Operational Research in Engineering Sciences: Theory and Applications Vol. 5, Issue 3, 2022, pp. 40-67 ISSN: 2620-1607 eISSN: 2620-1747 DOI: https://doi.org/10.31181/oresta110722105k * Corresponding author. sunilnits18@gmail.com (S. Kumar), saikat.jumtech@gmail.com (S.R. Maity), lokeswar.nits@gmail.com (L. Patnaik) OPTIMIZATION OF WEAR PARAMETERS FOR DUPLEX- TIALN COATED MDC-K TOOL STEEL USING FUZZY MCDM TECHNIQUES Sunil Kumar 1, 2, Saikat Ranjan Maity 1*, Lokeswar Patnaik 3 1 Department of Mechanical Engineering, National Institute of Technology Silchar, India 2 Department of Mechanical Engineering, Amrita School of Engineering, India 3 School of Mechanical Engineering, Sathyabama Institute of Science and Technology (Deemed to be University), India Received: 06 April 2022 Accepted: 07 July 2022 First online: 11 July 2022 Research paper Abstract: The present work evaluates the effects of different tribological process parameters on the measured responses such as hardness, coefficient of friction, surface roughness, wear mass loss and wear depth of duplex-TiAlN coated MDC-K tool steel material. The considered tribological process parameters are load, sliding velocity, and sliding distance. A full factorial design with 27 experimental runs is employed and based on the response values, an optimal combination of the tribological process parameters is subsequently determined. Different multi-objective optimization techniques, like overall evaluation criteria and fuzzy-based multi-criteria decision- making methods (fuzzy evaluation based on distance from the average solution, fuzzy technique for order of preference by similarity to ideal solution, and fuzzy complex proportional assessment) are utilized to identify the optimal intermixes of the considered tribological process parameters. Sensitivity analysis with respect to changing weights of the responses is performed to validate the derived rankings of the trials, whereas the results of analysis of variance revealed the most significant parameters were influencing the responses. In addition to this, two different published problems related to optimization of wear parameters were solved using the proposed method to check its capability. Keywords: MDC-K tool steel, Duplex-TiAlN coating, Fuzzy MCDM, Sensitivity analysis, Optimization. 1. Introduction MDC-K hot work tool steel contains a high percentage of chromium along with tungsten, molybdenum, and vanadium, which substantially enhances its mechanical and wear properties required for its application in the manufacturing of extrusion Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 41 dies, die casting dies, hot stamping dies, and forging dies. Untreated tool steel is commercially available with a hardness of ~22 HRC, constraining its application in die manufacturing. Therefore, heat treatment of tool steel becomes mandatory using different hardening processes to attain the desired levels of hardness and toughness. These properties of tool steel mainly depend on its chemical composition, alloying elements, and secondary carbides formation during the hardening processes (Joshy et al. 2019, Kumar et al. 2021a, and Soleimany et al. 2019). The alloying elements can be divided into two classes, i.e., one is responsible for carbide formation and the other is accountable for changing the tempering kinetics during the heat treatment process (Podgornik et al. 2018a and Podgornik et al. 2016b). Further, the hardened tool steel requires surface modifications, such as nitriding (gas nitriding, salt bath nitriding or plasma nitriding) and deposition of ceramic- based hard coatings. Plasma nitriding has broader advantages over salt bath nitriding and gas nitriding. It allows much closer control of the microstructure during nitriding and is able to provide a surface without the formation of a compound layer. When plasma nitriding is integrated with the physical vapor deposition (PVD) process, it is known as duplex surface treatment. During plasma nitriding, nitrogen diffuses to the surface and forms two different zones, i.e., the compound zone and diffusion zone. The compound zone is made up of Fe4N and Fe2-3N, whereas, the diffusion zone is formed by diffused nitrogen atoms making the surface harder (Aghajani et al. 2017 and Kumar et al. 2020a, 2022a). In addition to the application on nitride surfaces, ceramic coatings, such as TiN, CrN, TiAlN, TiCN, AlCrN, CrAlN, etc. have widely been employed in the manufacturing, tooling, and biomedical industries due to their high resistance to wear, oxidation, corrosion, chemical stability and biocompatibility (Chaliampalias et al. 2017, Prabhu et al. 2018, Kumar et al. 2020b, 2021b, 2022b, 2021c and Patnaik et al. 2021a, 2021b, 2021c, 2021d, 2020a, 2022). Many researchers have observed excellent mechanical, wear, and corrosion properties of TiAlN film coatings (Fu et al. 2019 and Ozkan et al. 2020). Various experimental works have already been conducted to study the tribological, frictional, and wear behaviors of TiAlN coated surfaces under different conditions of normal load, sliding velocity, and sliding distance (Sen et al. 2020, Chowdhury et al. 2017, M’Saoubi et al. 2013, Kumar et al. 2021d, 2022c and Kuo et al. 2018). However, investigations to study the influences of various tribological process parameters on the wear behavior of TiAlN coated surfaces remain unexplored. In addition to this, Saravanan et al. (2015 and 2016) and Patnaik et al. (2021e and 2021f) adopted the Box-Behnken experimental design plan (L15 orthogonal array) and conducted 15 experiments to derive a suitable combination of process parameters for TiN coated SS 316L steel. Out of those 15 experimental runs, one experiment was repeated three times, resulting in performing only 13 actual experiments. Similar studies have been performed by Kumar et al. (2022d & 2022e), where L16 orthogonal array was adopted to perform the wear experiment for CrN/TiAlN coating. According to the authors, the use of a small set of experimental runs may not always be sufficient to determine the most suitable parameters for a specific process, and there should be sufficient experimental observations to study the process