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:
[1]

P. Achuthamenon SylajakumariR. 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. AliyuM. U. AzamD. 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. BaiJ. 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. BaradeswaranA. 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. BaradeswaranS. C. VettivelA. E. PerumalN. 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. BehrooziS. 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. BirjandiF. AkhyaniR. 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. ChakrabortyS. 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. ChangH. AkilR. B. Nasir and A. Khan, Optimization on wear performance of UHMWPE composites using response surface methodology, Tribol. Int., 88 (2015), 525-262. 

[12]

C. DangY. YaoT. OlugbadeJ. 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. FuentesE. AlmandozR. PierruguesR. MartínezR. J. RodríguezJ. 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. GajalakshmiN. 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. GirishB. 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. GongQ. LiL. 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. GuL. LiM. AiY. XuY. XuG. 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. HaseliR. 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. HuangZ. 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. KhatkarR. VermaS. S. KharbA. 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. Patnaik, Morphology and wear behavior of monolayer TiAlN and composite AlCrN/TiAlN coated plasma nitrided DAC-10 tool steel, Arabian J. Sci. Eng., (2022).

[25]

S. KumarS. R. Maity and L. Patnaik, Friction and tribological behavior of bare nitrided, TiAlN and AlCrN coated MDC-K hot work tool steel, Ceram. Int., 46 (2020), 17280-17294. 

[26]

S. Kumar, S. R. Maity and L. Patnaik, Effect of annealing on structural, mechanical and tribological properties of Cr-(CrN/TiAlN) coating, Adv. Mater. Proces. Technol., (2021), 1–14.

[27]

S. Kumar, S. R. Maity and L. Patnaik, Mechanical and scratch behaviour of TiAlN coated and 3D printed H13 tool steel, Adv. Mater. Proces. Technol., (2021), 1–15.

[28]

S. KumarS. R. Maity and L. Patnaik, Effect of heat treatment and TiN coating on AISI O1 cold work tool steel, Mater. Today: Proceed., 26 (2020), 685-688. 

[29]

S. Kumar, S. R. Maity and L. Patnaik, Relation between mechanical and tribological properties of plasma nitrided and TiCrN coated YXR-7 tool steel, In AIP Conference Proceedings, Indore, India, (2021), 020033.

[30]

S. KumarS. R. Maity and L. Patnaik, Effect of tribological process parameter on the wear and frictional behaviour of Cr-(CrN/TiN) composite coating: An experimental and analytical study, Ceram. Int., 47 (2021), 16018-16028. 

[31]

S. Kumar, S. R. Maity and L. Patnaik, Application of box-behnken method for multi-response optimization of turning parameters for DAC-10 hot work tool steel, In Recent Advances in Mechanical Engineering, Springer Singapore, (2021), 407–415. doi: 10.1007/978-981-15-7711-6_42.

[32]

S. KumarS. R. Maity and L. Patnaik, A comparative study on wear behaviors of hot work and cold work tool steel with same hardness under dry sliding tribological test, Mater. Today: Proceed., 44 (2021), 949-954. 

[33]

S. Kumar, L. Patnaik, S. M. Shafi and S. R. Maity, Relative effect of wear parameters on the wear behavior of TiAlN coated tool steel and parametric optimization using MCDM method, Advances in Materials and Processing Technologies, (2022), 1–22.

[34]

S. Z. Luo and W. Z. Liang, Optimization of roadway support schemes with likelihood-based MABAC method, Appl. Soft Comput., 80 (2019), 80-92. 

[35]

S. Z. Luo and L. N. Xing, A hybrid decision making framework for personnel selection using BWM, MABAC and PROMETHEE, Int. J. Fuzzy Syst., 21 (2019), 2421-2434. 

[36]

H. MaQ. MiaoG. ZhangW. LiangY. WangZ. Sun and H. Lin, The influence of multilayer structure on mechanical behavior of TiN/TiAlSiN multilayer coating, Ceram. Int., 47 (2021), 12583-12591. 

[37]

J. E. A. N. Ming-DerL. I. U. Cheng-WuY. A. N. G. Pao-Hua and H. O. Wen-Hsien, Optimization of wear behavior of DLC coatings through optimization of deposition conditions, Mater. Sci., 26 (2020), 269-280. 

