V.Resmi Prasad ,Dr. R. Rajesh and Dr. D. Thirumalaikumarasamy
Keywords: Alternatives, Fuzzy analytic hierarchy process (AHP), MCDM, Technique for order performance by similarity to ideal solutions (TOPSIS).
Abstract:
Magnesium alloys are inherently negative electrochemical potential and are very reactive compared to other Engineering metals. They are prone to galvanic corrosion and micro cracks. Various Coating Materials or Alternatives and the required Criteria and Sub-criteria, for the selection of Alternatives, for AZ31B magnesium alloy substrate are identified for corrosion resistance, by means of Literature Review. Criteria weight and the rank of the alternatives are usually vague and hence uncertainty prevails. The best Alternative from several potential “Candidatesâ€, subject to several Criteria and Sub Criteria, need to get decided. In such cases, Multi criteria decision making (MCDM) techniques help in determining the MOST suitable coating material. This paper concentrates on the selection of coating material for the Magnesium alloy substrate. The problem is subjective, uncertain and equivocates in nature. Hence in this study, Fuzzy analytic hierarchy process (AHP) is applied to obtain the weights of Criteria and Technique for order performance by similarity to ideal solutions (
TOPSIS) is utilised for ranking the Alternatives.
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Selection of coating material for magnesium alloy using Fuzzy AHP-TOPSIS Abstract Magnesium alloys are inherently negative electrochemical potential and are very reactive compared to other Engineering metals. They are prone to galvanic corrosion and micro cracks. Various Coating Materials or Alternatives and the required Criteria and Sub-criteria, for the selection of Alternatives, for AZ31B magnesium alloy substrate are identified for corrosion resistance, by means of Literature Review. Criteria weight and the rank of the alternatives are usually vague and hence uncertainty prevails. The best Alternative from several potential “Candidates”, subject to several Criteria and Sub Criteria, need to get decided. In such cases, Multi criteria decision making (MCDM) techniques help in determining the MOST suitable coating material. This paper concentrates on the selection of coating material for the Magnesium alloy substrate. The problem is subjective, uncertain and equivocates in nature. Hence in this study, Fuzzy analytic hierarchy process (AHP) is applied to obtain the weights of Criteria and Technique for order performance by similarity to ideal solutions (TOPSIS) is utilised for ranking the Alternatives. Key words: Alternatives, Fuzzy analytic hierarchy process (AHP), MCDM, Technique for order performance by similarity to ideal solutions (TOPSIS). Introduction In solving an MCDM problem, the decision environment affects the decision outcome in which the criteria knowledge is known or uncertain. The decision -making environment can be classified into three types: certainty, uncertainty, and risk. a. Certainty:- In this environment, a Decision Maker (DM) is fully aware of the criteria and it can be quantified by means of numbers. b. Uncertainty:- Uncertain environment means, the DM has only less knowledge about the criteria at the time of assignment. c. Risk:- From the historical data, the risk factors can be identified and the necessary steps can be taken. Zimmerman (2001) proposed that fuzzy sets can be used to model uncertainty. 1.1 Fuzzy Logic Unlike usual “True or False" procedure, “Degrees of Truth" is being adopted by Fuzzy Logic for finding or solving data that are uncertain. Fuzzy Logic is like crisp logic in many ways. While Crisp sets take the values 0 or 1, Fuzzy sets accept input values that ranges between 0 and 1. Hence the membership function becomes μc:X→[0,1]. 1.2 Fuzzy Composition If we represent P as a fuzzy relation from X to Y and Q as from Y to Z respectively, the configuration of P and Q is a Fuzzy relation that is described as µPoQ (xi, zk) = max (min (µP (xi, yj), µQ (yj, z and k) ) ). The triangular function represented by x(a, b, c) is having three parameters ‘a’ (min), ‘b’ (mid) and ‘c’ (max) and trapezoidal function represented by x(a, b, c, d) has 4 parameters and ‘ a ’ (min), ‘ b ’, ‘ c ’ (essential) and ‘ d ‘ (max) that determine the triangular or trapezoidal shape. Fig 1. represents the triangle and trapezoidal functions. The Triangular and Trapezoidal Functions are described as shown in Eq. (1.1) & Eq. (1.2) 0, x ≤ a (x - a) / (b - a), x ϵ (a, b) Eq. (1.1) (c - x) / (c - b), x ϵ (b, c) 0, x ≥ c 0, x ≤ a (x - a) / (b - a), x ϵ (a, b) Eq. (1.2) 1, x ϵ (b, c) (d - x ) / (d - c), x ϵ (c, d) 1.3 Linguistic variables and Linguistic values Linguistic Variables are those values that can be conveyed in the way of spoken language. Fuzzy Sets always represent imprecise terms. Let L, M and H represent three fuzzy sets that have the Member ship Functions, µZ, µM, µH respectively. They are referred as Less, Medium and High. (Dombi 1990). Fuzzy logic is shown in Fig 2. 1.4 α - Cuts for Fuzzy Sets Fuzzy sets can be decomposed in to classical sets of weighted combination by applying the principle of Identity of Resolution. Alpha cuts connects Fuzzy sets and Crisp sets .