behavior. Moreover, in the earlier investigations, there has been limited participation of the decision makers and equal weights (relative importance) have usually been assigned to the considered responses. Thus, there is a huge opportunity to adopt different multi-criteria decision-making (MCDM) techniques allowing the Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 42 involvement of a group of decision makers in deciding the relative importance of various responses under a fuzzy environment. These MCDM techniques are very popular in the material selection for various applications (Maity and Chakraborty 2013 and Prasad et al. 2014). To the best of the authors’ knowledge, the application of any of the fuzzy MCDM tools in studying the tribological properties of duplex-TiAlN coated MDC-K tool steel is really limited. Thus, this paper proposes a simultaneous application of three other fuzzy MCDM techniques, in the form of fuzzy technique for order of preference by similarity to ideal solution (F-TOPSIS), fuzzy evaluation based on distance from the average solution (F-EDAS) and fuzzy complex proportional assessment (F-COPRAS) methods, to investigate effects of different tribological process parameters, like load, sliding velocity and sliding distance on different responses, i.e. hardness, coefficient of friction, surface roughness, wear mass loss and wear depth of duplex-TiAlN coated MDC-K tool steel material. Based on the experimental observations, the most appropriate combination of those tribological process parameters is also singled out using each of the multi-objective optimization methods under consideration. All these fuzzy MCDM techniques are easy to comprehend, robust and mathematically sound. The fuzzy-TOPSIS method endeavors to identify the best alternative based on its minimum distance from the positive ideal solution and maximum distance from the negative ideal solution (Yu and Pan 2021; de Lima Silva et al. 2020 and Petrović et al. 2019). On the other hand, the fuzzy-EDAS method assigns a ranking order to the candidate alternatives based on the positive and negative distances from the average solution (Keshavarz Ghorabaee et al. 2017). The fuzzy-COPRAS method selects the most apposite alternative considering both the positive ideal and negative ideal solutions while taking into account the performance of the alternatives with respect to different criteria and the corresponding criteria weights (Zhan et al. 2020). It adopts a step-wise ranking and evaluating procedure of the alternatives in terms of their significance and utility degree. It is worthwhile to mention here that as the considered multi-objective optimization techniques have different mathematical treatments and have their own advantages and disadvantages, the ranking lists of the alternatives derived using these methods are supposed to vary, and it would be interesting to identify the best performing mathematical tool that would lead to the attainment of the most desired responses for duplex-TiAlN coated MDC-K tool steel. 2. Methodology 2.1. Preparation of the specimen In this paper, chromium-rich MDC-K tool steel is used as the substrate material and its composition is provided in Table 1. The dimension of the sample (Ø55 mm and thickness 5 mm) is attained using a tool room lathe (Mysore KIRLOSKAR, Model: EP-2215) and high precision hydraulic surface grinding machine (Kingston, Model: KG-CL 3060 AH). The turned substrate is then heat-treated, followed by plasma nitriding. Vacuum hardening is performed at ~1080°C temperature in the absence of oxygen, whereas, quenching is performed in the same chamber in a nitrogen environment under a pressure of ~2 MPa. Application of tempering (at ~0.14 MPa gas pressure and cooled to ~92°C) helps to reduce extra hardness and brittleness while imparting enough toughness to the treated material. Hardness is measured using a Wilson Holbert micro-hardness testing machine, i.e., 460 HV. Furthermore, to Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 43 increase the corresponding surface hardness, plasma nitriding is performed in presence of hydrogen (75%) and nitrogen (25%) at ~0.8 kV potential. Table 1. Composition of MDC-K tool steel Element Cr W V Mn C Si wt% 4.4 2 1.7 0.5 0.4 0.3 The TiAlN coating is deposited on the plasma nitrided MDC-K tool steel surface using the magnetron sputtering method. Before the deposition process, the substrates are cleaned ultrasonically using an alkaline solution, followed by ethanol for 10-15 minutes. Later, distilled water is used to re-clean the substrate and is dried with ethanol. The substrate surface is then etched using titanium (Ti) ions under a pulse bias of -1000V with an 80% duty cycle for four minutes. The TiAlN film is finally deposited using titanium (Ti) and aluminum (Al) cathode (50:50) under a nitrogen gas pressure of 2.5 Pa. The DC bias is -40V and the temperature is maintained at ~315oC for 30 min to attain a film thickness of 3.5 µm. 2.2. Selection of process parameters Based on the full-factorial design plan, 27 experiments are conducted using DUCOM TR20LE Tribometer (ASTM: G99 standard) to investigate the effects of various tribological process parameters, like load, sliding velocity, and sliding distance on the considered responses, i.e., hardness, coefficient of friction, surface roughness, wear mass loss and wear depth of duplex-TiAlN coated MDC-K tool steel material. The past literature (Łępicka et al. 2017 & 2019, Ramezani et al. 2018, and Patnaik et al. 2020b, 2021g) suggests that load, sliding velocity, and sliding distance are the most influential parameters influencing the wear properties of TiAlN coated materials. During the experiments, the range of each of these parameters is decided based on pilot experiment runs. When the experiments are conducted at a load less than 10 N load, sliding velocity less than 0.1 m/s, and sliding distance less than 1000 m, no significant effect on the wear properties is noticed due to the lower contact period between the pin and disc surfaces. At 20 N load, 0.3 m/s sliding velocity and 2000 m sliding distance, a wider and deeper wear track is observed on the surface with heavy abrasion