3/ SiC composite Taguchi Load, Sliding speed and distance Wear rate and CoF Sathish et al. (2019) [61] Mg-(5.6Ti +3Al)2.5B4C composites Taguchi Load, Sliding velosity and distance Wear rate Bramaramba et al. (2020) [8] Ferritic ductile cast iron Taguchi Load, Time, Grade and Heat treatment Wear mass loss and Hardness Premnath (2020) [50] Al-SiC nanocomposites Desirability approach Number of passes, Rotationa a nd Transverse speed Tensile strength, Microhardness and Wear loss Rajmohan et al. (2020) [52] Magnesiumsilicon composites Grey-Fuzzy algorithm integrated with Taguchi Load, Speed, Distance and Weight of SiC Wear rate and CoF
Literature review (continue)
 Author (Year) Materials Optimization Technique Process parameter Wear responses Khatkar et al. (2021) [22] AZ91D-SiC -Gr composites Taguchi SiC and Graphite percentage, ]Applied load, Sliding speed and distance Wear rate Rao et al. (2021) [55] Al6061/WC composites A hybrid Gray relational analysis integrated with teaching learningbased optimization Volumetric percentage of WC, Load, Sliding velosity and distance Wear rate and CoF Kumar et al. (2021) [30] Cr-(CrN/ TiN) coating Taguchi Load, Sliding velosity and distance and Coolant type Ra, CoF and Wear mass loss Patnaik et al. (2021) [40] AlCrN coating RSM Load, Sliding velosity and distance Ra, CoF, Disc mass loss, Wear depth and Hardness Patnaik et al. (2021) [41] Silver alloyed a-C coating RSM Load, Sliding velosity and distance Ra, CoF, Disc mass loss, and Hardness Kumar et al. (2021) [31] TiAlN coating RSM Cutting speed, Feed rate and Depth of cut Ra and Tool wear rate
 Author (Year) Materials Optimization Technique Process parameter Wear responses Khatkar et al. (2021) [22] AZ91D-SiC -Gr composites Taguchi SiC and Graphite percentage, ]Applied load, Sliding speed and distance Wear rate Rao et al. (2021) [55] Al6061/WC composites A hybrid Gray relational analysis integrated with teaching learningbased optimization Volumetric percentage of WC, Load, Sliding velosity and distance Wear rate and CoF Kumar et al. (2021) [30] Cr-(CrN/ TiN) coating Taguchi Load, Sliding velosity and distance and Coolant type Ra, CoF and Wear mass loss Patnaik et al. (2021) [40] AlCrN coating RSM Load, Sliding velosity and distance Ra, CoF, Disc mass loss, Wear depth and Hardness Patnaik et al. (2021) [41] Silver alloyed a-C coating RSM Load, Sliding velosity and distance Ra, CoF, Disc mass loss, and Hardness Kumar et al. (2021) [31] TiAlN coating RSM Cutting speed, Feed rate and Depth of cut Ra and Tool wear rate
