Selection of the Best Material for an Axle in Motorcycle using fuzzy AHP and Fuzzy TOPSIS Methods

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1 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp Selection of the Best Material for an Axle in Motorcycle using fuzzy AHP and Fuzzy TOPSIS Methods Amit Sharma Assistant Professor Department of Mechanical Engg. HIT, Bahadurgarh, Haryana, INDIA amitrohtak11@gmail.com Atul Sharma Assistant Professor Department of Mechanical Engg. MIT, Moradabad, U.P., INDIA atulcsss.nitj@gmail.com Dr. Anish Sachdeva Associate Professor Department of Industrial and Production Engineering National Institute of Technology, Jalandhar, Punjab, INDIA anishsachdeva@gmail.com ABSTRACT The choice of materials plays an important role in the decision-making process of the manufacturing organizations. The materials affect many aspects of a product and the manufacturing process too. The improper selection of material can result in a defective final product, which may cause fatal injury. Thus, if satisfactory results are to be expected, immense importance must be given for proper selection of the materials. There are numerous choices and various criteria influencing the selection of material for a particular application. These criteria range from mechanical, electrical, and physical properties to corrosion resistance and economic considerations of the materials. The large number of available materials, together with the complex relationships between various selection parameters, often makes the selection process a difficult task. The problem of selecting a material for an engineering application from among two or more alternatives on the basis of several criteria can be treated as a multi-criteria decision-making (MCDM problem. There are some MCDM techniques such fuzzy AHP, ANP, fuzzy TOPSIS and VIKOR. In this research work our focus on selection the best material for an axle in motorcycle using "fuzzy analytical hierarchy process" commonly known as fuzzy AHP evolved from Saaty's AHP and "fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS method" and then finds the correlation between the findings of these two methods, and check the significant relationship between Ranks obtained by using fuzzy AHP (R1 and Ranks obtained by using fuzzy TOPSIS (R. Keywords: AHP, TOPSIS, ANP,VIKOR and MCDM. I. INTRODUCTION The choice of material for a particular product is a challenging task, as the selected material directly determines the visible quality and the cost of the product. Material selection is a continuous process, aiming to choose the best material for a given application to satisfy a predetermined set of requirements. The material selection decision is made during the initial design stage of the product life cycle, i.e., when the component is first designed or when it is redesigned. An incorrectly chosen material can lead not only to a premature failure of the component, but also to an unnecessary cost. During the last few decades, many new materials and material types have been developed like ceramics, plastics, composites etc. At present, numerous engineering materials exist than even before like alloy steel, stainless steel, ceramics, plastics, composites etc. This gives an opportunity to the designer for innovation by utilizing those materials in products that provide enhanced performance at a lower cost. Hence, the designer faces the difficult task of identifying the best material among the enormous set of alternatives while considering different selection criteria ranging from technological, economical, and environmental. The main purpose of material selection process is to recognize the predominant selection criteria and then to obtain the most appropriate combination of those conflicting criteria according to the requirements. Thus, while selecting the best material for a specific application, the designer needs to consider a large number of qualitative as well as quantitative criteria. Selecting the material for an industrial application from among two or more alternatives on the basis of several conflicting criteria can be treated as a multi-criteria decision-making (MCDM problem. Different Alternatives to select the Material for an axle: After discussion with R&D, Production, Quality, Maintenance, Sales staff and Management authority of motorcycle manufacturing companies and the axle manufacturer companies, we found out some main alternatives those are used in making an axle in motorcycle. The main alternatives of materials those are used by the different manufacturers of motorcycles are AISI-15B5, AISI- 510B1, AISI-4135, AISI-51B37, AISI-30 and AISI-304 (AISI - American Iron and Steel Institute. MCDM Techniques: Multiple criterion decision-making (MCDM refers to making decisions in the presence of multiple,