[38]

L. Natrayan and M. S. Kumar, Optimization of wear behaviour on AA6061/Al2O3/SiC metal matrix composite using squeeze casting technique-Statistical analysis, Mater. Todays: Proceed., 27 (2020), 306-310. 

[39]

D. Pamučar and G. Ćirović, The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC), Expert Sys. Appl., 42 (2015), 3016-3028. 

[40]

L. PatnaikS. R. Maity and S. Kumar, Modeling of wear parameters and multi-criteria optimization by box-behnken design of AlCrN thin film against gamma-irradiated Ti6Al4V Counterbody, Ceram. Int., 47 (2021), 20494-20511. 

[41]

L. Patnaik, S. R. Maity and S. Kumar, Evaluation of gamma irradiated Ti6Al4V and silver alloyed aC coatings as friction pair via response surface methodology, Adv. Mater. Process. Technol., (2021), 1–18.

[42]

L. Patnaik, S. R. Maity and S. Kumar, Lubricated sliding of CFRPEEK/AlCrN film tribo-pair and its effect on the mechanical properties and structural integrity of the AlCrN film, Mater. Chem. Phy., (2021), 124980.

[43]

L. Patnaik, S. R. Maity and S. Kumar, Evaluation of crack resistance and adhesive energy of AlCrN and Ag doped aC films deposited on chrome nitrided 316 LVM stainless steel, Adv. Mater. Proces. Technol., (2021), 1–22.

[44]

L. Patnaik, S. R. Maity and S. Kumar, Comparative study on the structural make-up and mechanical behavior of silicon and silver doped amorphous carbon films, Silicon, (2022), 1–18.

[45]

L. PatnaikS. R. Maity and S. Kumar, Comprehensive structural, nanomechanical and tribological evaluation of silver doped DLC thin film coating with chromium interlayer (Ag-DLC/Cr) for biomedical application, Ceram. Int., 46 (2020), 22805-22818. 

[46]

L. PatnaikS. R. Maity and S. Kumar, Mechanical and tribological assessment of composite AlCrN or aC: Ag-based thin films for implant application, Ceram. Int., 47 (2021), 6736-6752. 

[47]

L. PatnaikS. R. Maity and S. Kumar, Effect of lubricated sliding wear against CFRPEEK on the nanomechanical properties of Ag alloyed Cr/DLC thin film, J. Mech. Behav. Biomed. Mater., 118 (2021), 104478. 

[48]

L. PatnaikS. R. Maity and S. Kumar, DLC/CrN or AlCrN/CrN composite films: The better candidate in terms of anti-Wear performance and lesser ion release in hip implant, Mater. Today: Proceed., 44 (2021), 1214-1220. 

[49]

L. Patnaik, S. R. Maity and S. Kumar, Structural and corrosion study of aC film with Ti, Cr and Ni interlayers, In AIP Conference Proceedings, Indore, India, (2021), 020073.

[50]

A. Premnath, Optimization of the process parameters on the mechanical and wear properties of Al-SiC nano-composites fabricated by friction stir processing using desirability approach, Silicon, 12 (2020), 665-675. 

[51]

J. U. PrakashS. AnanthG. Sivakumar and T. V. Moorthy, Multi-objective optimization of wear parameters for aluminium matrix composites (413/B4C) using grey relational analysis, Mater. Today: Proceed., 5 (2018), 7207-7216. 

[52]

T. RajmohanS. Vijayabhaskar and D. Vijayan, Multiple performance optimization in wear characteristics of Mg-SiC nanocomposites using grey-fuzzy algorithm, Silicon, 12 (2020), 1177-1186. 

[53]

R. S. RanaR. PurohitA. Kumar Sharma and S. Rana, Optimization of wear performance of Aa 5083/10 Wt. Sicp composites using Taguchi method, Proced. Mater. Sci., 6 (2013), 503-511. 

[54]

R. RanaR. S. Walia and Q. Murtaza, Characterization and parametric optimization of performance parameters of DLC-Coated tungsten carbide (WC) tool using TOPSIS, Coatings, 11 (2021), 760. 