α- cut αS ={x/S(x)≥ α} and is inclusive of all the constituents of the Universal Set X whose membership grades in (S) is either ≥ α. Method Since coating material selection problem belongs to MCDM problem, an integrated Fuzzy AHPTOPSIS is being employed for the solution procedure. TOPSIS can be used as an integrated tool with any other research techniques. It works best with Fuzzy AHP as Criteria Weights are calculated by AHP technique and final ranks of alternatives are obtained by applying TOPSIS .The steps involved are shown in Fig. 3. The assumptions of the model development are given in section 2.1.The fuzzy judgment matrix is constructed in section 2.2 and the fuzzy performance matrix is obtained in section 2.3. Execution of defuzzification in section 2.4, is to develop the crisp performance by the concepts of α-cut method and βrisk index. TOPSIS method is applied to obtain the priority ranking order for each coating material alternatives section 2.5. . 2.1 Assumptions This research work considers the scenario for selection of the suitable coating material from enlisted alternatives. The decision makers have to select the best material from several candidate alternatives that work under the same environmental conditions. In the proposed approach, the Evaluation Matrix and the Weight vectors are defined using the Triangular fuzzy Numbers (TFN). This is useful in final Pair wise comparison of criteria using the sub criteria evaluation score generated primarily. Table 2.1 shows the TFN for the Judgment Matrix (Yeh and Deng 1997). Five scales are detailed below .The membership function of the triangular fuzzy number �𝑛𝑛 is defined as µS (n) = 1 If n belongs to S 0 if n does not belong to S While executing 1� , , 5� , 7� , the Fuzzy judgment Eq. (2.1) matrix process, these Triangular fuzzy Numbers represent the following linguistic terms as tabulated in Table 2.2. 2.2 Formation of fuzzy judgment matrix The first step after assumptions have been made is to determine Fuzzy Judgment Matrix. The steps included are (a) MCDM problem formulation followed by hierarchical structure construction of the problem (b) Alternative performance determination. 2.2.1 Construction of Work Break Down Structure After defining all potential alternatives, required criteria and sub criteria of the problem, a hierarchical structure has to be constructed .Bottom- Up evaluation criteria has been employed and firstly each potential candidate is measured by means of sub-criteria. Sub-score is assigned to each criterion. The following sections explain the calculation procedures. 2.2.2 Evaluation of Tangible Sub-criteria The Fuzzy ratio scales for each tangible sub-criterion is created as shown in Table 2.3. The following rules are considered: For a positive sub criterion, a relative large fuzzy number will be assigned to the relative high interval value. If it is a negative sub-criterion, a relative small fuzzy number will be assigned to the relative high Interim Value. A fuzzy ratio scale represents a sub score (𝐺𝐺� ijk). This means, the Alternative’s (Ai) sub score with respect to each Sub-criterion (𝑐𝑐𝑗𝑗𝑗𝑗 ). 2.2.3 Evaluation of Intangible Sub-criteria Intangible sub-criteria are difficult to calculate objectively. In order to get a persistent and precise outcome from the decision maker’s subjective judgments, a group decision method has been proposed so that each decision maker (Ds) can grade individual alternative (Ai) on the same sub-criterion (𝑐𝑐𝑗𝑗𝑗𝑗 ). By following this procedure, an alternative can acquire several grades �𝐺𝐺 (ijks) different decision makers shown in Table 2.4. The above grades are composed in to synthetic sub-score (𝐺𝐺� ijks) by equations 2.2- 2.6 𝐺𝐺� ijks = (Lijks Mijks Uijks) Eq. (2.2) Lijk = min (Lijks ), s = 1,2,..., Eq. (2.3) Mijk = ∑ M𝑖𝑖𝑖𝑖𝑖𝑖s=1,2,……..,t Eq. (2.4) 𝑡𝑡 𝑠𝑠=1 Uijk =max (Uijks), s=1,2,.....,t Eq .(2.5) �𝐺𝐺 (ijk) =(Lijk Mijk Uijk) Eq. (2.6) 2.2.4. Attaining the Fuzzy Evaluation Matrix The sub scores (𝐺𝐺� ijk) of every potential candidates (Ai) related to sub-criteria (𝑐𝑐𝑗𝑗𝑗𝑗 ) can be seen in � ijk of each alternative related to each criterion, equation 2.7 is used. Table 2.5. To obtain the scores 𝐺𝐺 𝐺𝐺� 𝑖𝑖𝑖𝑖 = ∑𝑞𝑞𝑘𝑘−1 𝐺𝐺� 𝑖𝑖𝑖𝑖𝑖𝑖 , i = 1, 2 , .... , n j = 1, 2 ,...... , m k = 1, 2 ,...... , q Eq. (2.7) From Equation 2.7, a decision matrix like equation 2.8 can be formed. Eq (2.8) Weight vector to be calculated in section 2.3.2 by means of Normalization method. All the Criteria (Cj ) in equation 2.8 are get normalized through equation 2.9. A Fuzzy Judgment /Evaluation Matrix (A) is obtained in equation 2.10 following the normalization Eq. (2.9) Eq. (2.10) where 𝑎𝑎�𝑖𝑖𝑖𝑖 represents the Evaluation score of Alternatives (Ai) related to criteria (Cj ). 2.3 Obtaining fuzzy performance matrix The collective accomplishment of each coating material with respect to each Criterion is formulated in the form of Fuzzy performance matrix. It is attained by the multiplication of the Fuzzy judgment matrix with its respective Fuzzy weight vector. Hence there arises the need for the determination of Fuzzy Weight Vector. 2.3.1 Obtaining the fuzzy weight vector In order to represent the relative importance among each criterion, weight vector is to be defined. A pair wise comparison is required to obtain the Weight Vector. Satty’s scale 1-9 was used in Table 2.5 by each Decision maker (Ds) to carry out Pair wise Comparison for all criteria as Equation 2.11i and Equation 2.11 ii The fundamental scale of absolute numbers Eq. (2.11i) bjes = bjes-1 bjes = 1 if j≠ e if j=e Eq. (2.11ii) where score (𝑏𝑏𝑗𝑗𝑗𝑗𝑗𝑗 ) denotes the measurement of relative importance between each criterion by the Decision Maker Ds. Thus a Comprehensive Pair wise Comparison matrix (D) is obtained by combining the grades (𝑏𝑏𝑗𝑗𝑗𝑗𝑗𝑗 ) of all Decision makers. The equations 2.12 – 2.15 represent the combination: Eq. (2.12) Lje= min (bjes ), s= 1,2,… t j=1,2,… m e=1,2,… m Eq( 2.13) Eq. (2.14) Eq. (2.15) where a comprehensive score (𝑏𝑏𝑗𝑗𝑗𝑗 ) denotes the comparative