and erosion of the coating. High sliding velocity provides sufficient time to repeat the same contact point, and its combined effect with high load increases the interface temperature leading to deformation and erosion of the coating. Based on these results, the corresponding levels and ranges of the considered tribological parameters are determined, as exhibited in Table 2. Table 2. Experimental conditions Process parameters and their levels Process parameter Level Value Load (L) (in N) 3 10, 15, 20 Sliding velocity (SV) (in m/s) 3 0.1, 0.2, 0.3 Sliding distance (SD) (in m) 3 1000, 1500, 2000 Uncontrollable Parameters Parameter Description Disc size 60 mm diameter × 8 mm thickness Pin size 8 mm diameter × 30 mm length Temperature Ambient Humidity Ambient Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 44 2.3. Fuzzy-TOPSIS method Three different fuzzy-based MCDM techniques viz. F-TOPSIS, F-COPRAS, and F- EDAS are also employed for optimization of different tribological parameters to attain the most desired wear properties of duplex-TiAlN coated MDC-K tool steel. The TOPSIS method selects the most apposite alternative which is nearest to the positive- ideal solution and farthest from the negative ideal solution. Based on the negative- ideal solution, non-beneficial attributes get maximized and the beneficial attributes are minimized. On the other hand, based on the positive-ideal solution, beneficial attributes are maximized and non-beneficial attributes get minimized. Furthermore, the integration of fuzzy set theory with TOPSIS helps in dealing with ambiguity and subjectivity in the decision-making process. Usually, in a multi-objective parametric optimization problem involving a single decision maker/process engineer, equal importance is assigned to all the considered responses that also ease out the calculation steps. However, in a real-time machining environment, more than one decision maker participates in assigning importance to the varying responses. The ratings allotted to the responses are usually subjective and vary from one decision to the other. In this paper, in order to assign weight to each of the responses, the triangular linguistic fuzzy numbers of Table 3 is incorporated. In Table 4, the linguistic fuzzy weights allotted to the five responses by a panel of three decision makers are presented, which are finally aggregated in Table 5 to provide the corresponding fuzzy weights for all the responses. Table 3. Triangular linguistic fuzzy numbers Lowest LT (0, 0, 0.1) Lower LR (0, 0.1, 0.3) Low L (0.1, 0.3, 0.5) Medium M (0.3, 0.5, 0.7) High H (0.5, 0.7, 0.9) Higher HR (0.7, 0.9, 1) Highest HT (0.9, 1, 1) Table 4. Decision makers’ panel Table 5. Aggregated fuzzy weight Response Group of decision makers DM1 DM2 DM3 Ra L M LR COF M L LR WML L M L WD M M L HV HR H HT Response Fuzzy weight Ra (0.133, 0.3, 0.5) COF (0.133, 0.3, 0.5) WML (0.17, 0.37, 0.57) WD (0.23, 0.43, 0.63) HV (0.7, 0.87, 0.97) The procedural steps of the F-TOPSIS method are elucidated below (Shivakoti et al. 2017): Step 1: Based on the experimental dataset consisting of 27 observations and five responses, develop the initial decision/evaluation matrix U = [uij]27×5, where uij is the observed value of jth response (j = 1, 2, 3, 4, 5) at ith experimental trial (i = 1, 2...,27). Step 2: In order to make the performance criteria values of the above decision matrix dimensionless and comparable, normalize all the elements using the vector normalization procedure. Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 45 0.5 27 2 1 i =1, 2, ....., 27 ij ij ij i u x u          (1) where xij is the normalized value of uij. Step 3: Developed the fuzzy weighted normalized decision matrix ( ijN ~ ) while multiplying all the elements of the normalized decision matrix by the corresponding fuzzy weights of the considered responses. Step 4: The fuzzy positive ideal solution  M  and fuzzy negative ideal solution  M  is needed to be calculated using Eq. (2) and Eq. (3) respectively.     max min , i =1, 2, ...., 27ij ijM m j J or m j J where           1 2 3 4 5, , , ,M M M M M       (2)     min max , i =1, 2, ...., 27ij ijM m j J or m j J where           1 2 3 4 5, , , ,M M M M M       (3) Where,  1, 2, 3, 4, 5J  and  1, 2, 3, 4, 5J   J and J  associated with higher the better type and lower the better type respectively. In this paper, Ra, CoF, WML, WD are considered as lower the better and HV was considered as higher the better type. Step 5: The fuzzy Euclidean distance for each experimental result from the fuzzy positive ideal solution  id  and fuzzy negative ideal solution  id  is needed to be calculated using Eq. (4) and Eq. (5) respectively.   5 1 , m i = 1, 2, ....., 27; j = 1, 2, 3, 4 ,5 i ij i i d d m      (4)   5 1 , m i = 1, 2, ....., 27; j = 1, 2, 3, 4 ,5 i ij i i d d m      (5) where, d is the distance between two fuzzy numbers. Step 6: Defuzzified the positive ideal solution and negative ideal solution. Step 7: Calculate the closeness coefficient (CoCi) for each experimental run as its proximity to the ideal solution. i i i i d CoC d d      (6) Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 46 Step 8: Rank all the experimental runs based on the descending values of CoCi. Thus, the experimental run having the maximum CoCi value would be the best alternative, whereas, the worst alternative should have the minimum CoCi value. 2.4. Fuzzy-COPRAS method The COPRAS method usually deals with quantitative information and the candidate alternatives are ranked based on the relative weights of various criteria. However, while solving real-time decision-making problems with incomplete or vague information, this method fails to provide an accurate ranking of the alternatives under consideration. To avoid this deficiency, the COPRAS method is combined with the fuzzy set theory in this paper Use the fuzzy technique to calculate the relative priority of responses/criteria using a fuzzy number rather than the precise number (Sun 2010). In this way, the fuzzy-COPRAs technique was proposed to deal with the insufficiency in the conventional COPRAS method. The weight of the responses/criteria and ranking of the alternatives are evaluated using linguistic terms denoted by a fuzzy number. The following steps are used to perform the fuzzy- COPRAS decision-making Albayrak 2020). Step 1: Construct the normalized decision matrix using Eq. (1). Step 2: Construct the fuzzy weighted normalized matrix  X̂ using Eq. (7) and Eq. (8). ˆ ij j ij X w x  (7) j w is the fuzzy weight of criteria. 