Wear parameters and its levels
 Wear parameter Symbol Level Value Temperature (in $^{\circ}$C) T 4 25,100,200,300 Sliding velocity (in m/s) $S_v$ 4 0.01, 0.05, 0.1, 0.15 Applied load (in N) L 4 5, 10, 15, 20 Sliding distance (in m) $S_d$ 4 500, 1000, 1500, 2000
 Wear parameter Symbol Level Value Temperature (in $^{\circ}$C) T 4 25,100,200,300 Sliding velocity (in m/s) $S_v$ 4 0.01, 0.05, 0.1, 0.15 Applied load (in N) L 4 5, 10, 15, 20 Sliding distance (in m) $S_d$ 4 500, 1000, 1500, 2000
Experimental results (initial decision matrix)
 Experimental run (Alternative, WP) Wear parameters Wear responses (Criteria, WR) T $S_v$ L $S_d$ ${WR}_1$ (WR, × ${10}^{-8}$ ${mm}^3Nm^{-1}$) ${WR}_2$ (CoF) ${WR}_3$ (Ra, μm) ${WR}_4$ (WD, μm) ${WR}_5$ (Hv) ${WP}_1$ 25 0.01 5 500 8.45 0.58 7.8 2.71 1746 ${WP}_2$ 25 0.05 10 1000 8.31 0.56 7.1 2.87 1698 ${WP}_3$ 25 0.1 15 1500 9.71 0.55 6.7 2.98 1648 ${WP}_4$ 25 0.15 20 2000 10.89 0.53 5.9 3.68 845 ${WP}_5$ 100 0.01 10 1500 6.71 0.49 5.1 0.73 2576 ${WP}_6$ 100 0.05 5 2000 5.67 0.51 5.4 0.67 2781 ${WP}_7$ 100 0.1 20 500 6.77 0.56 7.3 1.63 2409 ${WP}_8$ 100 0.15 15 1000 7.2 0.52 6.4 0.84 2384 ${WP}_9$ 200 0.01 15 2000 8.54 0.46 3.9 1.47 2127 ${WP}_{10}$ 200 0.05 20 1500 8.24 0.57 7.5 2.14 1898 ${WP}_{11}$ 200 0.1 5 1000 6.72 0.59 8.1 0.89 2317 ${WP}_{12}$ 200 0.15 10 500 7.83 0.61 8.7 0.98 2235 ${WP}_{13}$ 300 0.01 20 1000 9.37 0.64 8.9 3.37 1107 ${WP}_{14}$ 300 0.05 15 500 8.71 0.68 9.1 2.93 1283 ${WP}_{15}$ 300 0.1 10 2000 9.12 0.67 8.7 3.29 997 ${WP}_{16}$ 300 0.15 5 1500 8.5 0.65 8.4 2.79 1321
 Experimental run (Alternative, WP) Wear parameters Wear responses (Criteria, WR) T $S_v$ L $S_d$ ${WR}_1$ (WR, × ${10}^{-8}$ ${mm}^3Nm^{-1}$) ${WR}_2$ (CoF) ${WR}_3$ (Ra, μm) ${WR}_4$ (WD, μm) ${WR}_5$ (Hv) ${WP}_1$ 25 0.01 5 500 8.45 0.58 7.8 2.71 1746 ${WP}_2$ 25 0.05 10 1000 8.31 0.56 7.1 2.87 1698 ${WP}_3$ 25 0.1 15 1500 9.71 0.55 6.7 2.98 1648 ${WP}_4$ 25 0.15 20 2000 10.89 0.53 5.9 3.68 845 ${WP}_5$ 100 0.01 10 1500 6.71 0.49 5.1 0.73 2576 ${WP}_6$ 100 0.05 5 2000 5.67 0.51 5.4 0.67 2781 ${WP}_7$ 100 0.1 20 500 6.77 0.56 7.3 1.63 2409 ${WP}_8$ 100 0.15 15 1000 7.2 0.52 