importance among each criterion which is represented in Triangular Fuzzy Numbers. Eq. (2.16) Each criterion has got its own importance. The following equation is used to calculate relative weight corresponds to each criterion. Eq. (2.17) The weights of each criterion are get solved sequentially by equation 2.17 and thereby obtains a Collective Fuzzy Weight Vector (W) as in equation 2.18 � 1, W � 2………..,W � m) W = (W 2.3.2 Synthesization of Fuzzy Weight Vector Eq. (2.18) The overall evaluation scores of each alternative (Ai) related to each criterion (𝐶𝐶𝑗𝑗 ) are found out in Fuzzy Judgment Matrix. This has been formulated without considering the relative weight between each � ) with criterion. The final Fuzzy Judgment Matrix (H) is obtained by multiplying each criterion weight (W ȷ the corresponding criterion (𝐶𝐶𝑗𝑗 ) .It is shown in equation 2.19. Eq. (2.19) where ℎ�𝑖𝑖𝑖𝑖 denotes the Fuzzy performance score of alternative (Ai) with respect to criterion (Cj) using Fuzzy Triangular Numbers (𝐿𝐿𝑖𝑖𝑖𝑖 ,𝑈𝑈𝑖𝑖𝑖𝑖 , 𝑀𝑀𝑖𝑖𝑖𝑖 ). 2.4 Formulation of Crisp performance matrix Crisp performance matrix is obtained by the execution of Defuzzification. This is done by the determination of interval performance cut, α, by considering the risk factors also. 2.4.1 Calculation of the Interval performance matrix α-cut method is applied to obtain the Interval performance matrix (Hα). Each Fuzzy Performance 𝛼𝛼 𝛼𝛼 Score (ℎ�𝑖𝑖𝑖𝑖) is agglomerated with α-cut to constitute an interval �ℎ𝑖𝑖𝑖𝑖𝑖𝑖 , ℎ𝑖𝑖𝑖𝑖𝑖𝑖 � respectively. The values 𝛼𝛼 𝛼𝛼 , ℎ𝑖𝑖𝑖𝑖𝑖𝑖 � can be found out by the equations 2.20 & 2.21 respectively. of �ℎ𝑖𝑖𝑖𝑖𝑖𝑖 L M L 𝛼𝛼 ℎ𝑖𝑖𝑖𝑖𝑖𝑖 = ij + α ( ij - ij) U M 𝛼𝛼 ℎ𝑖𝑖𝑖𝑖𝑖𝑖 =Uij- α ( ij - ij) Eq. (2.20) Eq. (2.21) 𝛼𝛼 𝛼𝛼 where [ℎ𝑖𝑖𝑖𝑖𝑖𝑖 ,ℎ𝑖𝑖𝑖𝑖𝑖𝑖 ] denote the respective left and right points of the Triangle range. The Overall interval performance matrix (H α ) can be obtained from the eqn 2.22, shown below. The α Value represents the Degree of Confidence of the Experts. Eq. (2.22) Larger the α value, stronger the Degree of Confidence of the Decision Maker. Continuous increase 𝛼𝛼 𝛼𝛼 in α value shows that there will be a narrow progress in the interval between ℎ𝑖𝑖𝑖𝑖𝑖𝑖 and ℎ𝑖𝑖𝑖𝑖𝑖𝑖 . Hence it clears that the evaluation of the Decision is always approximate to the Most Probable Value Mij of the Triangular Fuzzy Numbers (𝐿𝐿𝑖𝑖𝑖𝑖 , 𝑈𝑈𝑖𝑖𝑖𝑖 , 𝑀𝑀𝑖𝑖𝑖𝑖 ). 2.4.2 Risk Index and Defuzzification Decision making process is always accompanied by the risk issues. Hence experts also consider a Risk Index (β) in dealing with the problem. Defuzzification is executed by compounding the Risk Factor in order to obtain the crisp numbers. The Overall Crisp Performance Matrix (Hαβ) can be obtained from the equation 2.24 through equation 2.23. 𝛼𝛼 𝛼𝛼 𝛼𝛼 ℎ𝑖𝑖𝑖𝑖𝑖𝑖 =βℎ𝑖𝑖𝑖𝑖𝑖𝑖 +(1- β)ℎ𝑖𝑖𝑖𝑖𝑖𝑖 , , 0≤α≤1;0≤β≤1 Eq. (2.23) Eq. (2.24) where 𝐻𝐻𝛽𝛽𝛼𝛼 , denotes the Crisp performance score in which every alternative (Ai) corresponds to all Criteria (Cj) under Degree of confidence (α) and Risk index (β). 2.5 Ranking the alternatives using TOPSIS Hwang and Yoon (1981) framed the MCDM technique, namely, TOPSIS. This structure has been used to finalise the ranking order of the selected coating materials. This approach was employed as its logic is rational and understandable, involves straight computations, permits the pursuit of best potential candidate or alternative for each identified criterion expressed in an analytical form, and also the Fuzzy Weights are get added to the procedures of comparison. TOPSIS is to define two set of solutions, viz, the most and the least Ideal Solutions. The best or the most ideal solution always maximises the criteria that are beneficial and minimises those criteria that seem nonbeneficial. The least ideal solution maximises non –beneficial criteria and minimises the benefit criteria. We have to find the Optimal Alternative which is closest to the solution that is BEST and farthest from the solution that are LEAST. A “Relative Similarity To The Ideal Solution” has been considered in TOPSIS to select the BEST Potential Candidate in order to avoid the similarity between the defined solutions. The TOSIS model is calculated as follows. (a) Develop a Decision Matrix (D) for Alternative X11 X12………….X1j X21 X22………….X2j ..……………... D= .………………. Xi1 Xi2………….Xij .………………. Xm1 Xm2………. Xmj X1n X2n Eq. (2.25) Xin Xmn where Ai represents the possible alternatives, i = 1, . . . , m; Xj denotes the criteria corresponding to the performance of alternatives, j = 1,. . . , n; and Xij is a Crisp value which indicates the Performance rating of each alternative Ai with respect to each criterion X j. (b) Normalisation of decision matrix Obtain the normalised decision matrix R (=[rij]) and is calculated as Eq. (2.26) where Xij is the performance of alternate i to criterion j. (c) Obtaining Weighted Normalized matrix This matrix can be obtained by multiplying each column of R with its associated weight wj, that has already been calculated by AHP. Hence, the weighted normalized decision matrix V becomes V11 V12………….V1j…V1n V= V21 V22………….V2j...V2n . . …………. . . Vi1 Vi2………….Vij…Vin . ……………… .. Vm1 Vm2………….Vmj..Vmn w1r11 w2r12 ………….. wjr1j………wnr1n w1r21 =. w2r22…………..wjr2j……….wnr2n …………………….. w1ri1 Eq. (2.27) w2ri2 ……………wjrij……..wnrin ……………………. w1rm1 w2rm2……………wjrmj…….wnrmn (d) Determination of the Most and Least Ideal solutions The following equation can be used to obtain the positive and negative ideal solutions Eq. (2.28) where j = { j =1, 2, ..., n｜ j belongs to Benefit Criteria}, j' = { j = 1, 2, ..., n｜ j belongs to Non-Benefit Criteria}. (e) Determination of distance between the Positive and Negative ideal solutions