FUZZY INFORMATION AND ENGINEERING 2020, VOL. 12, NO. 1, 1–18 https://doi.org/10.1080/16168658.2020.1775332 FUZZY TOPSIS Application in Materials Analysis for Economic Production of Cashew Juice Extractor I. Emovon and W. O. Aibuedefe Department of Mechanical Engineering, Federal University of Petroleum Resources, Eﬀurun, Nigeria ABSTRACT ARTICLE HISTORY Received 8 February 2020 In this paper, a Multi-Criteria Decision-Making (MCDM) tool which Revised 18 April 2020 combines Fuzzy Set Theory (FST) with TOPSIS (Fuzzy TOPSIS) is pre- Accepted 25 May 2020 sented for selecting optimal material for the different components of the cashew juice extractor. The technique proposed utilise a KEYWORDS broad multiple criteria methodology in finding optimal material from FUZZY TOPSIS; cashew juice among alternative materials. The alternative materials are mild steel, extractor; economic stainless steel, galvanised steel, and alloy steel. To illustrate the appli- production; decision-makers; optimal material cability of the technique, a case study of the Auger material selection problem was used. The Auger was applied for the demonstration of the proposed method because it is the most critical component of the cashew juice extractor. The result of the analysis indicated that galvanised steel is the optimal material for the Auger. To validate the FUZZY TOPSIS method, the results obtained from it were compared with results obtained from FUZZY MOORA and FUZZY SAW meth- ods. The comparative analysis indicated that FUZZY TOPSIS produces completely same result with the FUZZY SAW method and very sim- ilar results with the FUZZY MOORA method. This is an indication of the suitability of the proposed technique in resolving the material selection problem of the cashew juice extractor. 1. Introduction The cashew tree (Anacardium occidentale) is an evergreen plant that yields cashew fruit comprising of cashew seed and apple . The origin of the tree can be traced to Brazil and was introduced by Portuguese voyagers to Nigeria and other parts of the world . The fruit produced by the cashew tree consisting of the cashew apple and a raw nut (seed), are of great economic importance. This is largely due to their nutritional and medicinal value. For example, the cashew apple contains ascorbic acid, niacin and vitamin C among other vitamins and minerals needed for human body wellbeing . In the world categorisation of production of edible nut, the cashew industry was ranked third in the year 2000, with a production capacity of 2 million tonnes valued at over 2 billion US dollars . Currently, the cashew global market is estimated to be 12 billion US dollars . Brazil is rated as the highest exporter of cashew having 60% of world export whilst the highest importer is the United States also having 60% of the world import. The international CONTACT I. Emovon email@example.com © 2020 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society of China & Operations Research Society of Guangdong Province. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 I. EMOVON AND W. O. AIBUEDEFE cashew market is anticipated to remain strong even in the future due to the high demand for the cashew by-product such as cashew nut  and juice drink. The cashew apple cannot be preserved for a substantial interval of time due to their perishable nature and as such it is either eaten raw or processed into a juice drink. However, in many developing nations across the globe majority of the cashew apple produced are wasted due to mainly lack of effective and economic facility (juice extractor) to process it into juice by the rural dwellers where the bulk of the fruits are produced. To eliminate or reduce wastage to the barest minimum and also guarantee an all-time of year obtainability of the cashew juice in developing countries, researchers’ have developed a different variant of the cashew juice extractor. Ogunsina and Lucas  produced a manually operated cashew juice extractor whose design was based on the principle of a screw press. The efficiency of the system was esti- mated to be 85.38%. Aviara et al.  developed an extractor with the capability of extracting juice from different fruit apple. In similar research work, Aremu and Ogunlade  devel- oped and carried out performance evaluation of a multi-fruit juice extractor. Sylvester and Abugh  designed and constructed an extractor solely for orange juice extraction. The performance evaluation of juice extractors has been investigated in the literature. Olaniyan  investigated the performance of an orange juice extractor. Machine efficiency was esti- mated to