6.4 0.84 2384 ${WP}_9$ 200 0.01 15 2000 8.54 0.46 3.9 1.47 2127 ${WP}_{10}$ 200 0.05 20 1500 8.24 0.57 7.5 2.14 1898 ${WP}_{11}$ 200 0.1 5 1000 6.72 0.59 8.1 0.89 2317 ${WP}_{12}$ 200 0.15 10 500 7.83 0.61 8.7 0.98 2235 ${WP}_{13}$ 300 0.01 20 1000 9.37 0.64 8.9 3.37 1107 ${WP}_{14}$ 300 0.05 15 500 8.71 0.68 9.1 2.93 1283 ${WP}_{15}$ 300 0.1 10 2000 9.12 0.67 8.7 3.29 997 ${WP}_{16}$ 300 0.15 5 1500 8.5 0.65 8.4 2.79 1321
Pairwise comparison vector for best to other criteria
 Best to Others ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ Best criteria: Wear rate (${WR}_1$) 1 2 7 5 3
 Best to Others ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ Best criteria: Wear rate (${WR}_1$) 1 2 7 5 3
Pairwise comparison vector for other to worst criteria
 Others to the worst criteria Worst criteria: Surface roughness (Ra) ${WR}_1$ 8 ${WR}_2$ 4 ${WR}_3$ 1 ${WR}_4$ 3 ${WR}_5$ 5
 Others to the worst criteria Worst criteria: Surface roughness (Ra) ${WR}_1$ 8 ${WR}_2$ 4 ${WR}_3$ 1 ${WR}_4$ 3 ${WR}_5$ 5
Weight of criteria and inconsistency rate
 Criteria ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ Weights 0.427 0.253 0.050 0.101 0.169 Ksi* 0.07
 Criteria ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ Weights 0.427 0.253 0.050 0.101 0.169 Ksi* 0.07
Normalized decision matrix
 Alternative ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ ${WP}_1$ 0.467 0.455 0.250 0.322 0.465 ${WP}_2$ 0.494 0.545 0.385 0.269 0.441 ${WP}_3$ 0.226 0.591 0.462 0.233 0.415 ${WP}_4$ 0.000 0.682 0.615 0.000 0.000 ${WP}_5$ 0.801 0.864 0.769 0.980 0.894 ${WP}_6$ 1.000 0.773 0.712 1.000 1.000 ${WP}_7$ 0.789 0.545 0.346 0.681 0.808 ${WP}_8$ 0.707 0.727 0.519 0.944 0.795 ${WP}_9$ 0.450 1.000 1.000 0.734 0.662 ${WP}_10$ 0.508 0.500 0.308 0.512 0.544 ${WP}_11$ 0.799 0.409 0.192 0.927 0.760 ${WP}_12$ 0.586 0.318 0.077 0.897 0.718 ${WP}_13$ 0.291 0.182 0.038 0.103 0.135 ${WP}_14$ 0.418 0.000 0.000 0.249 0.226 ${WP}_15$ 0.339 0.045 0.077 0.130 0.079 ${WP}_16$ 0.458 0.136 0.135 0.296 0.246