for each defined Coating Material Eq. (2.29) Eq. (2.30) ` (f) Estimation of the Relative Closeness to the PIS and NIS Eq. (2.31) (g) Prioritize or rank the Alternatives The potential coating materials are get ranked with respect to the Relative closeness values obtained Case Study The proposed methodology is applied to any Manufacturing Industry where the Thermal coating technique on Magnesium alloy is being employed. The problem is to select the best coating material among the alternatives identified from Literature review and Field survey. Minimum porosity, Optimal hardness, Optimal structure are the rules to be followed (Kulu 2009) in selection of coating. The process parameters like unmelted particles, roughness, bond strength, inclusion also plays a part in the selection. Similarly, the other criteria and sub criteria that are essential for the best alternative selection are determined. Then the Fuzzy AHP –TOPSIS Integration procedures are adopted in the problem 3.1 Problem definition In view of the studies conducted regarding the properties of AZ31B magnesium alloy which has been coated by means of thermal spray technique, especially High Velocity Oxy Fuel process, the following gaps got identified: • Micro Cracks in the splat intersection with the substrate can occur. • Poor bonding combination of the applied surface layer to the substrate material. • Appearance of porosity. • Distortion of the work piece due to thermal effect • Severe Temperature can cause vaporisation of either powder or some of its components. It can also cause the dissolution and transformation of phases. • Corrosion attack of Mg-Al alloys occur at α-Mg matrix/ intermetallic interfaces. • Galvanic corrosion between the substrate and coating is a serious problem • Detailed observation for the role of twins in corrosion process • Structural defects present in the coated surface can accelerate corrosion rate. Hence to fill all the aforementioned gaps, a suitable coating material to be identified for the low carbon steel. 3.2 Applying Methodology or Strategy for the Case Study Step 1 Obtaining the Fuzzy judgement Matrix. An expert survey was conducted by distributing questionnaire in various industries and based on their collective opinion, criteria and sub-criteria got determined. Thus, 6 Criteria and 39 Sub Criteria were identified. Criteria are as follows: Quantitative (Qut), Qualitative (Qul), Cost (C), Quality (Q), Coating Structure (CS), Risk Factors (R). Sub criteria selected are: Density, Thermal Conductivity, Thermal Expansion Coefficient, Hardness, Modulus of Elasticity, Elastic Recovery, Ultimate or Critical Load, Yield Stress, Melting Temperature, H/E ratio, H3/E2ratio, Material cost, Manufacturing cost, Availability, Accessibility, Wear Resistance, Coefficient of friction, Radiation Sensitivity, Hardenability, Workability, Appearance, Oxidation Resistance, Oxidation rate constant, Impact resistance. Toxicity, Adhesion to substrate, Bond strength, Durability, Brittleness, Compatibility of the materials, Possibility of surface treatment, Framed structure, Matrix nature, Mixed, Aging tendency, porosity, Geographic allocation, political stability and foreign policy, Exchange rate and economic position. The following Hierarchical Structure shows the various Criteria and Sub Criteria required for evaluating the best coating material. Results Computation of Weight Vector Fuzzy AHP is used to evaluate the fuzzy weight with the help of pair wise Comparison technique. It appears to be difficult to avoid the decision –makers’ substantial judgment or assessment. Hence, AHP is employed to solve this situation by a group decision-making technique which is get converted into the fuzzy form. Determining the Fuzzy Performance Matrix Fuzzy Judgement Score of each coating material is combined with the Weight Vector to develop the Fuzzy Performance Score of the respective candidate related to each criterion. Decision of Interval Performance matrix The Degree of confidence (α) of the decision maker and the risk factors are considered. Defuzzification is being carried out. The decision makers have decided to take α value as 0.85 Obtaining the Crisp performance matrix (Hαβ) Risk index (β) is applicable here for the Defuzzification process. The decision makers have unanimously decided to keep β= 0.2. Deciding the favourable and detrimental Ideal Solutions Here the TOPSIS technique is being employed for ranking the coating material alternatives. The Positive Ideal Solution (PIS) (hα+jβ) is being considered as the Most Favourable Crisp Performance Score and the Negative ideal Solution (NIS) (hα-jβ) is being treated as the least favourable Crisp Performance Score among all the identified coating materials on a criterion .equation 2.28 calculates both PIS and NIS respectively. Calculation of the Separation weigh up of each Alternative from the Ideal Solutions calculated. The distance between the Positive Ideal Solution and Negative Ideal Solution can be found out from the equations 2.29 and 2.30 respectively. Solution of the Net Performance Indicator for each Alternative This involves the calculation of “Closeness of Relation” to the Ideal Solutions for all the coating material alternatives using the equation 2.31. Prioritization of Potential Candidates Ranking among the seven alternatives have been done and the BEST alternative suitable for the substrate got identified and got recommended for further processes The results are tabulated as follows: Result Table 1: The Sub scores of all candidates with respect to all sub criteria Evaluation Score Coating Coating Selection Sub