11 12 1 21 22 2 1 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1, 2,3...., ; 1, 2,3,...., ˆ ˆ ˆ n n ij m m mn x x x x x x X X i m j n x x x                   (8) Step 3: Calculate the sum of fuzzy beneficial and non-fuzzy beneficial responses values using Eq. (9) and Eq. (10) respectively. 1 ˆ 1, 2,3...., ; 1, 2,3,......, k i ij j S x i m j n       (9)  1 ˆ 1, 2,3...., ; 1, 2, 3,......, k i ij j k S x i m j k k k n           (10) where, k denotes number of beneficial criteria and (n-k) denotes non-beneficial criteria. Step 4: Defuzzified the sum of beneficial and non-beneficial responses. Step 5: Determine the relative significance values (Qi) for each alternative using Eq. (11). Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 47 1 1 1, 2,3,...., 1 m i i i i m i i i S Q S i n S S             (11) Step 6: Determine the performance score of each alternative (Pi) using Eq. (12) and Eq. (13). respectively.  max max 1, 2,3,..., miQ Q i  (12) max 100%i i Q P Q   (13) Based on the performance score (Pi), ranking of alternative was determined. Higher performance score was attributed to best alternative whereas, lowest performance score was attributed to the worst alternative. 2.5. Fuzzy-EDAS method This method was developed by Ghorabaee et al. (2016), it needs a few computational steps to evaluate the process with good efficiency in comparison with other MCDM methods. Furthermore, it evaluates the alternatives based on the average solution for each response (criterion). In the present study, the EDAS method was integrated with the fuzzy numbers. The EDAS method is elaborated in fuzzy linguistic terms, which are further defined by the triangular fuzzy number (Table 3). In this method, the first step was to determine the average solution of each criterion. From the average solution, the positive and negative distance was calculated. The fuzzy weight of criteria was multiplied with positive and negative distance and then this value was normalized. Finally, an appraisal score was calculated for each alternative, and based on this score, a ranking of alternatives was derived. The following steps were used to determine the ranking using Fuzzy-EDAS (Polat and Bayhan 2020 and Stević et al. 2018; Vukasović et al. 2021). Step 1: Construct the average decision matrix (X) using following equation: ij n m X x      (14) 1 1 k p ij p ij x x k    (15) Where, the performance value of alternative  1iA i n  is represented by corresponding to the criteria  1ic j n  which assigned by the pth expert  1 p k  . Step 2: Determine the average solutions and form their corresponding matrix. 1 j m AV av        (16) Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 48 1 1 n j i ij av x n    (17) Where, jav denotes the average solution corresponding to each criterion. Step 3: Calculate the fuzzy positive and fuzzy negative distances from the average for beneficial and non-beneficial criteria. ij n m PDA pda        (18) ij n m NDA nda        (19) ij j j ij ij j j x av if j B k av pda x av if j N k av                                   (20) j ij j ij j ij j av x if j B k av pda av x if j N k av                                   (21) Where fuzzy positive and fuzzy negative distances are denoted by ij pda and ij nda respectively for ith alternative from the average solution in term of jth criterion. Step 4: Calculate the fuzzy weighted sum of positive and negative distances for each alternative using following equations. 1 m i i j ij sp w pda          (22) 1 m i i j ij sn w nda          (23) Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 49 Step 5: Normalize the value of fuzzy spi and fuzzy sni for each alternative as follows: max i i i i sp nsp k sp           (24) 1 max i i i i sn nsn k sn            (25) Step 6: Defuzzified the fuzzy normalized value of ij pda and ij nda for each alternative. Step 7: Determine appraisal score ( ) for each alternative using Eq. (26)   1 2 i i i as nsp nsn  (26) Step 8: Finally, rank the alternatives based on their appraisal score. The highest score corresponds to the best alternative, while the lowest score corresponds to the worst alternatives. To understand the proposed MCDM methods, a combined procedural flow diagram is presented in Figure 1, where each step is connected to the other denoting process involved in the MCDM methods. Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 50 Define a tribological process parameter and responses (criteria) Determine experimental run (alternatives) Construct the decision matrix Construct the normalized decision matrix Construct fuzzy weighted normalized decision matrix Determine fuzzy positive and negative ideal solution Determine fuzzy Euclidean distance from fuzzy positive and negative ideal solution Determine ranking of the experimental run Calculate the sum value of fuzzy beneficial and non-beneficial response Defuzzified the sum value of beneficial and non-beneficial response Calculate average value of responses Determine ranking of the experimental run Select best experimental run Is the best experiment number identical for fuzzy MCDM method? Perform sensitivity analysis by changing the weight Select the most suitable MCDM method No F u z z y T O P S IS F u z z y C O P R A S F u z z y E D A S Calculate closeness coefficient Determine the performance score Construct the matrices of positive and negative distance from average solution Calculate fuzzy normalized weighted sum of positive and negative distance Determine appraisal score Form a group comprises of three members Formulate the assessment Conversion of fuzzy linguistic term to crisp value Determine the fuzzy weight for the responses F u z z y W e ig h ta g e Determine ranking of the experimental run Calculate fuzzy weighted sum of positive and negative distance Yes Determine the relative significance value Defuzzified the Euclidean