 Alternative ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ ${WP}_1$ 0.467 0.455 0.250 0.322 0.465 ${WP}_2$ 0.494 0.545 0.385 0.269 0.441 ${WP}_3$ 0.226 0.591 0.462 0.233 0.415 ${WP}_4$ 0.000 0.682 0.615 0.000 0.000 ${WP}_5$ 0.801 0.864 0.769 0.980 0.894 ${WP}_6$ 1.000 0.773 0.712 1.000 1.000 ${WP}_7$ 0.789 0.545 0.346 0.681 0.808 ${WP}_8$ 0.707 0.727 0.519 0.944 0.795 ${WP}_9$ 0.450 1.000 1.000 0.734 0.662 ${WP}_10$ 0.508 0.500 0.308 0.512 0.544 ${WP}_11$ 0.799 0.409 0.192 0.927 0.760 ${WP}_12$ 0.586 0.318 0.077 0.897 0.718 ${WP}_13$ 0.291 0.182 0.038 0.103 0.135 ${WP}_14$ 0.418 0.000 0.000 0.249 0.226 ${WP}_15$ 0.339 0.045 0.077 0.130 0.079 ${WP}_16$ 0.458 0.136 0.135 0.296 0.246
Weighted normalized decision matrix
 Alternative ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ ${WP}_1$ 0.627 0.368 0.062 0.134 0.247 ${WP}_2$ 0.638 0.391 0.069 0.129 0.243 ${WP}_3$ 0.524 0.403 0.073 0.125 0.239 ${WP}_4$ 0.427 0.426 0.080 0.101 0.169 ${WP}_5$ 0.769 0.472 0.088 0.201 0.320 ${WP}_6$ 0.854 0.449 0.085 0.203 0.338 ${WP}_7$ 0.764 0.391 0.067 0.170 0.305 ${WP}_8$ 0.729 0.437 0.075 0.197 0.303 ${WP}_9$ 0.619 0.506 0.099 0.176 0.281 ${WP}_10$ 0.644 0.380 0.065 0.153 0.261 ${WP}_11$ 0.768 0.357 0.059 0.195 0.297 ${WP}_12$ 0.677 0.334 0.053 0.192 0.290 ${WP}_13$ 0.551 0.299 0.052 0.112 0.192 ${WP}_14$ 0.605 0.253 0.050 0.127 0.207 ${WP}_15$ 0.572 0.265 0.053 0.114 0.182 ${WP}_16$ 0.623 0.288 0.056 0.131 0.210
 Alternative ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ ${WP}_1$ 0.627 0.368 0.062 0.134 0.247 ${WP}_2$ 0.638 0.391 0.069 0.129 0.243 ${WP}_3$ 0.524 0.403 0.073 0.125 0.239 ${WP}_4$ 0.427 0.426 0.080 0.101 0.169 ${WP}_5$ 0.769 0.472 0.088 0.201 0.320 ${WP}_6$ 0.854 0.449 0.085 0.203 0.338 ${WP}_7$ 0.764 0.391 0.067 0.170 0.305 ${WP}_8$ 0.729 0.437 0.075 0.197 0.303 ${WP}_9$ 0.619 0.506 0.099 0.176 0.281 ${WP}_10$ 0.644 0.380 0.065 0.153 0.261 ${WP}_11$ 0.768 0.357 0.059 0.195 0.297 ${WP}_12$ 0.677 0.334 0.053 0.192 0.290 ${WP}_13$ 0.551 0.299 0.052 0.112 0.192 ${WP}_14$ 0.605 0.253 0.050 0.127 0.207 ${WP}_15$ 0.572 0.265 0.053 0.114 0.182 ${WP}_16$ 0.623 0.288 0.056 0.131 0.210
Border approximation area matrix (BAA)
 Criteria ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ G 0.641 0.369 0.067 0.150 0.250
 Criteria ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ G 0.641 0.369 0.067 0.150 0.250
Distance of alternative from BAA