assortment Al2O3Criteria Criteria Qualitative (QUL) TiO2 Composite NiCrBSi CoNiCrAlY duplex 1 3 1 7 5 5 7 Thermal Conductivity (TC) 3 7 3 9 3 7 9 1 3 7 7 3 1 Hardness (H) 3 7 3 3 9 7 3 Young's Modulus (E ) 5 5 3 3 7 3 5 Elastic Recovery (ER) 3 9 9 5 3 7 3 Critical Load (L) 3 3 3 5 3 5 3 Yield Stress (YS) 3 9 9 3 5 9 9 Melting Temperature (MT) 3 3 3 9 5 3 3 H/E ratio 3 5 3 9 3 9 9 H3/E2 ratio 7 3 7 5 9 3 3 Wear Resistance (WR) 5 9 5 3 9 5 3 Coefficient of Friction (COF) 1 9 9 3 5 3 7 Radiation Sensitivity (RS) 3 3 3 9 3 9 5 Workability (W) 7 5 3 9 7 5 7 Appearance (AP) 5 3 7 5 3 9 5 Oxidation Resistance (OR) 5 9 5 3 5 5 9 Oxidation Rate Constant (ORC) 9 5 7 7 5 5 7 Impact Resistance (IR) 1 9 5 3 3 7 9 3 5 9 5 7 3 (TEC) (QUN) Ni-Zn-Cu-P/Ni-P Si3N4 Density (D) Thermal Expansion Coefficient Quantitative Zn/Al-Mn 316 SS Possibility of Surface Treatment (ST) 5 1 Material (MTL) 5 5 7 5 9 7 3 Manufacturing (MN) 3 7 9 3 7 3 5 Availability (A) 3 3 1 7 3 7 3 Accessibility (AC) 1 7 3 9 3 5 3 Toxicity (T) 3 5 7 5 5 9 9 Adhesion to Substrate (AS) 1 7 9 3 5 3 3 Bond Strength (BS) 3 3 1 7 3 9 9 Durability (D) 1 7 3 9 9 3 3 Brittleness (B) 5 3 5 7 9 5 3 5 7 3 3 5 3 7 Matrix (M) 3 5 3 3 3 9 5 Framed (F) 1 9 9 5 7 5 7 Mixed (MX) 3 5 7 5 3 9 5 Aging Tendency (AT) 3 7 9 3 5 5 9 Porosity (P) 3 3 1 7 5 5 7 Geographical Location (GL) 1 7 3 9 3 7 9 3 3 5 7 7 3 1 1 7 3 3 9 7 3 Cost (CST) Quality (Q) Compatibility of the material (COM) Coating Structure (CS) Risk Factors (RF) Political Stability & Foreign Policy (PF) Exchange Rate & Economic Position (EP) Result Table 2: Rating of each coating material with respect to all Criteria Evaluation Score Coating Selection Sub Criteria 316SS Zn/Al-Mn Al2O3-TiO2 Composite Ni-Zn-Cu- Si3N4 NiCrBSi CoNiCrAlY P/Ni-P duplex Quantitative (QUN) (17,35,57) (35,57,75) (24,49,67) (43,65,81) (37,59,77) (39,61,79) (35,55,71) Qualitative (QUL) (25,39,55) (39,57,67) (35,53,67) (29,47,61) (29,47,63) (33,51,65) (37,53,67) Cost (CST) (6,12,20) (14,22,30) (14,20,26) (16,24,30) (14,22,28) (14,22,30) (6,14,22) Quality (Q) (10,18,30) (20,32,44) (18,28,38) (22,34,44) (24,36,44) (20,32,40) (22,34,42) Coating Structure (5,13,23) (19,29,37) (21,29,35) (13,23,33) (23,33,41) (23,33,39) (23,33,41) (3,5,11) (11,17,23) (5,11,17) (13,19,23) (13,19,23) (11,17,23) (9,13,17) (CS) Risk Factors (RF) Result Table 3 :The fuzzy judgment scores of each Coating Material relating to each criterion Evaluation Score Coating Selection Criteria 316SS Zn/Al-Mn Al2O3-TiO2 Si3N4 NiCrBSi CoNiCrAlY Ni-Zn-Cu-P/Ni-P duplex Composite Quantitative (QUN) (0.09,0.24,0.64) (0.18,0.4,0.84) (0.12,0.36,0.75) (0.22,0.47,0.9) (0.19,0.44,0.86) (0.20,0.47,0.88) 0.18,0.45, 0.79 Qualitative (QUL) (0.15,0.3,0.63) (0.23,0.43,0.77) (0.21,0.40,0.77) (0.17,0.36,0.70) (0.17,0.36,0.73) (0.2,0.39,0.75) (0.22,0.4,0.77) Cost (CST) (0.08,0.23,0.6) (0.2,0.42,0.9) (0.2,0.38,.8) (0.23,0.46,0.9) (0.2,.42,0.84) (0.2,0.42,0.9) (0.08,0.27,0.66) Quality (Q) (0.09,0.22,0.57) (0.19,0.39,0.84) (0.17,0.34,0.72) (0.21,0.41,0.84) (0.22,0.44,0.84) (0.19,0.39.0.76) (0.21,0.41,0.8) (0.05,0.18,0.49) (0.21,0.41,0.78) (0.23,.41,0.74) (0.14,0.32,0.7) (0.25,0.46,0.87) (0.25,0.46,0.83) (0.24,0.44,0.81) (0.06,0.12,0.42) (0.21,0.42,0.87) (0.1,0.27,0.64) 0.25,0.47,0.87 (0.25,0.47,0.87) (0.21,0.42,0.87) (0.17,0.32,0.64) Coating Structure (CS) Risk Factors (RF) Result Table 4.a Four Pair wise Comparison Matrices DM 1 QUN QUL CST Q CS RF QUN 1 1/4 1/3 1/2 1/2 1/5 QUL 4 1 1/3 1/4 1/2 1/4 CST 3 3 1 1/4 1/2 1/3 Q 2 4 4 1 1/5 1/2 CS 2 2 2 5 1 1/4 RF 5 4 3 2 4 1 DM 1I QUN QUL CST Q CS RF QUN 1 1/5 1/2 1/4 1/3 1/6 QUL 5 1 1/4 1/5 1/2 1/5 CST 2 4 1 1/6 1/2 1/3 Q 4 5 6 1 1/2 1/2 CS 3 2 2 2 1 1/6 RF 6 5 3 2 6 1 DM 1II QUN QUL CST Q CS RF QUN 1 1/3 1/2 1/4 1/5 1/6 QUL 3 1 1/6 1/3 1/4 1/5 CST 2 6 1 1/4 1/2 1/3 Q 4 3 4 1 1/6 1/2 CS 5 4 2 6 1 1/4 RF 6 5 3 2 4 1 DM 1V QUN QUL CST Q CS RF QUN 1 1/4 1/2 1/5 1/3 1/6 QUL 4 1 1/5 1/3 1/2 1/4 CST 2 5 1 1/4 1/2 1/5 Q 5 3 4 1 1/5 1/2 CS 3 2 2 5 1 1/2 RF 6 4 5 2 2 1 Table 4b: Comprehensive Pair Wise Comparison Score Criteria QUN QUL CST Q CS RF QUN (1,1,1) (0.2,0.26,0.33) (0.33,0.46,0.5) (0.2,0.3,0.5) (0.2,0.34,0.5) (0.17,0.18,0.2) QUL (3,4,5) (1,1,1) (0.17,0.24,0.33) (0.2,0.28,0.33) (0.25,0.44,0.5) (0.2,0.23,0.25) CST (2,2.25,3) (3,4.5,6) (1,1,1) (0.17,0.23,0.25) (0.5,0.5,0.5) (0.2,0.3,0.33) Q (2,3.75,5) (3,3.75,5) (4,4.5,6) (1,1,1) (0.17,0.27,0.5) (0.5,0.5,0.5) CS (2,3.25,5) (2,2.5,4) (2,2,2) (2,4.5,6) (1,1,1) (0.17,0.29,0.5) RF (5,5.75,6) (4,4.5,5) (3,3.5,5) (2,2,2) (2,4,6) (1,1,1) CRITERIA WEIGHTS Criteria 1 (0.025, 0.039, 0.06) Criteria 2 (0.058, 0.094, 0.146) Criteria 3 (0.083, 0.134, 0.219) Criteria 4 (0.129, 0.210, 0.356) Criteria 5 (0.111, 0.207, 0.365) Criteria 6 (0.205, 0.316, 0.494) Table 5:Fuzzy performance score of each coating material related to each criterion Coating Selection Quantitative (QUN) Qualitative (QUL) 316 SS 0.002 0.009 0.038 0.009 0.028 Al2O3-TiO2 0.005 0.016 0.050 0.013 0.041 0.003 0.014 0.045 0.012 0.038 Si3N4 0.006 0.018 0.054 0.009 0.034 NiCrBSi 0.005 0.017 0.051 0.009 0.034 0.005 0.018 0.053 0.011 0.036 0.005 0.017 0.047 0.013 0.038 Cost (CST) Coating Structure Quality (Q) (CS) Criteria Zn/Al-Mn Composite CoNiCrAl Y Ni-Zn-CuP/Ni-P duplex 0.09 3 0.11 3 0.11 3 0.10 3 0.10 6 0.11 0 0.11 3 0.007 0.031 0.016 0.056 0.016 0.051 0.019 0.061 0.016 0.056 0.016 0.056 0.007 0.036 0.13 1 0.19 7 0.17 1 0.19 7 0.18 4 0.19 7 0.14 4 0.012 0.046 0.203 0.006 0.024 0.082 0.297 0.022 0.022 0.071 0.257 0.024 0.026 0.087 0.297 0.015 0.029 0.092 0.297 0.027 0.024 0..082 0.270 0.027 0.026 0..087 0.284 0.027 0.03 6 0.08 0 0.08 0 0.06 3 0.09 1 0.09 1 0.09 1 Risk Factors (RF) 0.165 0.012 0.039 