distance from positive and negative ideal solution Defuzzified the normalized weighted sum of positive and negative distance Figure 1. Combined procedural flow diagram for solving multi-objective problems Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 51 3. Results and discussion The tribological experiments were performed according to the full factorial design. Each test was repeated three times to ensure more accuracy in the measured response value. The average value of the responses is tabulated in Table 6. The performance characteristics of the duplex-TiAlN coating were analysed by obtaining Ra, COF, WML, WD, and HV. The experimental data were analysed to understand the effect of the tribological parameters on the measured responses. Table 6. Experimental design matrix with measured responses Experiment number (Alternative, EN) Tribological process parameters Responses (Criteria, C) L SV SD Ra, C1 COF, C2 WML, C3 WD, C4 HV, C5 EN1 20 0.1 1000 2.4 0.39 40.28 4.12 1227 EN2 15 0.1 2000 5.3 0.63 32.38 3.92 1213 EN3 10 0.3 2000 8.3 0.92 21.08 2.92 1147 EN4 20 0.2 1500 4.9 0.49 59.58 5.02 954 EN5 15 0.3 1000 6.2 0.79 54.68 4.42 1201 EN6 15 0.2 1000 5.5 0.68 30.08 3.82 1137 EN7 20 0.2 1000 4.6 0.47 51.98 4.52 1126 EN8 15 0.2 2000 5.9 0.74 27.08 4.12 1130 EN9 10 0.1 2000 6.7 0.74 16.08 2.42 1798 EN10 10 0.2 1000 6.6 0.75 11.68 1.92 1894 EN11 20 0.3 1500 5.2 0.61 63.68 5.52 798 EN12 10 0.1 1500 6.4 0.7 12.78 2.12 1911 EN13 10 0.3 1500 8.1 0.89 16.08 2.42 1498 EN14 20 0.3 2000 6.1 0.64 74.38 6.72 739 EN15 15 0.1 1000 4.9 0.58 17.98 2.82 1405 EN16 15 0.2 1500 5.7 0.71 41.18 4.22 1171 EN17 10 0.1 1000 6.3 0.75 10.14 1.18 1917 EN18 20 0.1 1500 3.1 0.41 46.68 4.32 1187 EN19 15 0.3 2000 6.9 0.87 49.38 5.42 878 EN20 10 0.3 1000 7.8 0.84 9.58 2.22 1471 EN21 20 0.3 1000 4.3 0.58 57.08 4.82 1031 EN22 10 0.2 2000 7.2 0.81 18.48 2.12 1784 EN23 20 0.1 2000 3.7 0.43 50.58 4.82 992 EN24 20 0.2 2000 5.4 0.52 62.28 5.42 912 EN25 15 0.1 1500 5.1 0.61 22.18 3.42 1415 EN26 15 0.3 1500 6.6 0.84 46.58 5.12 1115 EN27 10 0.2 1500 6.7 0.79 9.67 1.14 1983 3.1. Ranking of the alternatives using fuzzy MCDM methods The selection of the optimum conditions of the tribological process parameters was considered to reveal the applicability of fuzzy-TOPSIS, fuzzy-COPRAS, and fuzzy- EDAS method. Previously, the applicable steps of the techniques were discussed. After obtaining the weightage of the responses in accordance with the decision of the decision-maker, different MCDM techniques were used to rank the alternatives. Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 52 3.1.1. Ranking of the alternatives using fuzzy-TOPSIS method Value of each response was normalized using Eq. 1 to obtain the normalized matrix (Supplementary Table 1) and this value was further multiplied with fuzzy weight of responses (Table 5) to construct the fuzzy normalized weighted matrix (Supplementary Table 2). With the help of positive and negative ideal solutions closeness coefficient value was determined for each alternative (Table 7) and based on this coefficient value ranking of the alternative was obtained. Experiment number EN27 (L = 10 N, SV = 0.2 m/s, and SD = 1500 m) secured first rank with highest closeness coefficient value (0.843) whereas experiment number EN14 (L = 20 N, SV = 0.3 m/s, and SD = 2000 m) secured last rank with lowest closeness coefficient value (0.217) among all 27 number of experiments. Table 7. Coefficient of closeness and ranking of the alternatives Experiment number Positive ideal solution ( ) Negative ideal solution ( ) Closeness coefficient ( ) Rank EN1 0.178 0.300 0.628 11 EN2 0.215 0.310 0.591 13 EN3 0.237 0.285 0.546 16 EN4 0.291 0.224 0.435 22 EN5 0.295 0.229 0.438 21 EN6 0.220 0.301 0.578 14 EN7 0.248 0.273 0.524 17 EN8 0.232 0.289 0.555 15 EN9 0.137 0.415 0.752 5 EN10 0.111 0.446 0.801 4 EN11 0.335 0.176 0.344 25 EN12 0.109 0.449 0.804 3 EN13 0.187 0.350 0.651 10 EN14 0.399 0.111 0.217 27 EN15 0.140 0.393 0.737 6 EN16 0.253 0.270 0.516 19 EN17 0.088 0.473 0.843 2 EN18 0.207 0.317 0.605 12 EN19 0.344 0.168 0.328 26 EN20 0.164 0.372 0.694 8 EN21 0.278 0.239 0.462 20 EN22 0.148 0.403 0.731 7 EN23 0.247 0.269 0.521 18 EN24 0.316 0.197 0.385 24 EN25 0.166 0.368 0.689 9 EN26 0.310 0.211 0.405 23 EN27 0.088 0.473 0.843 1* *Most preferable setting of tribological process parameters 3.1.2. Ranking of the alternatives using fuzzy-COPRAS method In this method normalization of response value was similar to the fuzzy TOPSIS method. Hence, the same normalized decision matrix (Supplementary Table 1) and fuzzy normalized weighted matrix (Supplementary Table 2) were used for the fuzzy COPRAS method. The next step was to calculate the relative significance value for Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 53 each alternative using Eq. 11 and the calculated value tabulated in Table 8. The relative significance value performance score was obtained using Eq. 13 and with the help of this value ranking of alternatives was determined (Table 10). The highest performance score (100) was determined for experiment number EN27 (L = 10 N, SV = 0.2 m/s, and SD = 1500 m) and lowest performance score (41.359) was determined for the experiment number EN14 (L = 20 N, SV = 0.3 m/s, and SD = 2000 m). Table 8. Performance score and ranking of the alternatives Experiment number Relative significance value (Qi) Performance score (Ui) Rank EN1 0.089 72.557 11 EN2 0.081 66.523 13 EN3 0.077 63.328 16 EN4 0.065 53.273 23 EN5 0.069 56.402 20 EN6 0.080 65.073 14 EN7 0.074 60.319 18 EN8 0.078 63.344 15 EN9 0.105 86.033 5 EN10 0.114 92.962 4 EN11 0.058 47.014 26 EN12 0.114 93.270 3 EN13 0.091 74.459 10 EN14 0.051 41.359 27 EN15 0.102 83.410 7 EN16 0.074 60.617 17 EN17 0.122 99.546 2 EN18 0.082 66.837 12 EN19 0.058 47.734 25 EN20 0.097 78.944 8 EN21 0.068 55.616 21 EN22 0.102 83.656 6 EN23 0.072 58.895 19 EN24 0.061 50.247 24 EN25 0.094 77.123 9 EN26 0.066 53.966 22 EN27 0.122 100.000 1* *Most preferable setting of tribological process parameters 3.1.3. Ranking of the alternatives using the fuzzy-EDAS method In this method, initially, the average value of each response was calculated (Table 6). In the next step, positive (PDAij) and negative (NDAij) distances from the average solution were calculated (Supplementary Table 3 and Supplementary Table 4 respectively). Further, the fuzzy weight of the criterion was multiple with the value of positive and negative distances respectively, to obtain the fuzzy weighted sum of positive ( ) and negative distance ( ) from the average solution (Supplementary Table 5 and Supplementary Table 6 respectively). The next step is to calculate the normalized weighted sum of positive ( ) and negative ( ) distance from the Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 54 average solution (Table 9). Finally, the appraisal score was calculated using Eq. 21 for each alternative, and based on the appraisal score, a ranking of alternatives was derived (Table 9). Experiment number EN27 (L = 10 N, SV = 0.2 m/s, and SD = 1500 m) was obtained first rank with the highest appraisal value (0.549) whereas experiment number EN14 (L = 20 N, SV = 0.3 m/s, and SD = 2000 m) was obtained last rank with the lowest appraisal value (0.070) among all 27 number of experiments. Table 9. Normalized weighted sum of positive and negative distance, appraisal score and ranking of the alternatives Experiment Number Normalized weighted sum of Normalized weighted sum of Appraisal value ( ) Rank EN1 0.266 0.126 0.196 21 EN2 0.932 0.016 0.474 3 EN3 0.212 0.319 0.265 16 EN4 0.136 0.579 0.358 10 EN5 0.000 0.390 0.195 22 EN6 0.065 0.129 0.097 26 EN7 0.157 0.344 0.250 17 EN8 0.090 0.190 0.140 24 EN9 0.692 0.063 0.377 9 EN10 0.849 0.066 0.458 4 EN11 0.053 0.766 0.410 6 EN12 0.837 0.032 0.435 5 EN13 0.456 0.184 0.320 14 EN14 0.070 0.073 0.072 27 EN15 0.416 0.000 0.208 20 EN16 0.002 0.205 0.104 25 EN17 0.019 1.000 0.509 2 EN18 0.235 0.233 0.234 18 EN19 0.000 0.699 0.349 11 EN20 0.520 0.148 0.334 12 EN21 0.096 0.484 0.290 15 EN22 0.675 0.116 0.395 7 EN23 0.206 0.447 0.326 13 EN24 0.104 0.662 0.383 8 EN25 0.314 0.000 0.157 23 EN26 0.000 0.452 0.226 19 EN27 1.000 0.091 0.546 1* *Most preferable setting of tribological process parameters Thus, according to all the proposed MCDM methods, experiment number EN27 (L = 10 N, SV = 0.2 m/s, and SD = 1500 m) was the most suitable parametric setting for the tribological test of duplex TiAlN coating. With this parametric setting, the desirable value of wear responses was obtained whereas, the undesirable value was obtained with the parametric setting of L = 20 N, SV = 0.3 m/s, and SD = 2000 m (experiment number EN14) and this parametric setting was the worst parametric seating suggested by all the proposed MCDM methods. Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 55 3.2. Sensitivity analysis Sensitivity analysis was conducted to understand the stability of the rankings under different sets of response weights (Table 10). Based on these weights, a ranking of alternatives was obtained using all the proposed MCDM methods (Fig. 2). There are four scenarios of a group of three decision makers (Table 10 (a-d)), and based on their opinion criteria weights were calculated (Table 10(a’-d’)). Table 10. Group of decision makers and fuzzy criteria weights (a) Opinion of the decision maker for scenario 1 Responses Scenario 1 DM1 DM2 DM3 Ra M M LR COF L LR L WML L M M WD M M LR HV HT HT H (a’) Fuzzy criteria weight of scenario 1 Responses Fuzzy criteria weight Ra (0.200, 0.367, 0.567) COF (0.067, 0.233, 0.433) WML (0.233, 0.433, 0.633) WD (0.200, 0.367, 0.567) HV (0.767, 0.900, 0.967) (b) Opinion of the decision maker for scenario 2 Responses Scenario 2 DM1 DM2 DM3 Ra LR L M COF M M L WML LT L M WD L L LR HV H HR HR (b’) Fuzzy criteria weight of scenario 2 Responses Fuzzy criteria weight Ra (0.033, 0.167, 0.367) COF (0.233, 0.433, 0.633) WML (0.133, 0.267, 0.433) WD (0.067, 0.233, 0.433) HV (0.567, 0.767, 0.933) (c) Opinion of the decision maker for scenario 3 Responses Scenario 3 DM1 DM2 DM3 Ra L LT L COF LR M L WML M LR M WD M L M HV HT H HR (c’) Fuzzy criteria weight of scenario 3 Responses Fuzzy criteria weight Ra (0.067, 0.200, 0.367) COF (0.133, 0.300, 0.500) WML (0.200, 0.367, 0.567) WD (0.233, 0.433, 0.633) HV (0.700, 0.867, 0.967) (d) Opinion of the decision maker for scenario 4 Responses Scenario 4 DM1 DM2 DM3 Ra LT L LR COF M LR M WML LT M M WD LR L L HV HR HT H (d’) Fuzzy criteria weight of scenario 4 Responses Fuzzy criteria weight Ra (0.033, 0.133, 0.300) COF (0.200, 0.367, 0.567) WML (0.200, 0.333, 0.500) WD (0.067, 0.233, 0.433) HV (0.700, 0.867, 0.967) The finding of sensitivity analysis for the F-TOPSIS method is represented in Figure 2(a). There are no changes observed in the ranking of experiment numbers EN6, EN9, EN10, EN11, EN12, EN14, EN19, and EN21 when the value of fuzzy weight was changed. But there were few changes observed in the ranking of experiment numbers EN1, EN2, EN13, EN15, EN17, EN20, EN22, EN24, EN25, EN26, and EN27. The ranking of the remaining experiment numbers was changed frequently and it was not stable at all. The sensitivity results of the F-COPRAS method (Figure 2(b)) showed that there was no effect of criteria weight change observed on the ranking of experiment numbers EN4, EN6, EN9, EN10, EN12, EN14, EN24, and EN26. Unlike the remaining experiment, numbers could not hold their actual ranking and there were changes observed with Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 56 criteria weight change. The F-EDAS method (Figure 2(c)) shows more consistent in their ranking of the experiment numbers against criteria weight change and the experiments are EN2, EN3, EN6, EN8, EN10, EN11, EN12, EN14, EN16, EN17, EN21, EN22, EN25, and EN27. But there were few experiments (EN5, EN7, EN9, and EN15) whose ranking slightly changed with criteria weight change. The rest of the experiment number changes its ranking frequently against criteria weight change. Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 57 Figure 2. Result of the sensitivity analysis for different ranking methods viz; (a) F- TOPSIS, (b) F-COPRAS, and (c) F-EDAS. From sensitivity analysis, it was noted that the F-EDAS method was less sensitive to criteria weight change compared to F-TOPSIS and F-COPRAS methods. Moreover was, it noticed that ranking of the best alternative (experiment number EN27) was changed with criteria weight change in F-TOPSIS and F-COPRAS methods. Thus, it can be said that the stability of the ranking given by the F-EDAS was the highest compared to F-TOPSIS and F-COPRAS methods. Thus, F-EDAS was the more robust method to solve this kind of multi-attributed problem. These obtained results were further validated by a comparative study, where Spearman’s rank correlation coefficient was calculated for each scenario of MCDM methods. 3.2.1. Comparison of MCDM methods Spearman’s rank correlation coefficient for F-TOPSIS methods is shown in Table 11(a). The correlation coefficient value of each scenario shows that there is a lack of inconsistency in the ranking of the F-TOPSIS method according to different fuzzy criteria weights. From Table 11(a), it can be seen that the correlation coefficient value for scenario-(1-2), scenario-(1-3), scenario-(1-4), scenario-(2-3), scenario-(2-4) and scenario-(3-4) are 0.989, 0.996, 0.998, 0.985, 0.989 and 0.996 respectively. It can be said that coefficient values are varying from 0.985 to 0.996. Similarly, for F-COPRAS method (Table 11(b)) the correlation coefficient is obtained for scenario-(1-2), scenario-(1-3), scenario-(1-4), scenario-(2-3), scenario-(2-4) and scenario-(3-4) are 0.992, 0.998, 0.997, 0.989, 0.993 and 1.000 respectively. Here the coefficient values are varying from 0.989 to 1.000 and this range is higher than the F-TOPSIS range of spearman coefficient value. For the F-EDAS method (Table 11(c)), the value of correlation coefficient value for all the scenarios is higher than 0.990. In other words, it can be said that the Spearman correlation coefficient for the scenario the of F-EDAS method is higher than the F-TOPSIS and F-COPRAS methods. Based on the overall Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 58 results of sensitivity analysis and correlation coefficient the F-EDAS method is the most robust method to solve the multi-attribute decision-making problem. Table 11. Spearman’s rank correlation coefficient (a) Coefficient values for F-TOPSIS Scenarios S2 S3 S4 S1 0.989 0.996 0.998 S2 - 0.985 0.989 S3 - - 0.996 (b) Coefficient values for F-COPRAS Scenarios S2 S3 S4 S1 0.992 0.998 0.997 S2 - 0.989 0.993 S3 - - 1.000 (c) Coefficient values for F-EDAS Scenarios S2 S3 S4 S1 0.990 0.995 0.994 S2 - 0.993 0.999 S3 - - 0.996 3.3. Other wear parameter optimization problems solved by the proposed methodology In this section, the proposed methodology solves two wear optimization problems, which have already been solved and published elsewhere. The first problem is the optimization of wear parameters for composite coating, while the second problem is to optimize the wear parameters for heat-insulated ceramic coating. 3.3.1. Optimization of wear parameter for composite coating This optimization problem was solved using the gray relation analysis (GRA) method (Raghavendra et al. 2021). Table 12 presents the alternatives for wear parameters and their criteria, based on which alternatives were ranked. Each criterion presented in Table 12 was identified as non-beneficial criteria, and the criteria weight (Table 14) was derived using the opinion of decision-makers as mentioned in Table 13. Table 12. List of alternatives and their criteria (Initial decision matrix) method (Raghavendra et al. 2021) Alternative (Specific wear rate, Ws) C1 (Pin Temperature, PT) C2 (Friction Coefficient, CoF) C3 EN1 0.3330 91.990 0.123 EN2 0.3470 92.140 0.038 EN3 0.8750 98.340 0.144 EN4 0.2520 90.760 0.089 EN5 1.1900 94.840 0.153 EN6 0.4000 73.960 0.089 EN7 1.5550 105.990 0.116 EN8 0.4770 78.660 0.011 Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 59 EN9 0.4750 88.760 0.065 EN10 0.8530 87.810 0.627 EN11 0.2920 86.910 0.046 EN12 0.6411 80.120 0.103 EN13 0.7020 93.690 0.112 EN14 1.2400 90.160 0.035 EN15 1.1710 111.780 0.119 EN16 0.7840 91.920 0.459 EN17 2.1320 110.380 0.104 EN18 1.4450 95.910 0.099 EN19 1.5500 88.480 0.119 EN20 1.3700 117.190 0.016 Table 13. Opinion of the decision maker for problem 1 Table 14. Fuzzy criteria weight for problem 1 Response DM1 DM2 DM3 Ws LR LR L PT L M M CoF L L M Responses Fuzzy criteria weight Ws (0.033, 0.100, 0.233) PT (0.233, 0.433, 0.633) CoF (0.167, 0.367, 0.567) One by one, each MCDM method (F-TOPSIS, F-COPRAS, and F-EDAS) was employed to derive the ranking of alternatives (Table 15). From the obtained results (Table 15), it was noticed that the ranking of the best alternative (EN6) remains similar to it obtained in the past study method (Raghavendra et al. 2021) [36]. Further, the correlation between rankings was studied by calculating Spearman’s rank correlation coefficient. It found these rankings have a good correlation as their coefficient value lies above 0.767, in the acceptable range. Table 15. Coefficient of closeness, performance score, appraisal score of alternatives, and its ranking Alternative F-TOPSIS F-COPRAS F-EDAS Rank method (Raghavendra et al. 2021) Closeness coefficient (CoCi) Rank Performance score (Ui) Rank Appraisal value ( ) Rank EN1 0.643 10 8.878 10 0.623 10 8 EN2 0.640 11 8.854 11 0.871 3 4 EN3 0.499 16 7.762 16 0.485 17 12 EN4 0.670 9 9.123 9 0.740 8 5 EN5 0.579 14 8.338 14 0.463 18 15 EN6 1.000 1 13.734 1 1.000 1 1 EN7 0.313 17 6.676 17 0.499 14 18 EN8 0.915 2 12.147 2 0.804 4 2 EN9 0.713 7 9.539 7 0.789 6 7 EN10 0.718 6 9.553 6 0.036 20 19 EN11 0.752 4 9.952 4 0.883 2 3 EN12 0.886 3 11.698 3 0.695 9 6 EN13 0.605 13 8.556 13 0.593 11 10 Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 60 EN14 0.683 8 9.232 8 0.792 5 9 EN15 0.162 19 6.009 19 0.497 16 16 EN16 0.637 12 8.807 12 0.196 19 17 EN17 0.199 18 6.147 18 0.498 15 20 EN18 0.555 15 8.153 15 0.571 12 14 EN19 0.718 5 9.569 5 0.534 13 13 EN20 0.018 20 5.468 20 0.786 7 11 3.3.1. Optimization of wear parameter for heat-insulated ceramic coating The WASPAS method was used to solve this optimization problem by Sahoo et al. in the past study (Sahoo et al. 2021). The evaluating criteria and alternative wear parameters are listed in Table 16. There are two criteria, namely weight loss, and friction coefficient, which are identified as non-beneficial criteria. The weights (Table 18) of these criteria were obtained based on the