 Alternative ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ ${WP}_1$ -0.014 -0.001 -0.004 -0.016 -0.003 ${WP}_2$ -0.003 0.022 0.002 -0.021 -0.007 ${WP}_3$ -0.117 0.034 0.006 -0.025 -0.011 ${WP}_4$ -0.214 0.057 0.014 -0.048 -0.081 ${WP}_5$ 0.128 0.103 0.021 0.051 0.070 ${WP}_6$ 0.213 0.080 0.018 0.053 0.088 ${WP}_7$ 0.123 0.022 0.000 0.021 0.055 ${WP}_8$ 0.088 0.068 0.009 0.047 0.053 ${WP}_9$ -0.021 0.137 0.033 0.026 0.031 ${WP}_10$ 0.003 0.011 -0.002 0.003 0.011 ${WP}_11$ 0.127 -0.012 -0.007 0.045 0.047 ${WP}_12$ 0.037 -0.035 -0.013 0.042 0.040 ${WP}_13$ -0.089 -0.070 -0.015 -0.038 -0.058 ${WP}_14$ -0.035 -0.116 -0.017 -0.023 -0.043 ${WP}_15$ -0.069 -0.104 -0.013 -0.035 -0.068 ${WP}_16$ -0.018 -0.081 -0.010 -0.018 -0.040
 Alternative ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ ${WP}_1$ -0.014 -0.001 -0.004 -0.016 -0.003 ${WP}_2$ -0.003 0.022 0.002 -0.021 -0.007 ${WP}_3$ -0.117 0.034 0.006 -0.025 -0.011 ${WP}_4$ -0.214 0.057 0.014 -0.048 -0.081 ${WP}_5$ 0.128 0.103 0.021 0.051 0.070 ${WP}_6$ 0.213 0.080 0.018 0.053 0.088 ${WP}_7$ 0.123 0.022 0.000 0.021 0.055 ${WP}_8$ 0.088 0.068 0.009 0.047 0.053 ${WP}_9$ -0.021 0.137 0.033 0.026 0.031 ${WP}_10$ 0.003 0.011 -0.002 0.003 0.011 ${WP}_11$ 0.127 -0.012 -0.007 0.045 0.047 ${WP}_12$ 0.037 -0.035 -0.013 0.042 0.040 ${WP}_13$ -0.089 -0.070 -0.015 -0.038 -0.058 ${WP}_14$ -0.035 -0.116 -0.017 -0.023 -0.043 ${WP}_15$ -0.069 -0.104 -0.013 -0.035 -0.068 ${WP}_16$ -0.018 -0.081 -0.010 -0.018 -0.040
Criteria function and ranking of alternative
 Alternative Criteria function ($S_i$) Rank ${WP}_1$ -0.038 10 ${WP}_2$ -0.006 9 ${WP}_3$ -0.113 11 ${WP}_4$ -0.273 15 ${WP}_5$ 0.373 2 ${WP}_6$ 0.452 1 ${WP}_7$ 0.222 4 ${WP}_8$ 0.266 3 ${WP}_9$ 0.205 5 ${WP}_10$ 0.026 8 ${WP}_11$ 0.201 6 ${WP}_12$ 0.071 7 ${WP}_13$ -0.270 14 ${WP}_14$ -0.234 13 ${WP}_15$ -0.289 16 ${WP}_16$ -0.168 12
 Alternative Criteria function ($S_i$) Rank ${WP}_1$ -0.038 10 ${WP}_2$ -0.006 9 ${WP}_3$ -0.113 11 ${WP}_4$ -0.273 15 ${WP}_5$ 0.373 2 ${WP}_6$ 0.452 1 ${WP}_7$ 0.222 4 ${WP}_8$ 0.266 3 ${WP}_9$ 0.205 5 ${WP}_10$ 0.026 8 ${WP}_11$ 0.201 6 ${WP}_12$ 0.071 7 ${WP}_13$ -0.270 14 ${WP}_14$ -0.234 13 ${WP}_15$ -0.289 16 ${WP}_16$ -0.168 12
Different Scenario of criteria weight for sensitivity analysis
 Scenarios Criteria weight ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ S1 0.500 0.125 0.125 0.125 0.125 S2 0.125 0.500 0.125 0.125 0.125 S3 0.125 0.125 0.500 0.125 0.125 S4 0.125 0.125 0.125 0.500 0.125 S5 0.125 0.125 0.125 0.125 0.500 S6 0.200 0.200 0.200 0.200 0.200