be 57.4%. Adebayo et al.  studied the performance evaluation of a motorised pineapple juice extracting machine. The juice extraction efficiency of the machine was found to be 87.5%. From the above, analysis although different variants of cashew juice extractor have been produced, most of the machines do not meet the requirement of the end-users in most developing nations. It is either the machine is too expensive for the end-users to purchase or the juice output quality from the machine is poor. This is due to majorly improper mate- rial selection for the production of the juice extractor. For example, if the auger of the juice extractor which squeezes out the juice from the cashew apple is made from mild steel or galvanised steel to reduce production cost, the juice will be contaminated and be unfit for human consumption. To assist researchers to design and produce machines that will be more appealing to local farmers and other end-users and for sustainable economic pro- duction, there is the need for a decision support system for material analysis. The support system will select optimal material from among different alternative materials whilst simul- taneously considering different decision criteria such as cost and corrosion resistance for the production of the different components of the cashew juice extractor. In the literature MCDM tools such as AHP, TOPSIS and VIKOR have been applied in selecting appropriate material in diverse fields. The tools are well-known for resolving multi- faceted real-life problems due to their intrinsic capability to judge various alternatives with regard to different decision criteria to select the optimum alternative. Hussain and Man- dal  adapted a combination of COPRAS and MOORA methods to select the optimum material for exhaust manifold which can give maximum performance at minimum cost. The authors chose the optimum material from among alternative materials such as car- burised steel, nitrided steel, hardened alloy steel, and cast alloy steel with regard to certain decision criteria. Moradian et al.  utilised three different MCDM tools; MOORA, TOPSIS and VIKOR methods to select the most appropriate material for a braking system of a motor vehicle while considering temperature deflection, tensile strength, density and cost as deci- sion criteria. Manalo and Magdaluyo  carried out a study to identify the best material for FUZZY INFORMATION AND ENGINEERING 3 usage as an interlayer in laminated glass windshield and windows. The authors utilised the COPRAS method in resolving the material selection decision-making problem. Sen et al.  applied COPRAS, MOORA, TOPSIS, ARAS and VIKOR in selecting the optimum mate- rial for a connecting rod whilst using decision criteria such as tensile strength and fracture toughness machining. However, there is no available research in the literature to the best of our knowledge that is concerned with the analysis of optimal material for sustainable economic production of the fruit juice extractor. Hence, in this paper, a Multi-Criteria Decision-Making (MCDM) tool is presented and recommended for optimal selection of material for economic pro- duction of the cashew juice extractor. The MCDM tool presented is an aggregation of FST and TOPSIS which is referred to as FUZZY TOPSIS methodology. TOPSIS method was chosen because the process is quite simple and the solution pro- cedure does not change irrespective of the number of decision criteria and alternatives. However, the vagueness of human judgment is a challenge in the use of the MCDM tool which makes it difficult for decision-makers to assign a precise numerical value . To address the challenge of the vagueness of human judgment, the application of FUZZY Set Theory (FST) in conjunction with MCDM tools such as TOPSIS becomes imperative since the fuzzy system allows the use of linguistic variables which decision-makers are more at ease with than the use of numerical precise value. In the literature Fuzzy system has been applied in conjunction with other MCDM methods in solving multi-criteria decision problems in various fields. Chang  used a FUZZY VIKOR methodology to evaluate the quality of hospital service in Taiwan. Tolga et al.  utilised Fuzzy Tomada de Decisao Multicriterio (TODIM) technique in solving health care multi-criteria decision problem. The Fuzzy rule has also been combined with swarm intelligence to enhance its effectiveness . For example, Anter et al.  applied the combination of Fuzzy logic with whale optimisation algorithms (WOA) and chaos theory for fault detection in a water treatment plant. 