[55]

T. B. Rao and G. R. Ponugoti, Characterization, prediction, and optimization of Dry sliding wear behaviour of Al6061/WC composites, transactions of the indian institute of metals, Silicon, 74 (2021), 159-178. 

[56]

J. Rezaei, Best-worst multi-criteria decision-making method: Some properties and a linear model, Omega, 64 (2016), 126-130. 

[57]

P. Sahoo, Wear behaviour of electroless Ni-P coatings and optimization of process parameters using Taguchi method, Mater. Des., 30 (2009), 1341-1349. 

[58]

I. Saravanan and A. E. Perumal, Wear behavior of ${\gamma}$-irradiated Ti6Al4V alloy sliding on TiN deposited steel surface, Tribol. Int., 93 (2016), 451-463. 

[59]

I. SaravananA. E. PerumalR. F. IssacS. C. Vettivel and A. Devaraju, Optimization of wear parameters and their relative effects on TiN coated surface against Ti6Al4V alloy, Mater. Des., 92 (2016), 23-35. 

[60]

I. SaravananA. E. PerumalS. C. VettivelN. Selvakumar and A. Baradeswaran, Optimizing wear behavior of TiN coated SS 316L against Ti alloy using Response Surface Methodology, Mater. Des., 67 (2015), 469-482. 

[61]

S. Sathish, V. Anandakrishnan and G. Manoj, Optimization of wear parameters of Mg-(5.6 Ti+ 3Al)-2.5 B4C composite, Indus. Lubr. Tribol., 27 (2019).

[62]

G. SinghS. L. I. Chan and N. Sharma, Parametric study on the dry sliding wear behaviour of AA6082-T6/TiB 2 in situ composites using response surface methodology, J. Brazilian Soci. Mech. Sci. Eng., 40 (2018), 1-12. 

[63]

Y. SinghP. SinghA. SharmaP. ChoudharyA. Singla and N. K. Singh, Optimization of wear and friction characteristics of Phyllanthus Emblica seed oil based lubricant using response surface methodology, Egyptian J. Petrol., 27 (2018), 11445-1155. 

[64]

B. StalinP. R. KumarM. RavichandranM. S. Kumar and M. Meignanamoorthy, Optimization of wear parameters using Taguchi grey relational analysis and ANN-TLBO algorithm for silicon nitride filled AA6063 matrix composites, Mater. Res. Express, 6 (2019), 106590. 

[65]

B. StalinP. R. KumarM. Ravichandran and S. Saravanan, Optimization of wear parameters and their relative effects on stir cast AA6063-Si3N4 Composite, Mater. Res. Express, 10 (2018), 106502. 

[66]

B. SureshaR. S. ShenoyR. BhatP. K. Sohan and R. Hemanth, Optimization of wear behaviour of boron nitride filled polyaryletherketone composites by Taguchi approach, Mater. Res. Express, 19 (2019), 085329. 

[67]

L. I. TongC. C. Chen and C. H. Wang, Optimization of multi-response processes using the VIKOR method, Int. J. Adv. Manuf. Technol., 31 (2007), 1049-1057. 

[68]

J. Wang and A. Misra, An overview of interface-dominated deformation mechanisms in metallic multilayers, Curr. Opin. Solid State Mater. Sci., 15 (2011), 20-28. 

[69]

J. WangG. WeiC. Wei and Y. Wei, MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment, Defence Technol., 16 (2020), 208-216. 

[70]

G. WeiY. HeF. LeiJ. WuC. Wei and Y. Guo, Green supplier selection with an uncertain probabilistic linguistic MABAC method, J. Intell. Fuzzy Syst., 39 (2020), 3125-3136. 

[71]

G. WeiC. WeiJ. Wu and H. Wang, Supplier selection of medical consumption products with a probabilistic linguistic MABAC method, Int. J. Environ. Res. Public Health, 16 (2019), 5082. 

[72]

P. WiecinskiJ. SmolikH. GarbaczJ. BonarskiA. Mazurkiewicz and K. J. Kurzydlowski, Microstructure and properties of metal/ceramic and ceramic/ceramic multilayer coatings on titanium alloy Ti6Al4V, Surf. Coat. Technol., 309 (2017), 709-718. 