0.206 0.266 0.042 0.134 0.431 0.252 0.019 0.87 0.237 0.050 0.150 0.431 0.295 0.050 0.150 0.431 0.280 0.042 0.134 0.431 0.295 0.035 0.102 0.318 0.318 Table 6: The collective interval performance rate of α-CUT coating material with respect to each criterion. Performance Score Coating assortment criteria Quantitative 316 SS Al2O3- Zn/Al-Mn TiO2 composite Si3N4 NiCrBSi CoNiCrAlY Ni-Zn-CuP/Ni-P duplex 0.014 0.014 0.021 0.012 0.019 0.016 0.024 0.015 0.022 0.016 0.024 0.015 0.022 0.025 0.038 0.037 0.052 0.034 0.049 0.030 0.044 0.030 0.045 0.033 0.047 0.034 0.049 Cost (CST) 0.027 0.046 0.050 0.077 0.046 0.069 0.055 0.081 0.050 0.075 0.050 0.077 0.031 0.052 Quality (Q) 0.041 0.069 0.073 0.114 0.064 0.099 0.078 0.118 0.082 0.045 0.073 0.110 0.078 0.116 0.031 0.055 0.071 0.108 0.071 0.105 0.056 0.089 0.081 0.121 0.081 0.119 0.081 0.121 0.035 0.064 0.120 0.178 0.077 0.121 0.135 0.192 0.135 0.192 0.120 0.178 0.092 0.135 (QUN) Qualitative 0.008 (QUL) Coating Structure (CS) Risk Factors (RF) Table 7: Comprehensive Crisp Performance Matrix Performance Score Coating assortment criteria 316SS Al2O3- Zn/Al-Mn TiO2 Composite 0.019 Ni-Zn-Cu- Si3N4 NiCrBSi CoNiCrAlY 0.017 0.022 0.021 0.022 0.021 P/Ni-P duplex Quantitative (QUN) 0.013 Qualitative (QUL) 0.035 0.049 0.046 0.041 0.042 0.045 0.046 Cost (CST) 0.042 0.072 0.064 0.076 0.070 0.072 0.048 Quality (Q) 0.064 0.106 0.092 0.110 0.052 0.103 0.109 Coating Structure (CS) 0.050 0.100 0.099 0.083 0.113 0.112 0.113 Risk Factors (RF) 0.059 0.167 0.112 0.180 0.180 0.167 0.126 Table 8: Separation measurement and ranking of each coating material Coating material 316SS Al2O3-TiO2 𝒔𝒔𝟎𝟎.𝟖𝟖𝟖𝟖+ 𝒊𝒊,𝟎𝟎.𝟐𝟐 0.077 0.112 𝒔𝒔𝟎𝟎.𝟖𝟖𝟖𝟖− 𝒊𝒊,𝟎𝟎.𝟐𝟐 Final Performance Score 0.127 0.076 0.621 0.405 Ranking 1 7 Zn/Al-Mn 4 Composite 0.062 0.094 0.603 Si3N4 0.044 0.068 0.604 3 NiCrBSi 0.065 0.064 0.498 5 CoNiCrAlY 0.112 0.082 0.422 6 0.068 0.105 0.607 Ni-Zn-Cu-P/Ni-P duplex 2 Discussions The attribute weights were obtained by Fuzzy AHP and the coating materials were evaluated with TOPSIS. The Fuzzy AHP –TOPSIS combination was made for the robust and consistent results. From the combination, 316 SS was evaluated as the best coating material for the low carbon SS and Al2O3-TiO2 as the least. References Aditya Chauhan & Rahul Vaish(2013).Hard coating material selection using multi-criteria decision making. Materials and Design 44 , 240–245. Anojkumar L. & Ilangkumaran & M. Vignesh (2015). A decision making methodology for material selection in sugar industry using hybrid MCDM techniques. Int. J. Materials and Product Technology, 51, No. 2. Ashby M.F.& Bre´chet Y.J.M. & Cebon D.& Salvo L. (2004).Selection strategies for materials and processes. Materials and Design 25 , 51–67. Chandra Prakash & M.K. Barua (2015). Integration of AHP-TOPSIS method for prioritizing the solutionsof reverse logistics adoption to overcome its barriers underfuzzy environment. Journal of Manufacturing Systems 385. Chia-Chi Sun ((2010). A performance evaluation model by integrating fuzzy AHP andfuzzyTOPSIS methods. Expert Systems with Applications 37, 7745–7754 Dobrza´nski L.A. & Madejski L.A. (2006). Prototype of an expert system for selection of coatings for metals. Journal of Materials Processing Technology 175 , 163–172. Dong-Hyun Jee & Ki-Ju Kang (2000).A method for optimal material selection aided with decision making theory. Materials and Design 21, 199-206. Georgios Athanasopoulo & CarlesRomevaRiba & Christina Athanasopoulou(2009).A decision support system for coating selection based on fuzzy logic and multi-criteria decision making. Expert Systems with Applications 36 , 10848–10853. HalilCalıs_kan(2013).Selection of boron based tribological hard coatings using multi-criteria decision making methods. Materials and Design 50, 742–749. HalilCalıs_kan & Bilal Kurs_uncu & CahitKurbanog˘lu & S_evki Yılmaz Guven(2013).Material selection for the tool holder working under hard milling conditions using different multi criteria decision making methods. Materials and Design 45 , 473–479. Holleck H. (1986).Material selection for hard coatings. Journal of Vacuum Science & Technology A 4, 2661 . Khorshidi R. & Hassani A. (2013).Comparative analysis between TOPSIS and PSI methods of materials selection to achieve a desirable combination of strength and workability in Al/SiC composite. Materials and Design 52, 999–1010. KrishnaVeni K.&.Rajesh R &.Pugazhendhi S (2012). Development of decision making model using Integrated AHP and DEA for vendor selection. Procedia Engineering 38,3700-3738. Kulu P. & Pihl T. (2001). Selection Criteria for Wear Resistant Powder Coatings Under Extreme Erosive Wear Conditions. JTTEE5 11:517-522. Mark Velasquez & Patrick T. Hester (2013). An Analysis of Multi-Criteria Decision Making Methods.International Journal of Operations Research Vol. 10, No. 2, 56-66. Maria Oksa & ErjaTurunen & Tomi Suhonen & TommiVaris , Simo-PekkaHannula (2011). Optimization and Characterization of High Velocity Oxy-fuelSprayed Coatings: Techniques, Materials, and Applications. Coatings 2011, 1, 17-52; doi:10.3390/coatings1010017. Martin Aruldoss & Miranda Lakshmi T. & PrasannaVenkatesan V. (2013). A Survey on Multi Criteria Decision Making Methods and Its Applications. American Journal of Information Systems, 1, No. 1, 31-43. MetinDag deviren & SerkanYavuz & NevzatKılınc (2009). Weapon selection using the AHP and TOPSIS methods under fuzzy environment. Expert Systems with Applications, 36, 8143–8151. Mustafa SabriGok & Abdullah CahitKaraoğlanl & AzmiErdoğan& AhmetTürk(2015). A Comparative Study of Wear Effect on the Microstructures Behavior of CoNiCrAlY Coatings fabricated by APS, HVOF andCGDS Coatings.https://www.researchgate.net/publication/266461131. NiteshVashishtha & Sanjay Sapate(2017). Abrasive Wear Maps for High Velocity Oxy Fuel(HVOF) sprayed WC-12Co and Cr 3 C 2 −25NiCrcoatings. Article in Tribology International ,DOI: 10.1016/j.triboint.2017.04.037. Rajesh R.