2 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp usually conflicting criteria. The problems of MCDM can be broadly classified into two categories: multiple attribute decision making (MADM and multiple objective decision making (MODM, depending on whether the problem is a selection problem or a design problem. Various MCDM techniques have been applied for solving the material selection problems. 1. Simple Additive Weighting (SAW Method.. Weighted Product Method (WPM. 3. Classical/Crisp Analytic Hierarchy Process (AHP Method. 4. Fuzzy Analytic Hierarchy Process (FAHP Method. 5. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS Method. 6. Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS Method. 7. Compromise Ranking Method (VIKOR/ VIšekriterijumsko KOmpromisno Rangiranje. II. LITERATURE REVIEW The selection of an optimal material for an engineering design from among two or more alternative materials on the basis of two or more attributes is a multiple attribute decision-making problem. Various approaches have been proposed in the past to help address the issue of material selection. Ashby (000 proposed multi objective optimization in materials design and selection, using 'utility' functions. Ashby et al. (004 provided a comprehensive review of the strategies or methods for materials selection, from which three types of materials selection methodology were identified: (i free searching based on quantitative analysis, (ii checklist/ questionnaire based on expertise capture, and (iii inductive reasoning and analog procedure. All of these methods use materials data in either a non-computerized or computerized form. Abdi et al [009] has investigated the design and configuration of manufacturing equipment requires crucial decision considering optimum capacity and functionality. The equipment selection problem might be involved with choosing between large-capacity machines versus a greater number of machines with smaller capacities, and/or dedicated facilities versus multi- product facilities. This paper investigates reconfigurable machining system characteristics in order to identify the crucial factors influencing the machine selection and the machine (reconfiguration. Furthermore, changeover cost and changeover time while switching from one product to the other are taken into account. In particular, a fuzzy analytical hierarchical process (FAHP model is proposed to integrate the decisive factors for the equipment selection process under uncertainty. The expected values of the normalized fuzzy sets are determined to identify the preference values of the alternative machines. The fuzzy multi-criteria model is analyzed within the fuzzy domains of the operational characteristics along with economic, quality and performance criteria. The proposed model is examined using monitoring sensitivity analysis through a case study. As a result, the alternative machines are prioritized with consideration of the inconsistency ratios. Kamal et al. [001] has investigating a modified tuning method of the simplest form of fuzzy PI controller is proposed and incorporated in a tuning formula based on the gain and phase margins, so as to achieve an appreciable improvement in the performance of the auto-tuner. In the modification, the scaling factors of the fuzzy PI controller are made to vary with respect to the plant's normalized dead-time and system state error, such that the system converges faster with smaller settling time. Phaseplane-based analyses are carried out to show that the modified tuning actually makes the FLC able to adapt the control environment. Numerical simulations and experiments are presented to show the validity of the proposed tuning methods. Jia-Fu Tang et al. [011] in this it is studied that Quality function deployment (QFD has been widely used to translate customer requirements (CRs into engineering characteristics (ECs in product improvement. Product planning house of quality (PPHOQ is of fundamental and strategic importance in the QFD system. In the construction process of the PPHOQ of matureperiod (MP product, correctly estimating the final priority ratings of ECs is essential, because it will largely affect the target value of ECs for improvement. To exploit competitive information of MP products, this paper develops a comprehensive and systematic methodology to rate the final priority of ECs for MP product improvement. The proposed method is on the basis of maximal deviation based approach (MDBA for dealing with the corporations' performance estimations of ECs, and it integrates AHP and scale method for analyzing the priority rating of achieving the improvement goal of performance evaluation (IGPE of each EC. LI Han-lun et al. [011] This study present the combination of the method of GIS and AHP together for the Urban fire which is a hidden danger for city safety. Therefore, the overall layout of fire fighting facilities is an important part of fire control planning in cities. It combines the method of GIS and AHP together. It considers the complicated data and their mutual influence, makes full use of spatial analysis, data processing and query. Planning and analysis will be more flexible and universal by utilizing this method, and the complexity of spatial location selection can be decreased considerably, which consequently may overcome the casualness and uncertainty of subjective site selection. And finally, the approach satisfies the planning requests of some related fire fighting department to a certain degree. Yusuf Tansel (011 has investigated an experimental design approach using TOPSIS method for the selection of computer-integrated manufacturing technologies. He uses a meta-model to solve a MADM problem. The meta-model is a multiple regression model which is constructed using combined DoE and TOPSIS. It is different from the conventional MADM approaches. The metamodel is constructed; it can easily facilitate the alternative evaluation process.