[73]

Y. X. XueJ. X. YouX. D. Lai and H. C. Liu, An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information, Appl. Soft Comput., 38 (2016), 703-713. 

[74]

Y. X. Xue, J. X. You, X. D. Lai, H. C. Liu, L. A. Puška, S. Kozarević, Ž. Stević and J. Stovrag, A new way of applying interval fuzzy logic in group decision making for supplier selection, Econ. Comput. Econ. Cybern. Stud. Res., 52 (2018).

[75]

E. ZarafshanS. GholamiR. Sheikh and S. S. Sana, Resource planning system for organisations-a soft computing approach, Int. J. Serv. Econ. Manag., 12 (2021), 272-293. 

[76]

E. K. ZavadskasZ. TurskisJ. Antucheviciene and A. Zakarevicius, Optimization of weighted aggregated sum product assessment, Elektronika ir Elektrotechnika, 122 (2012), 3-6. 

[77]

K. ZhangL. S. WangG. H. YueY. Z. ChenD. L. PengZ. B. Qi and Z. C. Wang, Structure and mechanical properties of TiAlSiN/Si3N4 multilayer coatings, Surf. Coat. Technol., 205 (2011), 3588-3595. 

[78]

D. ZindaniS. R. MaityS. Bhowmik and S. Chakraborty, A material selection approach using the TODIM (TOmada de Decisao Interativa Multicriterio) method and its analysis, Int. J. Mater. Res., 108 (2017), 345-354. 

show all references

References:
[1]

P. Achuthamenon SylajakumariR. 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. AliyuM. U. AzamD. 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. BaiJ. 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. BaradeswaranA. 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. BaradeswaranS. C. VettivelA. E. PerumalN. 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. BehrooziS. 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. BirjandiF. AkhyaniR. 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. ChakrabortyS. 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. ChangH. AkilR. B. Nasir and A. Khan, Optimization on wear performance of UHMWPE composites using response surface methodology, Tribol. Int., 88 (2015), 525-262. 

[12]

C. DangY. YaoT. OlugbadeJ. 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. FuentesE. AlmandozR. PierruguesR. MartínezR. J. RodríguezJ. 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. GajalakshmiN. 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. GirishB. 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. GongQ. LiL. 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. GuL. LiM. AiY. XuY. XuG. 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. HaseliR. 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. HuangZ. 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. KhatkarR. VermaS. S. KharbA. 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. Patnaik, Morphology and wear behavior of monolayer TiAlN and composite AlCrN/TiAlN coated plasma nitrided DAC-10 tool steel, Arabian J. Sci. Eng., (2022).

[25]

S. KumarS. R. Maity and L. Patnaik, Friction and tribological behavior of bare nitrided, TiAlN and AlCrN coated MDC-K hot work tool steel, Ceram. Int., 46 (2020), 17280-17294. 

[26]

S. Kumar, S. R. Maity and L. Patnaik, Effect of annealing on structural, mechanical and tribological properties of Cr-(CrN/TiAlN) coating, Adv. Mater. Proces. Technol., (2021), 1–14.

[27]

S. Kumar, S. R. Maity and L. Patnaik, Mechanical and scratch behaviour of TiAlN coated and 3D printed H13 tool steel, Adv. Mater. Proces. Technol., (2021), 1–15.

[28]

S. KumarS. R. Maity and L. Patnaik, Effect of heat treatment and TiN coating on AISI O1 cold work tool steel, Mater. Today: Proceed., 26 (2020), 685-688. 

[29]

S. Kumar, S. R. Maity and L. Patnaik, Relation between mechanical and tribological properties of plasma nitrided and TiCrN coated YXR-7 tool steel, In AIP Conference Proceedings, Indore, India, (2021), 020033.

[30]

S. KumarS. R. Maity and L. Patnaik, Effect of tribological process parameter on the wear and frictional behaviour of Cr-(CrN/TiN) composite coating: An experimental and analytical study, Ceram. Int., 47 (2021), 16018-16028. 