2. Methodology Multi-Criteria Decision-Making (MCDM) is a systematic approach to finding the optimal option from among practicable alternatives. In most real-life problems daily encountered in the industries, hospitals, a tertiary institution among others, decision-makers are faced with the challenge of making the best decision from among different alternatives whilst considering various criteria. To solve problems of this nature, different MCDM tools such as TOPSIS and AHP are available for use. However, each of the MCDM tools has one limitation or the other. For example, in the application of the Analytic Hierarchy Process (AHP) tool, as the number of decision-makers and criteria increases the complexity of the decision-making process also increases. The vagueness of the human judgment is also a challenge in the use of the MCDM tool which makes it difficult for decision-makers to assign a precise numerical value . To address the challenge of the vagueness of human judgment, the application of Fuzzy Set The- ory (FST) in conjunction with MCDM tools such as TOPSIS becomes imperative since the fuzzy system allows the use of linguistic variables which decision-makers are more at ease with. 4 I. EMOVON AND W. O. AIBUEDEFE 2.1. FUZZY TOPSIS Method FUZZY TOPSIS is a hybrid tool that combines the benefits of the FST with the TOPSIS tech- nique for solving the multi-criteria problem. TOPSIS is an acronym for Technique for Order of Preference by Similarity to Ideal Solution and is an MCDM tool which was originated by Hwang and Yoon in 1981 . It is a technique of compensatory combination that matches a set of alternatives solutions by ascertaining weights for each criterion . In the TOP- SIS methodology, the optimum alternative is the one having the shortest distance to the positive ideal solution and farthest from the negative ideal solution . TOPSIS method was chosen because the process is quite simple and the solution pro- cedure does not change irrespective of the number of decision criteria and alternatives. However, the technique is less efficient when the decision-makers are faced with uncer- tainty and vagueness generally involved in the multi-criteria decision-making process. Zadeh introduced the FST which utilises fuzzy numbers number which is more suitable for addressing problems that are very complex and not well defined than the crisp number [22,23]. The FST is the most important tool in modelling uncertainty and the area of pro- duction management it has aided research . The tool has also made life easier today due to its ability in using the linguistic variables to model human reasoning thereby pro- viding the solution to the problem in the past without a satisfactory solution . In most multi-criteria problems, the criteria on the basis decision are made are often of incompati- ble dimensions which may create a challenge in the evaluation process and to avoid such difficulty, there is a need for the fuzzy system . Aggregating FST in TOPSIS for criteria analysis makes the evaluation process simpler . Therefore, FUZZY TOPSIS is a more real- istic model for analysing optimal material for sustainable economic production of the fruit juice extractor. The steps of the FUZZY TOPSIS algorithm can be expressed as follows . Step 1: Construction of fuzzy decision matrix Ratings are generally assigned to alternatives with regards to decision criteria using linguis- tic variables which are then translated into Triangular Fuzzy Numbers (TFN). The linguistic variables and the corresponding TFN are indicated in Table 1. The ratings of m, alternatives with respect to n, criteria by K number of experts are then applied to form a decision matrix, X , expressed as: ⎡ ⎤ k k k x x ... x 11 12 1n k k k ⎢ ⎥ x x ... x 21 22 2n ⎢ ⎥ X = (1) ⎢ ⎥ . . . . . . . ⎣ ⎦ . . . k k k x x ... x m1 m2 mn Table 1. Fuzzy linguistic terms and corresponding TFN for each criterion and alternatives [26,27]. Importance Abbreviation TFN Very low/very poor VL 1,1,3 Low/poor L 1,3,5 Medium/fair M 3,5,7 High/good H 5,7,9 Very high/very good VH 7,9,9 FUZZY INFORMATION AND ENGINEERING 5 x is the k-th expert defined rating of alternative i with respect to criterion jand ij k k k k x = (a , b , c ) ij ij ij ij Step 2. Evaluation of the combined group decision matrix The rating by K number of decision-makers can be aggregated with Equation (2) to form a combined group decision matrix, X as follows: ij k k k a = min(a ), b = b , c = max(c ) (2) ij ij ij ij ij ij k k k=1 The combined group decision matrix, X is represented as follows: ij ⎡ ⎤ ... x 11 12 1n ⎢ ⎥ ... x 21 22 2n ⎢ ⎥ X = ⎢ ⎥ (3) ij . . . . . . . ⎣ ⎦ . . . x x ... x m1 m2 mn where x = (a , b , c ) ij ij ij ij Step 3: Computing the normalised fuzzy decision matrix, p ˜ ij In this phase, the beneficial criteria and the non-beneficial criteria are identified. For exam- ple, yield strength, thermal conductivity, and corrosion resistance are beneficial criteria while the cost is a non-beneficial criterion where the minimum value is desired. For the benefit criteria, normalisation is expressed as follows: a b c ij ij ij p ˜ = , , ,if j ∈ G, c = max(c ) (4) ij ij + + + j c c c j j j While for the non-beneficial criteria, normalisation is performed as follows: − − − a a a j j j p = , , ,if j ∈ H, a = min(a ) (5) ij ij a b c ij ij ij where G and H denotes beneficial and cost criteria respectively. Step 4: Computation of the weighted normalised fuzzy decision matrix, v ˜ ij v ˜ is computed by multiplying the normalised matrix with the criteria weight as follows: ij v ˜ = p ˜ × w (6) ij ij j where w is the fuzzy importance weight for criterion j and in a scenario involving more than one decision-maker in categorising the degree of importance of criteria, it is referred to as combined group criteria weight. For example, if there are K number of decision-makers in a group decision-making process, the group criteria weight is represented as follows: k 1 2 3 k W = [w , w , w , ... , w](7) j j j j j where w is the fuzzy weight of criterion j assigned by kth decision-maker and /k /k /k w = (a , b , c ). j j j j 6 I. EMOVON AND W. O. AIBUEDEFE The combined group criteria weight is derived as follows : / /k / /k / /k a = min(a ), b = b , c = max(c ) (8) j j j j j j k k k=1 / / / Therefore, the combine fuzzy weight of criterion j is expressed as w = (a , b , c ) j j j Step 5: Evaluation of the fuzzy positive ideal solution, A and fuzzy negative ideal solution, A + − The selection of A and A is performed as follows: + + + + + A = (v ˜ ,v , ... v ˜ ), where v ˜ = max(v ˜ ) (9) ij 1 2 n j − − − − − A = (v ˜ ,v , ... v ˜ ), where v ˜ = min(v ˜ ) (10) ij 1 2 n j + − Step 6: Computation of the distance from each alternative to A and A Applying the vertex method, the distances between each alternative and A can be + + + + determined . Since v ˜ = (a , b and c )and v ˜ = (a , b and c ) the distance between ij ij ij ij j j j j them d(v ˜ , v ˜ ) canbeexpressedasfollows: ij 2 2 2 + + + + d(v ˜ , v ˜ ) = [(a − a ) + (b − b ) + (c − c ) ] (11) ij ij ij ij j j j j Following the same approach, the distance between each alternative and A can be evaluated as follows: 2 2 2 − − − − d(v ˜ , v ˜ ) = [(a − a ) + (b − b ) + (c − c ) ] (12) ij ij ij ij j j j j Therefore, with regard to the whole decision criteria, the distance of each alternative to + − A and A can be determined respectively as follows : + + Y = d(v ˜ , v ˜ ), i = 1, 2, ... , m; j = 1, 2, ... n (13) ij i j j=1 − − Y = d(v ˜ , v ˜ ), i = 1, 2, ... , m; j = 1, 2, ... n (14) ij i j j=1 Step 7: Compute the closeness coefficient (CC ) for each alternative The closeness coefficient (CC ) for each alternative is evaluated as follows: CC = (15) − + Y + Y i i The alternatives are ranked based on the CC values and the best choice is the alternative with the highest value. FUZZY INFORMATION AND ENGINEERING 7 3. Case Study The cashew juice extractor consists of different components such as the Hopper, Chop- ping unit frame, Auger and perforation screen. For sustainable economic production of the machine, the most appropriate material whilst considering multiple decision criteria must be selected for the various components. The Auger conveyor which is an assembly of the shaft and screw is the most critical component of the cashew juice extractor. The function is to provide the shearing and compressing force requires for the crushing of the cashew apple and squeezing the juice out. The Auger is applied to illustrate how suitable is the FUZZY TOPSIS method in select- ing optimal material for the sustainable and economic production of the whole machine. In the application of the Auger in demonstrating the applicability of the FUZZY TOPSIS method, two cases are considered in the decision-making process; (1) the use of a group of decision-makers in obtaining an optimal material for the Auger and, (2) the use of a single decision-maker in selecting the appropriate material for the component. 