& Pugazhendhi V& Ganesh K. (2009).An analytic model for selection of and allocation among third party logistics service providers. Int. J. Enterprise Network Management, Vol. 3, No. 3. SalehiDoolabi M.& Ghasemi B.& . Sadrnezhaad S. K, Habibolahzadeh A., Jafarzadeh K. (2017). Evaluation and Selection of Optimal Oxygen/Fuel Ratiofor Best Mechanical Properties, Oxidation Resistanceand Microstructure of HVOF NiCoCrAlY Coatings Using AHP–VIKOR Method. Oxid Met DOI 10.1007/s11085-017-9797-2. SarojiniJajimoggala (2013). Decision making model for material selection using a hybrid MCDM technique. Int. J. Applied Decision Sciences, 6, No. 2. Thomas L. Saaty, (2008).Decision making with the analytic hierarchy process.Int. J. Services Sciences, 1, No. 1. VasileiosKatranidis & Sai Gu & Bryan Allcock & Spyros Kamnis (2017). Experimental study of high velocity oxy-fuel sprayed WC-17Co coatings applied on complex geometries. Part A: Influence of kinematic spray parameters on thickness, porosity, residual stresses and microhardness. Surface & Coatings Technology 311 ,206–215. Tables Table 2.1 Membership Function of the Triangular Fuzzy Number fuzzy number membership function ~ 1 (1, 1, 3) ~ n ( n - 2, n, n + 2 ) for n = 3, 5, 7 ~ 9 (7, 9, 9) Table 2.2 Lexical term and the Fuzzy ratio scale Linguistic Term Poor Satisfactory Good Very Good Excellent Fuzzy Ratio Scale 1� 3� 5� 7� 9� Table 2.3 Fuzzy ratio scales for a positive tangible sub-criterion Scale Sub-criterion ~ ~ 1 The interval value correspondence to 1 ~ ~ 3 The interval value correspondence to 3 ~ ~ 5 The interval value correspondence to 5 ~ ~ 7 The interval value correspondence to 7 ~ ~ 9 The interval value correspondence to 9 Table 2.4 Grades (𝐺𝐺� ijks) of Alternative (Ai) as per DM (Ds) on Sub-Criterion (Cjk) where j = 1, 2,.., m k = 1, 2... , q s = 1, 2…, t Table 2.5 A i Sub-Scores (𝐺𝐺𝑖𝑖𝑖𝑖𝑖𝑖 ) of Alternative (Ai) with respect to the Sub-criteria (𝑐𝑐𝑗𝑗𝑗𝑗 ). C1 C11 C2 C12 C21 Cm C22 ... Cm1 ... A1 ~ ~ ~ ~ G111 G112 G121 G122 A2 ~ ~ ~ ~ ~ G211 G212 G221 G222 ... G2m1 ... .. . .. . .. . .. . .. . Gn11 Gn12 Gn21 Gn22 .. . ... .. . ... .. . An ... ~ G1m1 ... Cmq ~ G1mq ~ Gnm1 G2mq .. . Gnmq Table 2.6 Saaty’s Scale Intensity of Definition Explanation importance 1 Equal importance Two activities contribute equally to the objective 2 Weak or slight 3 Moderate importance Experience and judgement slightly favour one activity over another 4 Moderate plus 5 Strong importance Experience and judgement strongly favour one activity over another 6 Strong plus 7 Very strong or demonstrated Any activity is favoured very strongly over importance another, its dominance demonstrated in practice 8 Very, very strong 9 Extreme importance The evidence favouring one activity over another is of the highest possible order of affirmation Reciprocals of If activity i has one of the above above non-zero A reasonable assumption numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i 1.1 - 1.9 If the activities are very close May be difficult to assign the best value but when compared with other contrasting activities the size of the small numbers would not be too noticeable, yet they can still indicate the relative importance of the activities. Case study Table 1: The selection criteria Coating Material Industrial Relevance in material Selection criteria selection Quantitative Qualitative Importance of the measurable Georgios Athanasopoulos parameters like hardness, elastic et.al. (2013), Dong-hyunJee. modulus etc are considered et.al (2000) The properties that can be expressed Georgios Athanasopoulos as a linguistic term rather than the et.al.(2013),Dong-hyunJee. crisp numbers et.al (2000) The economical aspects related to the Cost availability accessibility etc are studied Quality Coating Structure Risk Factors Reference used Rubayetkarim et.al (2016) , L.A.Dobrzanskiet,al (2016) The coating material-substrate Rubayetkarim et.al (2016), adherence properties are considered L.A.Dobrzanskiet,al (2016) The material structure of the coating material p.Kulu and t.pihlet.al. (2001) The various risk factors are identified Felix T.S. chanet.al prior to the selection (2007) Case study Table 2: The selection sub criteria Coating Material Relevance and Explanation in Selection criteria Material Selection Density Reference used The selected coating material should Georgios Athanasopoulos have low density and weight in order et.al. (2013) Dong-hyunJee to reduce the payload .et.al (2000) Thermal Low thermal conductivity is required conductivity for the coating material Georgios Athanasopoulos et.al.(2013),Dong-hyunJee .et.al (2000) The coating material with a Thermal expansion coefficient of thermal expansion coefficient which is higher than that of the H.Holleck et.al (1986) substrate to be selected Georgios Athanasopoulos et.al.(2013), DongHardness Maximum value of Hardness is hyunJee.et.al (2000), Aditya advisable chauhan et.al (2013),p.Kulu and t.pihl (2001), halilkaliscan (2013) et.al. Georgios Athanasopoulos Young’s modulus The value of modulus of elasticity should be minimum et.al.(2013) , Dong-hyunJee. et.al (2000), Aditya Chauhan et.al (2013), halilkaliscan (2013) et.al. At normal load, neither fatigue pits Critical load nor cracks could be found easily. But Georgios Athanasopoulos as the load increases, chances that the et.al. (2013) coatings may get either failed or worn through. Hence calculation of crucial load of the substrate is essential. Yield stress Stress affects adhesive / and or Georgios Athanasopoulos cohesive properties. It also causes et.al.