[31]

S. Kumar, S. R. Maity and L. Patnaik, Application of box-behnken method for multi-response optimization of turning parameters for DAC-10 hot work tool steel, In Recent Advances in Mechanical Engineering, Springer Singapore, (2021), 407–415. doi: 10.1007/978-981-15-7711-6_42.

[32]

S. KumarS. R. Maity and L. Patnaik, A comparative study on wear behaviors of hot work and cold work tool steel with same hardness under dry sliding tribological test, Mater. Today: Proceed., 44 (2021), 949-954. 

[33]

S. Kumar, L. Patnaik, S. M. Shafi and S. R. Maity, Relative effect of wear parameters on the wear behavior of TiAlN coated tool steel and parametric optimization using MCDM method, Advances in Materials and Processing Technologies, (2022), 1–22.

[34]

S. Z. Luo and W. Z. Liang, Optimization of roadway support schemes with likelihood-based MABAC method, Appl. Soft Comput., 80 (2019), 80-92. 

[35]

S. Z. Luo and L. N. Xing, A hybrid decision making framework for personnel selection using BWM, MABAC and PROMETHEE, Int. J. Fuzzy Syst., 21 (2019), 2421-2434. 

[36]

H. MaQ. MiaoG. ZhangW. LiangY. WangZ. Sun and H. Lin, The influence of multilayer structure on mechanical behavior of TiN/TiAlSiN multilayer coating, Ceram. Int., 47 (2021), 12583-12591. 

[37]

J. E. A. N. Ming-DerL. I. U. Cheng-WuY. A. N. G. Pao-Hua and H. O. Wen-Hsien, Optimization of wear behavior of DLC coatings through optimization of deposition conditions, Mater. Sci., 26 (2020), 269-280. 

[38]

L. Natrayan and M. S. Kumar, Optimization of wear behaviour on AA6061/Al2O3/SiC metal matrix composite using squeeze casting technique-Statistical analysis, Mater. Todays: Proceed., 27 (2020), 306-310. 

[39]

D. Pamučar and G. Ćirović, The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC), Expert Sys. Appl., 42 (2015), 3016-3028. 

[40]

L. PatnaikS. R. Maity and S. Kumar, Modeling of wear parameters and multi-criteria optimization by box-behnken design of AlCrN thin film against gamma-irradiated Ti6Al4V Counterbody, Ceram. Int., 47 (2021), 20494-20511. 

[41]

L. Patnaik, S. R. Maity and S. Kumar, Evaluation of gamma irradiated Ti6Al4V and silver alloyed aC coatings as friction pair via response surface methodology, Adv. Mater. Process. Technol., (2021), 1–18.

[42]

L. Patnaik, S. R. Maity and S. Kumar, Lubricated sliding of CFRPEEK/AlCrN film tribo-pair and its effect on the mechanical properties and structural integrity of the AlCrN film, Mater. Chem. Phy., (2021), 124980.

[43]

L. Patnaik, S. R. Maity and S. Kumar, Evaluation of crack resistance and adhesive energy of AlCrN and Ag doped aC films deposited on chrome nitrided 316 LVM stainless steel, Adv. Mater. Proces. Technol., (2021), 1–22.

[44]

L. Patnaik, S. R. Maity and S. Kumar, Comparative study on the structural make-up and mechanical behavior of silicon and silver doped amorphous carbon films, Silicon, (2022), 1–18.

[45]

L. PatnaikS. R. Maity and S. Kumar, Comprehensive structural, nanomechanical and tribological evaluation of silver doped DLC thin film coating with chromium interlayer (Ag-DLC/Cr) for biomedical application, Ceram. Int., 46 (2020), 22805-22818. 

[46]

L. PatnaikS. R. Maity and S. Kumar, Mechanical and tribological assessment of composite AlCrN or aC: Ag-based thin films for implant application, Ceram. Int., 47 (2021), 6736-6752. 

[47]

L. PatnaikS. R. Maity and S. Kumar, Effect of lubricated sliding wear against CFRPEEK on the nanomechanical properties of Ag alloyed Cr/DLC thin film, J. Mech. Behav. Biomed. Mater., 118 (2021), 104478. 