 Scenarios Criteria weight ${WR}_1$ ${WR}_2$ ${WR}_3$ ${WR}_4$ ${WR}_5$ S1 0.500 0.125 0.125 0.125 0.125 S2 0.125 0.500 0.125 0.125 0.125 S3 0.125 0.125 0.500 0.125 0.125 S4 0.125 0.125 0.125 0.500 0.125 S5 0.125 0.125 0.125 0.125 0.500 S6 0.200 0.200 0.200 0.200 0.200
Value of Spearman's rank correlation coefficient between MCDM methods
 MCDM methods MABAC TOPSIS MOORA VIKOR TODIM WASPAS MABAC 1.000 0.974 0.973 0.974 1.000 0.977 TOPSIS 0.974 1.000 1.000 1.000 1.000 0.997 MOORA 0.973 1.000 1.000 1.000 1.000 0.997 VIKOR 0.974 1.000 1.000 1.000 1.000 0.997 TODIM 1.000 1.000 1.000 1.000 1.000 0.997 WASPAS 0.977 0.997 0.997 0.997 0.997 1.000
 MCDM methods MABAC TOPSIS MOORA VIKOR TODIM WASPAS MABAC 1.000 0.974 0.973 0.974 1.000 0.977 TOPSIS 0.974 1.000 1.000 1.000 1.000 0.997 MOORA 0.973 1.000 1.000 1.000 1.000 0.997 VIKOR 0.974 1.000 1.000 1.000 1.000 0.997 TODIM 1.000 1.000 1.000 1.000 1.000 0.997 WASPAS 0.977 0.997 0.997 0.997 0.997 1.000
Initial decision matrix for selection of optimal wear parameters for AlCrN coated stainless steel [49]
 Alternative Wear parameters Wear responses (Criteria) Load Sliding velocity Sliding distance Ra, in $\mu$m CoF Disc mass loss (Ml, in mg) WD (Wd-, in $\mu$m) Microhardness (Hv) ${WP}_1$ 10 10 2000 1.5 0.27 52.8 5 1441 ${WP}_2$ 15 20 1000 3.6 0.58 39.7 4.6 421 ${WP}_3$ 10 30 1000 6.6 0.76 22.5 1.2 902 ${WP}_4$ 10 10 1000 2.2 0.4 21.8 2.8 1201 ${WP}_5$ 15 30 1500 5.8 0.63 48 4.9 274 ${WP}_6$ 15 20 2000 3.1 0.44 67.8 8.6 335 ${WP}_7$ 10 20 1500 2.7 0.52 20.4 2.9 1007 ${WP}_8$ 10 30 2000 5.7 0.64 27 3.3 821 ${WP}_9$ 15 10 1000 1.3 0.26 64.1 8.4 651 ${WP}_10$ 5 30 1000 6.9 0.73 9.7 1.5 1435 ${WP}_11$ 5 20 2000 4.2 0.6 17.6 2.2 1777 ${WP}_12$ 10 20 1500 2.7 0.52 21.3 3.1 994 ${WP}_13$ 5 10 1500 2.6 0.38 19.4 1.8 2021 ${WP}_14$ 5 20 1000 5 0.65 6.9 1.1 1549 ${WP}_15$ 10 20 1500 2.8 0.49 21.3 3.1 1001
 Alternative Wear parameters Wear responses (Criteria) Load Sliding velocity Sliding distance Ra, in $\mu$m CoF Disc mass loss (Ml, in mg) WD (Wd-, in $\mu$m) Microhardness (Hv) ${WP}_1$ 10 10 2000 1.5 0.27 52.8 5 1441 ${WP}_2$ 15 20 1000 3.6 0.58 39.7 4.6 421 ${WP}_3$ 10 30 1000 6.6 0.76 22.5 1.2 902 ${WP}_4$ 10 10 1000 2.2 0.4 21.8 2.8 1201 ${WP}_5$ 15 30 1500 5.8 0.63 48 4.9 274 ${WP}_6$ 15 20 2000 3.1 0.44 67.8 8.6 335 ${WP}_7$ 10 20 1500 2.7 0.52 20.4 2.9 1007 ${WP}_8$ 10 30 2000 5.7 0.64 27 3.3 821 ${WP}_9$ 15 10 1000 1.3 0.26 64.1 8.4 651 ${WP}_10$ 5 30 1000 6.9 0.73 9.7 1.5 1435 ${WP}_11$ 5 20 2000 4.2 0.6 17.6 2.2 1777 ${WP}_12$ 10 20 1500 2.7 0.52 21.3 3.1 994 ${WP}_13$ 5 10 1500 2.6 0.38 19.4 1.8 2021 ${WP}_14$ 5 20 1000 5 0.65 6.9 1.1 1549 ${WP}_15$ 10 20 1500 2.8 0.49 21.3 3.1 1001