3 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp III. RESEARCH METHODOLOGY The selection of best material is a typical multi criteria decision making problem to deal with the uncertain judgment of decision maker, a fuzzy modification of analytic hierarchy process (AHP method is applied as an evaluation tool, where uncertain and imprecise judgments of decision maker are translated into the fuzzy number. Fuzzy extent analysis method is used to calculate the weight for the matrix for the criteria and alternative. In the fuzzy approach comparing criteria is very important. In these criteria is compared with each alternative. (a Fuzzy Analytic Hierarchy Process (AHP Method Complex problems involving subjective judgments are suitable for the application of Analytical Hierarchy Process (AHP approach. The AHP proposed by Saaty in1980 has been recognized as a powerful tool for flexible multi-criteria decision making for complex problems considering both qualitative and quantitative aspects. It organizes the critical aspects of a problem into a hierarchical structure similar to a family tree. By reducing complex decisions to a series of simple comparisons and rankings, synthesizing the results, the AHP helps the analysts to arrive at the best decision and provides a clear rationale for the choices made. AHP is based on a firm theoretical foundation. Analytical Hierarchy Process (AHP is an approach to decision making that involves structuring multiple choice criteria into a hierarchy, assessing the relative importance of these criteria, comparing alternatives for each criterion, and determining an overall ranking of the alternatives. (b Main steps Involved in Fuzzy AHP (1 Organizing problem hierarchically: The problem is structured as a family tree in this step. At the highest level is the overall goal of this decision making problem, and the alternatives are at the lowest level. Between them are criteria and sub-criteria. Fig. 1. A simple AHP hierarchy ( Development of judgment matrices by pair wise comparisons: The judgment matrices of criteria or alternatives can be defined from the reciprocal comparisons of criteria at the same level or all possible alternatives. Pair wise comparisons are based on a standardized evaluation schemes. (3 Calculating local priorities from judgment matrices: Several methods for deriving local priorities (i.e. the local weights of criteria and the local scores of alternatives from judgment matrices have been developed, such as the eigenvector method (EVM, the Logarithmic Least Squares Method (LLSM, the Weighted Least Squares Method (WLSM, the goal programming method (GPM and the fuzzy programming method (FPM. (4 Alternatives ranking: The final step is to obtain global priorities (including global weights and global scores by aggregating all local priorities with the application of a simple weighted sum. Then the final ranking of the alternatives are determined on the basis of these global priorities. The triangular fuzzy number, because of its popularity, is used to represent the fuzzy relative importance. The membership function of triangular fuzzy numbers can be described as: x l, 1 x m m l µ N ~ ( x = (1 u x, u m m < x u 0,otherwise Where l, m, and u are also considered as the lower bound, the mean bound, and the upper bound, respectively. The triangular fuzzy number Ñ is often represented as (l, m, u. After pair wise comparisons are finished at a level, a fuzzy reciprocal judgment matrix à can be established as: a% 11 a% 1 K a% 1n a% a% O a% 1 n à = {ã ij } = M M M M M K M a% n1 a% n a% nn. ( Where n is the number of the related elements at this level, and ã ij = (1/ã ji After constructing Ã, fuzzy priorities w i, i = 1,... n, should be calculated in the traditional fuzzy AHP methods. Many fuzzy prioritization approaches have been developed, such as the method based on the fuzzy modification of the LLSM, judgment matrices, shows a new way to deal with the prioritization problem from fuzzy reciprocal comparisons in the fuzzy AHP. A Fuzzy AHP based on Extent Analysis method, which can also derive priorities from fuzzy pair wise comparisons. (c Fuzzy AHP based on Extent Analysis Method Let X = {x 1, x. x n } be an object set, and U = {u 1, u. u n } be a goal set. According to the method of extent analysis, when each object is taken and extent analysis for each goal is to be performed respectively. Then M 1 gt, M gt. M m gt i = 1,..., n becomes the values of extent analysis of ith object for m goals. j Where, all M gt are triangular fuzzy numbers, j (1,... m represents the number of goals (criteria considered for decision making, i (1,... m represents the number of objects (alternatives for which decision needs to be made.