3.1. Case Study 1 3.1.1. Group Decision-Making Data Collection In this case study, a group of three decision-makers (DM1, DM2, and DM3) was used to determine the optimal material for Auger from among four alternatives (alloy steel, gal- vanised steel, stainless steel, and mild steel) based on certain decision criteria. The various criteria are; yield strength (C1), thermal conductivity (C2), corrosion resistance (C3), and cost (4). To obtain data for the FUZZY TOPSIS analysis, the three decision-makers were asked to assign a level of importance to the alternative materials using the linguistic variable scale in Table 1. The assigned linguistic variable to the alternatives by DM1, DM2, and DM3 are presented in Tables 2–4 respectively. The linguistic variable ratings in Tables 2–4 are then replaced with the corresponding TFN and results are indicated in Tables 5–7. The degree of importance of the four decision criteria was however ascertained by a single decision- maker. The ratings assigned to the decision criteria by the decision-maker are presented in Table 8. 3.1.2. Group Decision-Making Data Analysis The rating obtained from the three decision-makers in Tables 5–7 are aggregated by applying Equation (2) and the group combine decision matrix generated is indicated in Table 9. The application of Equation (2) is demonstrated with the result for, A1C1, as follows: a = min (7,5,7) = 5; b = (9 + 7 + 9) = 8.3333; c = max (9,9,9) = 9. 11 11 11 Table 2. Decision-maker 1 (DM1). Criteria Alternatives C1C2C3 C4 Alloy steel (A1) VH H H VH Galvanised steel (A2) H H M VL Stainless steel (A3) L L VH VH Mild steel (A4) M H L L 8 I. EMOVON AND W. O. AIBUEDEFE Table 3. Decision-maker 2 (DM2). Criteria Alternatives C1 C2 C3 C3 A1 H VH H VH A2 H M H L A3 VL L VH VH A4 L H M M Table 4. Decision-maker 3 (DM3). Criteria Alternatives C1 C2 C3 C4 A1 VH VH H VH A2 H H H VL A3 VL L H VH A4 L H L M Table 5. Fuzzy number representation for DM1. Alternatives C1C2C3C4 A1 799579579799 A2 579579357113 A3 135135799799 A4 357579135135 Table 6. Fuzzy number representation for DM2. Alternatives C1C2C3C4 A1 579799579799 A2 579359579135 A3 113135799799 A4 135579357357 Table 7. Fuzzy number representation for DM3. Alternatives C1C2C3C4 A1 799799579799 A2 579579579113 A3 113135579799 A4 135579135357 Having obtained the combined group decision matrix, next, the matrix is normalised using Equations (4) and (5) and the normalised matrix is shown in Table 10. The nor- malised matrix is then multiplied with decision criteria weight in Table 8 using Equation (6) to produce a weighted normalised matrix. The weighted normalised matrix is presented in Table 11. Equations (9) and (10) are then applied to data in Table 11 respectively, to + − determined A and A and the results produced are indicated in Table 12. The distance of each alternative material from A is then evaluated by using data in Tables 11 and 12 as input to Equation (11) and the results obtained are presented in Table 13. The application of Equations 11 is illustrated with results obtained for, A1C1, A1C2, FUZZY INFORMATION AND ENGINEERING 9 Table 8. Decision criteria rating. Decision criteria Linguistic rating Fuzzy number Yield strength H 5,7,9 Thermal conductivity M 3,5,7 Corrosion resistance H 5,7,9 Cost VH 7,9,9 Table 9. Combined group decision matrix. Alternatives C1C2C3C4 A1 5 8.3333 9 5 8.3333 9 5 7 9 7 9 9 A2 5 7 9 3 6.3333 9 3 6.3333 9 1 1.6667 5 A3 1 1.6667 5 1 3 5 5 8.3333 9 7 9 9 A4 1 3.6667 7 5 7 9 1 3.6667 7 1 4.3333 7 Table 10. Normalised fuzzy decision matrix based on group decision-making. Alternatives C1C2C3C4 A1 0.5556 0.9259 1.0000 0.5556 0.9259 1.0000 0.5556 0.7778 1.0000 0.1429 0.1111 0.1111 A2 0.5556 0.7778 1.0000 0.3333 0.7037 1.0000 0.3333 0.7037 1.0000 1.0000 0.6000 0.2000 A3 0.1111 0.1852 0.5556 0.1111 0.3333 0.5556 0.5556 0.9259 1.0000 0.1429 0.1111 0.1111 A4 0.1111 0.4074 0.7778 0.5556 0.7778 1.0000 0.1111 0.4074 0.7778 1.0000 0.2308 0.1429 Table 11. Weighted normalised fuzzy decision matrix based on group decision-making. Alternatives C1C2C3C4 A1 2.7778 6.4815 9.0000 1.6667 4.6296 7.0000 2.7778 5.4444 9.0000 1.0000 1.0000 1.0000 A2 2.7778 5.4444 9.0000 1.0000 3.5185 7.0000 1.6667 4.9259 9.0000 7.0000 5.4000 1.8000 A3 0.5556 1.2963 5.0000 0.3333 1.6667 3.8889 2.7778 6.4815 9.0000 1.0000 1.0000 1.0000 A4 0.5556 2.8519 7.0000 1.6667 3.8889 7.0000 0.5556 2.8519 7.0000 7.0000 2.0769 1.2857 + − Table 12. Fuzzy positive ideal solution A and negative ideal solution A based on group decision- making. A 2.7778 6.4815 9.0000 1.6667 4.6296 7.0000 2.7778 6.4815 9.0000 7.0000 5.4000 1.8000 A 0.5556 1.2963 5.0000 0.3333 1.6667 3.8889 0.5556 2.8519 7.0000 1.0000 1.0000 1.0000 and A1C3 respectively in Table 13 as follows: 2 2 2 d(v ˜ , v ˜ ) = [(2.7778 − 2.7778) + (6.4815 − 6.4815) + (9 − 9) ] = 0.000 + 2 2 2 d(v ˜ , v ˜ ) = [(1.6667 − 1.6667) + (4.6296 − 4.6296) + (7 − 7) ] = 0.000 + 2 2 2 d(v ˜ , v ˜ ) = [(2.7778 − 2.7778) + (5.4444 − 6.4815) + (9 − 9) ] = 0.5987 To calculate the distance of each alternative from A , Equation (12) is applied to data in Tables 11 and 12 and the computed results are indicated in Table 14. The application of Equation (12) is demonstrated with results obtained for A1C1, A1C2, and A1C3 respectively 10 I. EMOVON AND W. O. AIBUEDEFE Table 13. Distance of each alternative from A based on group decision-making. Alternatives C1C2C3C4 A1 0.0000 0.0000 0.5987 5.6569 A2 0.5987 1.1759 1.6826 0.0000 A3 2.5337 3.9000 0.0000 3.6389 A4 5.1753 0.9623 2.8698 1.1547 Table 14. Distance of each alternative from A based on group decision-making. Alternatives C1C2C3C4 A1 6.6732 4.3647 3.5168 0.0000 A2 5.9037 3.6409 2.9518 5.6569 A3 0.0000 0.0000 4.3382 0.0000 A4 2.1924 3.9000 0.0000 3.6389 Table 15. CC and corresponding alternatives ranking based on group decision-making. + − Alternatives Y Y (CC ) Rank i i A1 6.2556 14.5547 0.6994 2 A2 3.4573 18.1533 0.8400 1 A3 10.0726 4.3382 0.3010 4 A4 10.1620 9.7312 0.4892 3 in Table 14 as follows: − 2 2 2 d(v ˜ , v ˜ ) = [(2.7778 − 0.5556) + (6.4815 − 1.2963) + (9 − 5) ] = 6.6732 − 2 2 2 d(v ˜ , v ˜ ) = [(1.6667 − 0.3333) + (4.6296 − 1.6667) + (7 − 3.8889) ] = 4.3647 − 2 2 2 d(v ˜ , v ˜ ) = [(2.7778 − 0.5556) + (5.4444 − 2.8519) + (9 − 7) ] = 3.5168 + − Finally, utilising Equations (13)–(15), Y , Y and CC are calculated respectively and the i i results produced are shown in Tables 15. The various materials alternatives are ranked based on CC values and the rankings are also indicated in Table 15 and Figure 1. From Table 15 and Figure 1, the alternative with the ranking of 1 is the galvanised steel (A2), hence it is optimal material suitable for the Cashew juice extractor Auger. The least suitable material for the system is stainless steel (A3) having rank 4 among all alternative materials. The result of the analysis of the FUZZY TOPSIS is dependent on several factors such as the quality of the decision-makers, degree of importance attached to different deci- sion criteria. In the production of juice extracting machine, in most cases, parts having direct contact with the fruits are fabricated from stainless steel. The galvanised steel (A2) outcome of this FUZZY TOPSIS analysis was intending to produce a prototype machine at the barest minimum cost. However, production for commercial purposes more consideration should be given to the quality of juice produced from the machine rather than a cost criterion that was given the highest importance in this paper. FUZZY INFORMATION AND ENGINEERING 11 Figure 1. Alternatives, CC values, and corresponding rank based on group decision-making. Figure 2. Ranking of diﬀerent methods based on group decision-making. 3.1.3. Comparison of Methods Based on Group Decision-Making To validate the FUZZY TOPSIS technique for application in materials analysis for economic production of cashew juice extractor, the method was compared with two other MCDM approaches; FUZZY MOORA and FUZZY SAW. The three methods are very useful tools in investigating the multi-criteria decision-making problem. The comparative analysis results of the three approaches are indicated in Table 16 and Figure 2. From Table 16 and Figure 2, the FUZZY TOPSIS and FUZZY SAW method produces the same ranking for the four alternative materials. On the other hand, the FUZZY TOPSIS and FUZZY MOORA methods produce very similar results having the same ranking for alter- native materials, A3 and A4 and a rank difference of one between A1 and A2. From, the 12 I. EMOVON AND W. O. AIBUEDEFE Table 16. Ranking of diﬀerent methods based on group decision-making. Alternatives FUZZY TOPSIS FUZZY MOORA FUZZY SAW A1 2 1 2 A2 1 2 1 A3 4 4 4 A4 3 3 3 comparative analysis it is obvious that the proposed technique is a viable tool for solv- ing the material selection problem for the cashew juice extractor. Although the approach was applied in analysing material selection problem for the cashew juice extractor, the technique is also capable of solving other multi-criteria decision problem. The Spearman rank correlations test has also been used by different authors in the literature to show the degree of similarity among the various MCDM tools see the work of [30,31]. On this basis, the Spearman rank correlation test was carried out. The evaluated Spearman rank correla- tion coefficient between FUZZY TOPSIS and FUZZY MOORA; FUZZY TOPSIS and FUZZY SAW of 0.8095 and 1 respectively further indicated the viability of the proposed FUZZY TOPSIS methodology. 