[48]

L. PatnaikS. R. Maity and S. Kumar, DLC/CrN or AlCrN/CrN composite films: The better candidate in terms of anti-Wear performance and lesser ion release in hip implant, Mater. Today: Proceed., 44 (2021), 1214-1220. 

[49]

L. Patnaik, S. R. Maity and S. Kumar, Structural and corrosion study of aC film with Ti, Cr and Ni interlayers, In AIP Conference Proceedings, Indore, India, (2021), 020073.

[50]

A. Premnath, Optimization of the process parameters on the mechanical and wear properties of Al-SiC nano-composites fabricated by friction stir processing using desirability approach, Silicon, 12 (2020), 665-675. 

[51]

J. U. PrakashS. AnanthG. Sivakumar and T. V. Moorthy, Multi-objective optimization of wear parameters for aluminium matrix composites (413/B4C) using grey relational analysis, Mater. Today: Proceed., 5 (2018), 7207-7216. 

[52]

T. RajmohanS. Vijayabhaskar and D. Vijayan, Multiple performance optimization in wear characteristics of Mg-SiC nanocomposites using grey-fuzzy algorithm, Silicon, 12 (2020), 1177-1186. 

[53]

R. S. RanaR. PurohitA. Kumar Sharma and S. Rana, Optimization of wear performance of Aa 5083/10 Wt. Sicp composites using Taguchi method, Proced. Mater. Sci., 6 (2013), 503-511. 

[54]

R. RanaR. S. Walia and Q. Murtaza, Characterization and parametric optimization of performance parameters of DLC-Coated tungsten carbide (WC) tool using TOPSIS, Coatings, 11 (2021), 760. 

[55]

T. B. Rao and G. R. Ponugoti, Characterization, prediction, and optimization of Dry sliding wear behaviour of Al6061/WC composites, transactions of the indian institute of metals, Silicon, 74 (2021), 159-178. 

[56]

J. Rezaei, Best-worst multi-criteria decision-making method: Some properties and a linear model, Omega, 64 (2016), 126-130. 

[57]

P. Sahoo, Wear behaviour of electroless Ni-P coatings and optimization of process parameters using Taguchi method, Mater. Des., 30 (2009), 1341-1349. 

[58]

I. Saravanan and A. E. Perumal, Wear behavior of ${\gamma}$-irradiated Ti6Al4V alloy sliding on TiN deposited steel surface, Tribol. Int., 93 (2016), 451-463. 

[59]

I. SaravananA. E. PerumalR. F. IssacS. C. Vettivel and A. Devaraju, Optimization of wear parameters and their relative effects on TiN coated surface against Ti6Al4V alloy, Mater. Des., 92 (2016), 23-35. 

[60]

I. SaravananA. E. PerumalS. C. VettivelN. Selvakumar and A. Baradeswaran, Optimizing wear behavior of TiN coated SS 316L against Ti alloy using Response Surface Methodology, Mater. Des., 67 (2015), 469-482. 

[61]

S. Sathish, V. Anandakrishnan and G. Manoj, Optimization of wear parameters of Mg-(5.6 Ti+ 3Al)-2.5 B4C composite, Indus. Lubr. Tribol., 27 (2019).

[62]

G. SinghS. L. I. Chan and N. Sharma, Parametric study on the dry sliding wear behaviour of AA6082-T6/TiB 2 in situ composites using response surface methodology, J. Brazilian Soci. Mech. Sci. Eng., 40 (2018), 1-12. 

[63]

Y. SinghP. SinghA. SharmaP. ChoudharyA. Singla and N. K. Singh, Optimization of wear and friction characteristics of Phyllanthus Emblica seed oil based lubricant using response surface methodology, Egyptian J. Petrol., 27 (2018), 11445-1155. 

[64]

B. StalinP. R. KumarM. RavichandranM. S. Kumar and M. Meignanamoorthy, Optimization of wear parameters using Taguchi grey relational analysis and ANN-TLBO algorithm for silicon nitride filled AA6063 matrix composites, Mater. Res. Express, 6 (2019), 106590. 