4 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp The value of fuzzy synthetic extent with respect to the ith object is defined as: S i = Where, S i is also a fuzzy number m j n m j= 1 M gi i= 1 j= 1 M j gi 1 (3 To obtain the estimates for the vectors of weights under each criterion, we need to consider a principle of comparison for fuzzy numbers. It is required to determine the greatest or the least fuzzy number among the several fuzzy synthetic extents. Let M1 and M are convex fuzzy numbers and characterized by (a 1, b 1, c 1 and (a, b, c respectively. The degree of possibility of M 1 < M is defined as: sup y V (M 1 > M = x [min?(µ M 1 (x, µ M (y] If b 1 > b 1 and µ M 1(x = µ M (y then we have V(M 1 > M = 1 i.e. V (M 1 > M = 1 iff M 1 > M To compare M 1 and M, We need both the values of V(M 1 > M and V(M > M 1. V(M > M 1 shown in Figure 3.3 is represented by point D. V(M > M 1 = hgt (M 1 M = µm 1 (d Where d is the ordinate of the highest intersection point D between µ M 1 and µ M. The ordinate of D is given by the following equation V (M > M 1 = µ M1 (d = a1 a ( b c ( b a 1 1 Fig.. The Intersection between M 1 and M.(4 The degree of possibility for a convex fuzzy number to be greater than k convex fuzzy numbers M_i (i=1, k can be defined by: V (M > M 1, M.M k = V [(M > M 1 and (M > M and.(m > M k ] = min V (M > M i ; i =1,.., k If d' (A 1 = min V (S i > S k Then, for k = 1, n; k i The weight vector is given by: W' = {d' (A 1, d' (A d' (An} T The normalized weight vector is obtained by normalization W = {d (A 1, d (A. d (A n } T Where W and W' are non fuzzy numbers. (d Fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS Method The TOPSIS method was developed by Hwang and Yoon (1981. This method is based on the concept that the chosen alternative should have the shortest. TOPSIS gives a solution that is not only closest to the hypothetically best, that is also the farthest from the hypothetically worst. Main steps involved in fuzzy TOPSIS The procedural steps of TOPSIS method are enlisted below: Step 1: Determine the alternatives and identify the pertinent evaluation criteria: Determine the alternatives and identify the pertinent evaluation criteria. Step : Construct a decision matrix: Construct a decision matrix based on all the information available for the criteria. Each row of the decision matrix is allocated to one alternative and each column to one criterion. Therefore, an element, mij of the decision matrix shows the performance of ith alternative with respect to jth criterion. Step 3: Obtain the normalized decision matrix, Dij: Obtain the normalized decision matrix, Dij using the following equation: Dij = m ij 1 M j= 1m ij (5 Step 4: Decide on the relative importance or weight of different criteria: Fuzzy extent analysis method is used to calculate the weight for the criteria. The calculation for the weight of criteria is similar as in Fuzzy Analytic Hierarchy Process (AHP Method. Step 5: Obtain the weighted normalized matrix, Vij: Obtain the weighted normalized matrix. Vij = W i D ij (6 Step 6: Obtain the ideal (best and the negative ideal (worst solutions: Obtain the ideal (best and the negative ideal (worst solutions using the following equations: V + max min = {( i Vij / j J,( i Vij / j J /i = 1,, 3 N} (7 V min max = {( i Vij / j J,( i Vij / j J / i = 1,, 3 N} (8 Where, J = (j = 1,,...,M/j is associated with beneficial attributes and J'= (j = 1,,...,M/j is associated with non-beneficial attributes. Step 7: Obtain the separation measures: Obtain the separation measures. The separations of each alternative from the ideal and the negative ideal solutions are calculated by the corresponding Euclidean distances, as given in the following equations: + M 0.5 S i = { ( V V + },i = 1,, 3...N,. (9 j= 1 ij j M 0.5 j= 1 ij j S i = { ( V V }, i = 1,, 3...N,... (10