decision of the expert panel (Table 17). Table 16. List of criteria and alternatives (Sahoo et al. 2021) Alternative (Weight loss (Wl), mg) C1 (Friction coefficient (CoF), µ) C2 EN1 0.19 0.077 EN2 0.60 0.084 EN3 4.70 0.026 EN4 5.10 0.040 EN5 3.50 0.079 EN6 9.20 0.064 EN7 14.20 0.080 EN8 9.30 0.080 EN9 9.90 0.067 EN10 20.20 0.090 EN11 11.20 0.087 EN12 17.00 0.057 EN13 19.20 0.078 EN14 13.50 0.070 EN15 9.20 0.170 EN16 9.20 0.063 Table 17. Opinion of the decision maker for problem 2 Table 18. Fuzzy criteria weight for problem 2 Response DM1 DM2 DM3 Wl LT LR L CoF L L M Response Fuzzy criteria weight Wl (0.033, 0.133, 0.300) CoF (0.167, 0.367, 0.567) The obtained criteria weights were integrated with MCDM methods as described in sections 2.4, 2.5, and 2.6 to derive the ranking of alternatives. The derived rankings are listed in Table 19, and a minor deviation can be observed in the ranking of alternatives. But this deviation does not affect the overall results. The ranking of the best alternative remains the same for each MCDM method, which exactly matches the past result (Sahoo et al. 2021). Although, these rankings have an excellent correlation among them as Spearman’s rank correlation coefficient values are equal and more than 0.85. Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 61 Table 19. Final preference values of alternatives and its ranking Alternative F-TOPSIS F-COPRAS F-EDAS Rank (Sahoo et al. 2021) Closeness coefficient (CoCi) Rank Performance score (Ui) Rank Appraisal value ( ) Rank EN1 0.988 1 246.310 1 0.731 1 1 EN2 0.985 2 199.395 2 0.683 4 3 EN3 0.948 4 75.490 4 1.000 3 2 EN4 0.938 5 61.938 5 0.885 2 4 EN5 0.962 3 88.167 3 0.638 5 5 EN6 0.797 7 19.312 7 0.602 7 7 EN7 0.520 13 8.259 13 0.400 13 12 EN8 0.789 8 18.375 8 0.489 10 11 EN9 0.765 9 16.726 9 0.563 8 9 EN10 0.049 16 4.137 16 0.242 15 15 EN11 0.696 11 12.859 11 0.415 12 13 EN12 0.321 14 5.900 14 0.515 9 8 EN13 0.131 15 4.597 15 0.323 14 14 EN14 0.567 12 9.189 12 0.478 11 10 EN15 0.755 10 14.560 10 0.014 16 16 EN16 0.797 6 19.344 6 0.610 6 6 3. Conclusions This study focuses on the optimization of the wear parameters for duplex-TiAlN coated MDC-K tool steel. Three different fuzzy MCDM methods were proposed to solve this optimization problem. A total of five wear responses, namely surface roughness, friction coefficient, wear mass loss, wear depth, and hardness, were identified as the criteria to evaluate the alternatives, which consist of different combinations of wear parameters such as applied load, sliding velocity, and sliding distance. The criteria weight was determined using triangular fuzzy numbers that are integrated into fuzzy MCDM methods to solve the problem. The following conclusions are drawn from the results:  The obtained results showed that alternative EN27 (L = 10 N, SV = 0.2 m/s, and SD = 1500 m) to be the best alternative whereas EN14 (L = 20 N, SV = 0.3 m/s, and SD = 2000 m) as the worst alternative parameters for duplex-TiAlN coated MDC-K tool steel.  These results were tested and validated by performing a comprehensive sensitivity analysis. Additionally, two sets of wear parameters from the literature were also solved using the proposed methodology to substantiate its capability. The result obtained from the proposed methodology was found similar to the result obtained in the literature.  The validation result proved that the F-EDAS method is more robust and less sensitive to the criteria weight change. Hence, it can be further used to solve Kumar et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 40-67 62 this type of multi-decision-making problem with some modifications (either addition or removal of new alternatives or criteria). The proposed methodology is designed to solve the multi-criteria such as the selection of optimal parameters for duplex-TiAlN coating, where three wear parameters (load, sliding velocity, and sliding distance) and five wear responses (Ra, COF, WML, WD, and Hv) were considered to solve the above problem. Further, It was noticed that if some new evaluating criteria were introduced, the calculation process becomes lengthy which grows exponentially for high-dimensional decision-making problems. 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Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.matdes.2014.10.051 https://doi.org/10.1016/j.triboint.2020.106310 https://doi.org/10.1007/s13369-017-2673-1 https://doi.org/10.1134/S0031918X19090035 https://doi.org/10.5755/j01.ee.29.3.16818 https://doi.org/10.1016/j.eswa.2010.04.066 https://doi.org/10.3846/tede.2021.14427 https://doi.org/10.1016/j.eswa.2020.114238 https://doi.org/10.1016/j.eswa.2020.114542 Optimization of Wear Parameters for Duplex-TiAlN Coated MDC-K Tool Steel Using Fuzzy MCDM Techniques 67 Appendix Nomenclature L Load (N) FT Fuzzy-TOPSIS SV Sliding velocity (m/s) FC Fuzzy-COPRAS SD Sliding distance (m) FE Fuzzy-EDAS Ra Average surface roughness (µm) TOPSIS Technique for order of preference by similarity to ideal solution CoF Coefficient of friction COPRAS Complex proportional Assessment WML Wear mass loss (mg) EDAS Evaluation based on distance from the average solution WD Wear depth (µm) S1 Scenario 1 HV Vickers hardness S2 Scenario 2 EN Experiment number S3 Scenario 3 MCDM Multi-criteria decision making S4 Scenario 4 Optimization of wear parameters for duplex-TiAlN coated mdc-k tool steel using fuzzy mcdm techniques Sunil Kumar 1, 2, Saikat Ranjan Maity 1*, Lokeswar Patnaik 3 1. Introduction 2. Methodology 2.1. Preparation of the specimen 2.2. Selection of process parameters 2.3. Fuzzy-TOPSIS method 2.4. Fuzzy-COPRAS method 2.5. Fuzzy-EDAS method 3. Results and discussion 3.1. Ranking of the alternatives using fuzzy MCDM methods 3.1.1. Ranking of the alternatives using fuzzy-TOPSIS method 3.1.2. Ranking of the alternatives using fuzzy-COPRAS method 3.1.3. Ranking of the alternatives using the fuzzy-EDAS method 3.2. Sensitivity analysis 3.2.1. Comparison of MCDM methods 3.3. Other wear parameter optimization problems solved by the proposed methodology 3.3.1. Optimization of wear parameter for composite coating 3.3.1. Optimization of wear parameter for heat-insulated ceramic coating 3. Conclusions References