Criteria function and ranking of alternative
 Alternative Criteria function ($S_i$) Rank ${WP}_1$ 0.0594 9 ${WP}_2$ -0.1347 12 ${WP}_3$ -0.0636 11 ${WP}_4$ 0.1960 4 ${WP}_5$ -0.2922 14 ${WP}_6$ -0.3116 15 ${WP}_7$ 0.1324 5 ${WP}_8$ -0.0609 10 ${WP}_9$ -0.1414 13 ${WP}_10$ 0.0971 8 ${WP}_11$ 0.2010 3 ${WP}_12$ 0.1233 7 ${WP}_13$ 0.3284 1 ${WP}_14$ 0.2114 2 ${WP}_15$ 0.1288 6
 Alternative Criteria function ($S_i$) Rank ${WP}_1$ 0.0594 9 ${WP}_2$ -0.1347 12 ${WP}_3$ -0.0636 11 ${WP}_4$ 0.1960 4 ${WP}_5$ -0.2922 14 ${WP}_6$ -0.3116 15 ${WP}_7$ 0.1324 5 ${WP}_8$ -0.0609 10 ${WP}_9$ -0.1414 13 ${WP}_10$ 0.0971 8 ${WP}_11$ 0.2010 3 ${WP}_12$ 0.1233 7 ${WP}_13$ 0.3284 1 ${WP}_14$ 0.2114 2 ${WP}_15$ 0.1288 6
Initial decision matrix for selection of optimal wear parameters for DLC coated tungsten carbide [78]
 Alternative Wear parameters Wear responses (Criteria) Depth of cut (DoC, in mm) Cutting speed (Vc, in m/min) Feed rate (f, in mm /rev) Temperature in cutting zone (Tc, in $^{\circ}$C) Ra, in $\mu$m Flank wear (Wf, in $\mu$m) ${WP}_1$ 0.375 480 0.125 72.8 0.565 96.25 ${WP}_2$ 0.375 600 0.25 80 0.491 100.67 ${WP}_3$ 0.375 720 0.375 79.6 0.64 113.33 ${WP}_4$ 0.635 480 0.25 79.3 0.389 85.33 ${WP}_5$ 0.635 600 0.375 133.6 0.558 86.25 ${WP}_6$ 0.635 720 0.125 112.2 0.319 94.25 ${WP}_7$ 0.895 480 0.375 160.4 0.482 96.25 ${WP}_8$ 0.895 600 0.125 167.7 0.46 103.75 ${WP}_9$ 0.895 720 0.25 202 0.467 115.42
 Alternative Wear parameters Wear responses (Criteria) Depth of cut (DoC, in mm) Cutting speed (Vc, in m/min) Feed rate (f, in mm /rev) Temperature in cutting zone (Tc, in $^{\circ}$C) Ra, in $\mu$m Flank wear (Wf, in $\mu$m) ${WP}_1$ 0.375 480 0.125 72.8 0.565 96.25 ${WP}_2$ 0.375 600 0.25 80 0.491 100.67 ${WP}_3$ 0.375 720 0.375 79.6 0.64 113.33 ${WP}_4$ 0.635 480 0.25 79.3 0.389 85.33 ${WP}_5$ 0.635 600 0.375 133.6 0.558 86.25 ${WP}_6$ 0.635 720 0.125 112.2 0.319 94.25 ${WP}_7$ 0.895 480 0.375 160.4 0.482 96.25 ${WP}_8$ 0.895 600 0.125 167.7 0.46 103.75 ${WP}_9$ 0.895 720 0.25 202 0.467 115.42
Criteria function and ranking of alternative