5 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp Step 8: The relative closeness: The relative closeness of a particular alternative to the ideal solution is computed as follows: Si Pi = S (11 i + Si Step 9: A set of alternatives is arranged in the descending order, according to Pi value: A set of alternatives is arranged in the descending order, according to Pi value, indicating the most preferred and the least preferred solutions. IV. DATA COLLECTION AND ANALYSIS Fuzzy AHP and Fuzzy TOPSIS approaches to selection of the best material for an axle in motorcycle and then find the correlation between the rankings obtained using these two methods and then apply Student's t-test to check the Significant of Rank correlation coefficient. The criteria considered in selection process are Cost of raw material, Hardenability of raw material, Availability of raw material, Chemical Composition of material, and Mechanical Properties (Yield strength of material. By interviewing in manufacturing companies and the axle manufacturer companies' criteria and alternatives are taken into account. In the following steps of the decision-making process, the fuzzy comparison judgment matrices are decided according to the suggestions of the R&D, Production, Quality, Maintenance, Sales staff. In order to construct the matrix for the criteria and alternative there is the need to consider the fuzzy judgment score. These fuzzy judgment score are very important when importance of one factor is relative to the other. For example yield strength is between two and three time more important than cost. Similarly the other criteria are taken into account for the construction of matrix. The imprecise and uncertain assessments of the R&D, Production, Quality, Maintenance, Sales staff are translated into corresponding triangular fuzzy numbers according to Table 1. This approach is multi criteria decision making approach. Table 1 shows the triangular fuzzy conversion scale. This scale is not optimal and robust. Slight change in the parameters of the scale will not create an important influence on the results of the decision unless the attribute preferences are reordered. Table 1. Triangular fuzzy conversion scale in the fuzzy analytic hierarchy process Linguistic scale Triangular fuzzy scale Triangular fuzzy reciprocal scale The fuzzy comparison judgment matrices are decided according to the suggestions of the R&D, Production, Quality, Maintenance, Sales staff. The fuzzy comparison judgments matrix of the five main criteria of an axle with respect to the overall goal is shown in Table. Fuzzy extent analysis method is used to calculate the weight for the criteria's. The combination of the weight vectors obtained by pair wise comparisons is shown in Table 3. Table.. Fuzzy comparison matrices for five criteria Criteria Cost Hardenability Availability Chemical Mechanica (On B Scale Composition Properties for ease (%C in final (Yield forging Product strength process Cost (1, 1, 1 (/3, 1, (/3, 1, (/5, 1/, (1/3, /5, /3 1/ Hardenability (1/, 1, 3/ (1, 1, 1 (/3, 1, (/5, 1/, (1/3, /5, /3 1/ Availability (1/, 1, 3/ (1/, 1, 3/ (1, 1, 1 (/5, 1/, (1/3, /5, /3 1/ Chemical Composition (3/,, 5/ (3/,, 5/ (3/,, 5/ (1, 1, 1 (1/, /3, 1 Mechanical Properties (, 5/, 3 (, 5/, 3 (, 5/, 3 (1, 3/, (1, 1, 1 (Yield strength Table 3. Shows the combination of the weight vectors obtained by pair wise comparisons. Fig. 3. Priority Score Table 4. Ranking of the alternatives of materials Just equal (1, 1, 1 (1, 1, 1 Equally important (1/, 1, 3/ (/3, 1, Weakly more important (1, 3/, (1/, /3, 1 Strongly more important (3/,, 5/ (/5, 1/, /3 Very strongly more important (, 5/, 3 (1/3, /5, 1/ Absolutely more important (5/, 3, 7/ (/7, 1/3, /5 From Table 3, calculation to select the best material for an Axle in motorcycle by using fuzzy AHP, we find that alternative i.e.