(2013) Dong-hyunJee delamination and cracking. .et.al (2000) The coating material should have Melting high melting point to withstand high Temperature operating temperatures without melting away Georgios Athanasopoulos et.al. (2013) Dong-hyunJee. et.al (2000) halilkaliscan (2013) et.al., H/E ratio Lower the ratio, lesser the wear rate. Aditya chauhan et.al (2013) halilkaliscan (2013) et.al., H3/E2 ratio Lower the ratio, lesser the wear rate. Aditya chauhan et.al (2013) Georgios Athanasopoulos Wear Resistance Minimum wear resistance et.al. (2013), halilkaliscan (2013) et.al., Coefficient of Minimum coefficient of friction is friction preferred halilkaliscan (2013) et.al., Individual sample testing to be done Georgios Athanasopoulos Radiation for the prediction of the radiation et.al. (2013) Dong-hyunJee. Sensitivity sensitivity of the materials et.al (2000) It is the measure of potential of the Harden ability material or the rate of reduction in hardness after quenching from high temperature Georgios Athanasopoulos et.al.(2013) Dong-hyunJee. et.al (2000) Workability Appearance Oxidation Resistance The workability of the material to be Georgios Athanasopoulos selected from the alternatives should et.al.(2013) Dong-hyunJee. be higher et.al (2000) Good quality aesthetic appearance is Georgios Athanasopoulos preferred et.al.(2013) Very high oxidation resistance is required for the material to be selected for coating Georgios Athanasopoulos et.al.(2013) Dong-hyunJee. et.al (2000), M. SalehiDoolabi (2017) et.al. The low rate of oxidation is preferred Oxidation rate constant in the best coating material for thermodynamically stable oxide formers with slow growth rates Very high impact resistance is Impact Resistance required for the material to be selected for coating Most cost effective material to be Material cost Manufacturing Cost NitishVashishtha (2016) et.al selected from the alternative selected for coating. The manufacturing cost of the coating material should be economical. p.Kulu and t.pihl (2007) et.al. L.A.Dobrzanskiet,al (2016) L.A.Dobrzanskiet,al (2016) The alternatives that are identified Availability should ensure the availability at the MehmetSevkli (2010) right time at right quantity and quality The means to access the selected Accessibility coated material in an economical and easy manner is very important MehmetSevkli (2010) Toxicity Adhesion to substrate The coating material should be less Dong-hyunJee .et.al toxic in nature. (2000 ) The coating material to be selected should have the best adhesiveness to halilkaliscan (2013 ) et.al. the identified substrate. The quality and durability of bonded joints, coated systems depend on Bond strength various factors and hence effective halilkaliscan (2013 ) et.al. quantitative tests to determine the bonding strength are required Adhesion, abrasion, accelerated light aging, stain resistance etc to be Durability considered for the testing of the durability and the appropriate Maria Oksa.(2011) et.al (2011) selection to be made Although brittle coatings are tolerant to wear and external concentrated loads, they can be subjected to Brittleness occasional severe stress L.A.Dobrzanskiet, al (2016 ) concentration. Hence testing is essential to select the appropriate materials. Compatibility of the material Possibility of surface treatment There should be chemical, process, mechanical compatibilities between coating material and substrate Georgios Athanasopoulos et.al.(2013) The coating should support the Georgios Athanasopoulos surface treatment procedures for et.al.(2013) Dong-hyunJee. further modifications et.al (2000) Framed structure The optimal structure which guarantees high wear resistance. p.Kulu and t.pihl (2001) A structure with a Hard Phase Matrix structure Content < 50% to be preferred in the p.Kulu and t.pihl (2001) case of a direct impact Mixed structure Double cemented matrix structure p.Kulu and t.pihl (2001) Temperature aging increases the Aging tendency stiffness of the substrate. Georgios Athanasopoulos Temperature dependence of the aged et.al. (2013) Dong-hyunJee. materials become less significant than et.al (2000) that of the virgin materials Georgios Athanasopoulos Porosity Coating hardness and particle et.al. (2013) Dong-hyunJee. temperature should be controlled to et.al (2000), p.Kulu and reduce the porosity. t.pihl (2001), vasileios katrasidis (2017) et.al. Geographical Geographical factors should be location considered to avoid the risk. Felix T.S. chan (2007) et.al The Foreign policies and the Political stability prevailing political conditions and and Foreign policy related social factors will affect the Felix T.S. chan (2007) et.al coating material procurement. Exchange rate and Economic position Money value and the financial position also plays a role in the coating material selection. Felix T.S. chan (2007) et.al Figure Captions Figure 1. Figure example of a typical fuzzy membership and properties Figure 2. Figure represents the working steps of Fuzzy Logic Figure 3. Steps in model development using Fuzzy AHP-TOPSIS integration . Figure 4. Figure represents the schematic diagram for the combination of fuzzy AHP and TOPSIS of the proposed model Figure 5. Figure represents the Work Break down structure Fig 1. Fig 2. Fig 3. Fig 4. 1 Material A A1 B A1 A1 Material 1 Fig 5. A1 A1 A1 A1 E D C A1 Material 2 A1 A1 A1 A1 A1 Material 3 F A1 A1 A1 A1