3.2. Case Study 2 3.2.1. Data Collection In many real-life problems, multiple decision-makers are generally involved in the decision- making process, however, in some scenarios, a single decision-maker is utilised in obtaining the appropriate solution. This case study is used to demonstrate analysis involving a single decision-maker. In case study 1, a group of three decision-makers (DM1, DM2, and DM3) was used to ascertain the best material for the Auger from among four alternatives with respect to four decision criteria. Since, case study 2 involves the use of a single decision-maker in the decision-making process, DM1 data in Table 5 is utilised as input data for the FUZZY TOPSIS method analysis. The rating assigned to the decision criteria (C1, C2, C3, and C4) in Table 8 used for the FUZZY TOPSIS analysis in case study 1 is also used as criteria weights in case study 2. 3.2.2. Data Analysis The FUZZY TOPSIS analysis for a decision-making process involving a single decision-maker starts with decision matrix normalisation as opposed to the group decision-making pro- cess which begins with individual rating aggregation. Applying Equations (4) and (5) to data in Table 5, the normalised matrix is generated and the result is shown in Table 17. The weighted normalised matrix is then obtained by applying Equation (6) to data in Tables 8 and 17 and the result produced is presented in Table 18. Having evaluated the weighted normalised matrix, the Fuzzy positive idea solution and Fuzzy Negative solution are obtained by applying Equation 9 and 10 to data in Table 18 respectively, and the results + − generated are presented in Table 19. The distances of each alternative from A and A are then obtained by applying Equations (11) and (12) to data in Tables 18 and 19 respectively + − and the results produced are shown in Tables 20 and 21. Finally, Y , Y and CC are evalu- i i ated by applying Equations (13)–(15) to data in Tables 20 and 21 and the results obtained FUZZY INFORMATION AND ENGINEERING 13 Table 17. Normalised decision matrix. Alternatives C1C2C3C4 A1 0.7778 1.0000 1.0000 0.5556 0.7778 1.0000 0.5556 0.7778 1.0000 0.1429 0.1111 0.1111 A2 0.5556 0.7778 1.0000 0.5556 0.7778 1.0000 0.3333 0.5556 0.7778 1.0000 1.0000 0.3333 A3 0.1111 0.3333 0.5556 0.1111 0.3333 0.5556 0.7778 1.0000 1.0000 0.1429 0.1111 0.1111 A4 0.3333 0.5556 0.7778 0.5556 0.7778 1.0000 0.1111 0.3333 0.5556 1.0000 0.3333 0.2000 Table 18. Weighted normalised matrix. Alternatives C1C2C3C4 A1 3.8889 7.0000 9.0000 1.6667 3.8889 7.0000 2.7778 5.4444 9.0000 1.0000 1.0000 1.0000 A2 2.7778 5.4444 9.0000 1.6667 3.8889 7.0000 1.6667 3.8889 7.0000 7.0000 9.0000 3.0000 A3 0.5556 2.3333 5.0000 0.3333 1.6667 3.8889 3.8889 7.0000 9.0000 1.0000 1.0000 1.0000 A4 1.6667 3.8889 7.0000 1.6667 3.8889 7.0000 0.5556 2.3333 5.0000 7.0000 3.0000 1.8000 + − Table 19. Fuzzy positive ideal solution A and negative ideal solution A A 3.8889 7.0000 9.0000 1.6667 3.8889 7.0000 3.8889 7.0000 9.0000 7.0000 9.0000 3.0000 A 0.5556 2.3333 5.0000 0.3333 1.6667 3.8889 0.5556 2.3333 5.0000 1.0000 1.0000 1.0000 Table 20. Distance of each alternative from A . Alternatives C1C2C3C4 A1 0.0000 0.0000 1.1036 5.8875 A2 1.1036 0.0000 2.4910 0.0000 A3 4.0367 2.3376 0.0000 5.8875 A4 2.4910 0.0000 4.0367 3.5325 Table 21. Distance of each alternative from A . Alternatives C1C2C3C4 A1 4.0367 2.3376 3.1945 0.0000 A2 3.1945 2.3376 1.5972 5.8875 A3 0.0000 0.0000 4.0367 0.0000 A4 1.5972 2.3376 0.0000 3.6804 are presented in Table 22 and Figure 3. The different materials alternatives are ranked with respect to CC values and the rankings produced are also shown in Table 22 and Figure 3. It is obvious from Table 22 and Figure 3, the optimum material is galvanised steel, A2, having rank 1 while the worst material is stainless steel, A3, having rank 4 among the four alternative materials. This result generated whilst utilising a single decision-maker, in the decision-making process is completely the same result previously obtained when three Table 22. CC and corresponding alternatives rank- ing. + − Alternatives Y Y CC Rank A1 6.9912 9.5688 0.577826 2 A2 3.5946 13.0169 0.783606 1 A3 12.2618 4.0367 0.247671 4 A4 10.0602 7.6153 0.430838 3 14 I. EMOVON AND W. O. AIBUEDEFE Figure 3. Alternatives, CC values, and corresponding rank. Table 23. Ranking of the proposed method in compari- son with other methods. Alternatives FUZZY TOPSIS FUZZY MOORA FUZZY SAW A1 2 1 2 A2 1 2 1 A3 4 4 4 A4 3 3 3 decision-makers were used in the decision-making process. This could be attributed to the similarity of the rating assigned to the four alternative materials against the four decision criteria by the three decision-makers; DM1, DM2, and DM3 as DM 1 rating were applied as input data for TOPSIS analysis in case study 2. If the degree of similarity of the rating assigned by the three decision-makers was low there would have been a difference in the results obtained from the single decision-makers decision-making scenario; case study 2 and the group decision-makers decision-making scenario; case study 1. 