6 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp material AISI 10B1 is best for criteria cost of raw material, Hardenability of raw material and availability. But alternative 3 i.e. material AISI 4135 is best for criteria Chemical Composition and Mechanical Properties (Yield strength. We also note from the Table 3 that weight for criteria Chemical Composition and Mechanical Properties (Yield strength is very high then other three criteria. So after doing all calculation using fuzzy AHP, we can easy note from Table 4 that the material AISI 4135 is best alternative for an axle and after that the material AISI 51B37, AISI 15B5,AISI 10B1, AISI 304 and AISI 30 are the best alternative in ascending order of their rank. Fuzzy Technique for Order Preference by Similarity to Ideal Solution (Fuzzy TOPSIS Method to select the best material for an axle in motorcycle: In order to select the best material for an axle by using fuzzy TOPSIS method first we have to determine the alternatives and identify the pertinent evaluation criteria. By interviewing the R&D, Production, Quality, Maintenance, Sales staff and Management authority of motorcycle manufacturing companies and Axle manufacturer companies' criteria and alternatives are taken into account. The main alternatives of materials those are used by the different manufacturers of motorcycles are AISI 15B5, AISI 10B1, AISI 4135, AISI 51B37, AISI 30 and AISI 304. The criteria considered in selection process are Cost of raw material, Hardenability of raw material, Availability of raw material, Chemical Composition of material, and Mechanical Properties (Yield strength of material. The normalized decision matrix, Dij using the equation No.5. The weighted normalized matrix using the equation No.6. The ideal (best and the negative ideal (worst solutions using the equations 7 & 8. The separations of each alternative from the ideal and the negative ideal solutions are calculated by the corresponding Euclidean distances, as given in the equations No. 9 &10. The relative closeness of a particular alternative to the ideal solution is computed by using the equation No. 11. A set of alternatives is arranged in the descending order, according to Pi value, indicating the most preferred and the least preferred solutions. Table 10, shows the relative closeness value of each alternative material. Now, the alternative materials are arranged in descending order according to their relative closeness values as in Table 11. It is observed that alternative 4 i.e. material AISI 15B37 is the best choice. The final ranking of the material is shows in Table 11. It is quite clear that selection of the best material for an axle involves a large number of considerations. The use of fuzzy TOPSIS method is observed to be quite capable and computationally easy to evaluate and select the best material for an axle from a given set of alternatives. This method uses the measures of the considered criteria with their relative importance in order to arrive at the final ranking of the alternative material. Thus, this popular MCDM method can be successfully employed for solving any type of decision-making problems having any number of criteria and alternatives. Table 5. Quantitative information for 6 Materials S.No. Alternative Cost of Hardena Chemical Mechanical Availability Materials Raw bility of Composition Properties of Material Raw (%C (Yield raw (Rs/Kg Material Strength material (HRB (MPa 1 AISI-15B AISI-10B AISI AISI-51B AISI AISI Note: The availability of the raw material is decided according to scale according to availability of raw material present in market, very commonly available 1, commonly available 3, moderately available 5 and hardly available 7. Table 6. The normalized decision matrix S.No. Alternative Cost Hardenability Chemical Mechanical Availability Materials Composition Properties (Yield Strength 1 AISI-15B AISI-10B AISI AISI-51B AISI AISI Table 7. The weighted normalized matrix Table 8. Ideal and negative ideal solutions Table 9. Separation measures

7 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp Table 10. Relative closeness values Table 13. Correlation Table Material AISI- AISI- AISI- AISI- AISI- AISI- 15B5 10B B P i Fig. 4. Relative Closeness Table 11 Alternatives of material is arranged in the descending order, according to Pi V. CORRELATION As the aim of the research work was to find out the best material for an axle in motorcycle and different rankings found for the best material for an axle in motorcycle by using fuzzy AHP and fuzzy TOPSIS method. We have to find correlation between these rankings i.e. finding the degree of relationship and the direction of relationship between two rankings. r = 1 6 i= 1 d t nn ( 1 r = 1 n 6* 8 66 ( 1 Therefore Rank correlation coefficient, r = Student's t-test for Testing Significant of Rank