 Alternative Criteria function ($S_i$) BWM-MABAC Ranking TOPSIS Ranking [78] ${WP}_1$ 0.040 3 4 ${WP}_2$ 0.032 4 3 ${WP}_3$ -0.143 8 5 ${WP}_4$ 0.408 1 1 ${WP}_5$ 0.007 5 6 ${WP}_6$ 0.379 2 2 ${WP}_7$ -0.064 7 7 ${WP}_8$ 0.006 6 8 ${WP}_9$ -0.381 9 9
 Alternative Criteria function ($S_i$) BWM-MABAC Ranking TOPSIS Ranking [78] ${WP}_1$ 0.040 3 4 ${WP}_2$ 0.032 4 3 ${WP}_3$ -0.143 8 5 ${WP}_4$ 0.408 1 1 ${WP}_5$ 0.007 5 6 ${WP}_6$ 0.379 2 2 ${WP}_7$ -0.064 7 7 ${WP}_8$ 0.006 6 8 ${WP}_9$ -0.381 9 9
Initial decision matrix for selection of optimal wear parameters for AA6063/SiCp composite [31]
 Alternative Wear parameters Wear responses (Criteria) Load (L, in N) Sliding distance ($S_d$, in m) Wt ($\%$) of SiC Wear rate (WR, in $10^{-3}$ ${mm}^3/m$) Frictional force (FF, in N) Specific wear rate (SWR, in $10^{-3}$ ${mm}^3/m$) ${WP}_1$ 20 523 3.5 11.03 12.01 0.5515 ${WP}_2$ 20 1046 7 4.486 3.56 0.2243 ${WP}_3$ 20 1570 10.5 2.83 2.15 0.1415 ${WP}_4$ 30 523 7 9.311 4.15 0.3103 ${WP}_5$ 30 1046 10.5 5.194 8.17 0.1731 ${WP}_6$ 30 1570 3.5 5.34 13.22 0.178 ${WP}_7$ 40 523 10.5 10.016 17.56 0.2504 ${WP}_8$ 40 1046 3.5 7.58 19.05 0.1895 ${WP}_9$ 40 1570 7 5.427 6.61 0.1356
 Alternative Wear parameters Wear responses (Criteria) Load (L, in N) Sliding distance ($S_d$, in m) Wt ($\%$) of SiC Wear rate (WR, in $10^{-3}$ ${mm}^3/m$) Frictional force (FF, in N) Specific wear rate (SWR, in $10^{-3}$ ${mm}^3/m$) ${WP}_1$ 20 523 3.5 11.03 12.01 0.5515 ${WP}_2$ 20 1046 7 4.486 3.56 0.2243 ${WP}_3$ 20 1570 10.5 2.83 2.15 0.1415 ${WP}_4$ 30 523 7 9.311 4.15 0.3103 ${WP}_5$ 30 1046 10.5 5.194 8.17 0.1731 ${WP}_6$ 30 1570 3.5 5.34 13.22 0.178 ${WP}_7$ 40 523 10.5 10.016 17.56 0.2504 ${WP}_8$ 40 1046 3.5 7.58 19.05 0.1895 ${WP}_9$ 40 1570 7 5.427 6.61 0.1356
Criteria function and ranking of alternative
 Alternative Criteria function ($S_i$) BWM-MABAC Ranking GRA-PCA Ranking [31] ${WP}_1$ 0.168 9 9 ${WP}_2$ 0.941 2 3 ${WP}_3$ 1.133 1 1 ${WP}_4$ 0.521 7 7 ${WP}_5$ 0.912 4 4 ${WP}_6$ 0.876 5 5 ${WP}_7$ 0.463 8 8 ${WP}_8$ 0.681 6 6 ${WP}_9$ 0.933 3 2
 Alternative Criteria function ($S_i$) BWM-MABAC Ranking GRA-PCA Ranking [31] ${WP}_1$ 0.168 9 9 ${WP}_2$ 0.941 2 3 ${WP}_3$ 1.133 1 1 ${WP}_4$ 0.521 7 7 ${WP}_5$ 0.912 4 4 ${WP}_6$ 0.876 5 5 ${WP}_7$ 0.463 8 8 ${WP}_8$ 0.681 6 6 ${WP}_9$ 0.933 3 2
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