[65]

B. StalinP. R. KumarM. Ravichandran and S. Saravanan, Optimization of wear parameters and their relative effects on stir cast AA6063-Si3N4 Composite, Mater. Res. Express, 10 (2018), 106502. 

[66]

B. SureshaR. S. ShenoyR. BhatP. K. Sohan and R. Hemanth, Optimization of wear behaviour of boron nitride filled polyaryletherketone composites by Taguchi approach, Mater. Res. Express, 19 (2019), 085329. 

[67]

L. I. TongC. C. Chen and C. H. Wang, Optimization of multi-response processes using the VIKOR method, Int. J. Adv. Manuf. Technol., 31 (2007), 1049-1057. 

[68]

J. Wang and A. Misra, An overview of interface-dominated deformation mechanisms in metallic multilayers, Curr. Opin. Solid State Mater. Sci., 15 (2011), 20-28. 

[69]

J. WangG. WeiC. Wei and Y. Wei, MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment, Defence Technol., 16 (2020), 208-216. 

[70]

G. WeiY. HeF. LeiJ. WuC. Wei and Y. Guo, Green supplier selection with an uncertain probabilistic linguistic MABAC method, J. Intell. Fuzzy Syst., 39 (2020), 3125-3136. 

[71]

G. WeiC. WeiJ. Wu and H. Wang, Supplier selection of medical consumption products with a probabilistic linguistic MABAC method, Int. J. Environ. Res. Public Health, 16 (2019), 5082. 

[72]

P. WiecinskiJ. SmolikH. GarbaczJ. BonarskiA. Mazurkiewicz and K. J. Kurzydlowski, Microstructure and properties of metal/ceramic and ceramic/ceramic multilayer coatings on titanium alloy Ti6Al4V, Surf. Coat. Technol., 309 (2017), 709-718. 

[73]

Y. X. XueJ. X. YouX. D. Lai and H. C. Liu, An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information, Appl. Soft Comput., 38 (2016), 703-713. 

[74]

Y. X. Xue, J. X. You, X. D. Lai, H. C. Liu, L. A. Puška, S. Kozarević, Ž. Stević and J. Stovrag, A new way of applying interval fuzzy logic in group decision making for supplier selection, Econ. Comput. Econ. Cybern. Stud. Res., 52 (2018).

[75]

E. ZarafshanS. GholamiR. Sheikh and S. S. Sana, Resource planning system for organisations-a soft computing approach, Int. J. Serv. Econ. Manag., 12 (2021), 272-293. 

[76]

E. K. ZavadskasZ. TurskisJ. Antucheviciene and A. Zakarevicius, Optimization of weighted aggregated sum product assessment, Elektronika ir Elektrotechnika, 122 (2012), 3-6. 

[77]

K. ZhangL. S. WangG. H. YueY. Z. ChenD. L. PengZ. B. Qi and Z. C. Wang, Structure and mechanical properties of TiAlSiN/Si3N4 multilayer coatings, Surf. Coat. Technol., 205 (2011), 3588-3595. 

[78]

D. ZindaniS. R. MaityS. Bhowmik and S. Chakraborty, A material selection approach using the TODIM (TOmada de Decisao Interativa Multicriterio) method and its analysis, Int. J. Mater. Res., 108 (2017), 345-354. 

Figure 1.  (a) Cross-sectional FE-SEM micrograph and (b) corresponding line EDS of CrN/TiAlSiN coating
Figure 2.  Representation of $ G_- $, G and $ G_+ $
Figure 3.  Algorithm of the proposed methodology
Figure 4.  Sensitivity analysis of BWM-MABAC method using criteria weight change
Figure 5.  Effect of dynamic matrices on the ranking of MABAC method
Figure 6.  Comparison between proposed MABAC and other developed MCDM methods
Table 1.  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
Table 2.  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
Table 3.  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
Table 4.  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
Table 5.  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
Table 6.  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
Table 7.  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
Table 8.  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
Table 9.  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
Table 10.  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
Table 11.  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
Table 12.  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
Table 13.  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
Table 14.  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
Table 15.  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
Table 16.  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
Table 17.  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
Table 18.  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
Table 19.  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
Table 20.  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
Table 21.  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
Table 22.  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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