correlation coefficient: To test whether the rank correlation coefficient is significant or not, null hypothesis was applied. To test the null hypothesis that the sample has been drawn from a population in which the considered variables are uncorrelated i.e. H 0 : ρ = 0 H 1 : ρ > 0 So that one-tailed test should be applied. We are know that, r = and n = 6 Under H 0, we get t = r. t = n 1 r t =.44 Tabulated t_0.05 at 4 (n- degree of freedom for one-tailed test =.13, which is less than the calculated value at 5% level of significance. Hence, the data is not consistent with the hypothesis of uncorrelated population. So we can reject H 0 i.e. the null hypothesis, and conclude that the correlation coefficient is significant at 5 % level. We can say there is a significant relationship between Ranks obtained by using fuzzy AHP (R 1 and Ranks obtained by using fuzzy TOPSIS (R. VI. CONCLUSION The choice of material for a particular product is a challenging task, as the selected material directly determines the visible quality and the cost of the product. Material selection is a continuous process, aiming to choose the best material for a given application to satisfy a predetermined set of requirements. The material selection decision is made during the initial design stage of the product life cycle, i.e., when the component is first designed or when it is redesigned. An incorrectly chosen material can lead not only to a premature failure of the component, but also to an unnecessary cost. During the last few decades, many new materials and material types have been developed. At present, numerous engineering materials exist than even before. The main purpose of material selection process is to recognize the predominant selection criteria and then to obtain the most appropriate combination of those conflicting criteria according to the requirements. In this research work an attempt has been made to aid the axle manufacturing companies and the motorcycle manufacturing

8 MIT International Journal of Mechanical Engineering, Vol. 4, No. 1, January 014, pp companies to select a best material for an axle by using fuzzy AHP and fuzzy TOPSIS method. The AHP is a powerful and flexible multi-criteria decision-making tool for dealing with complex problems where both qualitative and quantitative aspects need to be considered. The AHP helps analysts to organize the critical aspects of a problem into a hierarchy rather like a family tree. In future studies, other multi-criteria methods like ANP, fuzzy PROMETHEE and ELECTRE can be used to handle material selection problems for an axle. REFERENCES 1. Ashby, MF, (000, Multi-objective optimization in material design and selection, Materials & Design, 48.. Ashby MF, Brechet YJM, Cebon D and Salvo L. (004, Selection strategies for materials and processes, Materials & Design, Chan, JWK and Tong, TKL (006, Multi-criteria material selections and end-of-life product strategy: grey relational analysis approach, Materials & Design, Cheng, AC, Chen, CJ and Chen, CY (006, A fuzzy multiple criteria comparison of technology forecasting methods for predicting the new materials development, Technological Forecasting and Social Change, Deng, YM and Edwards, KL (007, The role of materials identification and selection in engineering design, Materials & Design, Edwards, KL (005, Selecting materials for optimum use in engineering components, Mater Des, Ermolaeva, NS, Kaveline, KG and Spoormaker JL (00, Material selection combined with optimal structural design: concept and some results, Materials & Design, Jalham, IS (006, Decision-making integrated information technology (IIT approach for material selection, International Journal of Computer Applications in Technology, Kamal, M., Al-Subhi and Al-Harbi (001, Application of the AHP in project management, International Journal of Project Management, Leung, L.C. and Chao D. (000, On Consistency and Ranking of Alternatives in Fuzzy AHP, European Journal of Operational Research, Liao, TW, (1996, A fuzzy multicriteria decision-making method for material Selection, Journal of Manufacturing Systems, Opricovic S. and G.-H. Tzeng, (004, "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS", European Journal of Operational Research, Rao, R.V. and Davim, JP (007, A decision-making framework model for material selection using a combined multiple attribute decision making method, International Journal of Advanced Manufacturing Technology, Saaty, T.L. (1990, How to make a decision: The Analytic Hierarchy Process, European Journal of Operational Research, Shanian, A and Savadogo O (006, TOPSIS multiplecriteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell. Journal of Power Sources, Wang, L., J. Chu and J. Wu (007, Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy process, International Journal of Production Economics, 107.