3.2.3. Comparison of Methods To further validate the FUZZY TOPSIS methodology for the analysis of material selection for cashew juice extractor, the results obtained from the single decision-maker rating are compared with FUZZY MOORA and FUZZY SAW methods. The results of the comparative analysis are shown in Table 23. From Table 23 and Figure 4, the three techniques rank alternative materials A3 and A4 the same, representing 50% of the overall materials having the same ranking. Comparing the FUZZY TOPSIS and FUZZY SAW methods, it can be observed that the duo produces the same ranking for all alternative materials. On the other hand, comparing FUZZY TOPSIS and FUZZY MOORA methods, it is obvious that the results produce by both techniques are very similar with both methodologies having the same rank for alternative materials, A3 and FUZZY INFORMATION AND ENGINEERING 15 Figure 4. Ranking of diﬀerent methods. A4 and a rank difference of one between A1 and A2. The Spearman rank correlation coeffi- cient between FUZZY TOPSIS and FUZZY MOORA; FUZZY TOPSIS and FUZZY SAW were also evaluated and results obtained are 0.8095 and 1 respectively. This has further shown that the proposed FUZZY TOPSIS methodology is capable of addressing the material selection analysis problem of the cashew juice extractor. 4. Discussion of Results Improper material selection may lead to the requirement of customers and manufacturers not being satisfied . It can also lead to failure of an assembly and reduction in product performance, thus efficiency and profitability affected adversely and organisation repu- tation damaged . To properly select materials for sustainable cashew juice extractor production and also produce a machine that will meet the requirement of the end-users of the product in developing countries, this paper presented a FUZZY TOPSIS methodol- ogy for solving a material selection problem. The technique proposed uses a multi-criteria methodology in finding optimal material from among alternative materials. The ‘Auger’ which is the most critical component of the cashew juice extractor was utilised to illustrate the applicability of the FUZZY TOPSIS method. In the application, two cases were consid- ered in the decision-making process. In Case 1 three decision-makers were involved in the decision-making process while in case 2 a single decision-maker was used in the decision- making process. The results obtained from the analysis of the FUZZY TOPSIS technique in case 1, indicated that galvanised steel (A2) is the optimum materials for the Auger having the highest performance value of 0.8400 while stainless steel (A3) is the least suitable mate- rial having the lowest performance value of 0.3010. The results of the analysis of the TOPSIS method were compared with that of the FUZZY MOORA and FUZZY SAW method to val- idate the proposed methodology. The comparative analysis indicated that FUZZY TOPSIS produces completely the same result with FUZZY SAW methods and very similar results with the FUZZY MOORA method and this is an indication of the viability of the proposed 16 I. EMOVON AND W. O. AIBUEDEFE methodology for the analysis of material selection problem of the cashew juice extractor. On the other hand, the result obtained from case 2 also showed that the best material for the Auger is the galvanised steel (A2) having the highest performance value of 0.7836 while the worst material is stainless steel (A3) having the lowest performance index of 0.2477. A comparative analysis was also carried out and the result of the analysis showed that FUZZY TOPSIS produced completely the same result with the FUZZY SAW method while it produces a very similar result to the FUZZY MOORA method. The ideal choice for the Auger would have been either the stainless steel or alloy steel since the Auger has direct contact with juice in the extraction process. However, the poor choice of material in the two case studies is as a result of the input data used in the analysis of the FUZZY TOPIS method. The decision-makers targeted galvanised steel and assigned the highest ratings to it with respect to almost all decision criteria including cost criterion. This is because their major consideration was reducing cost of production to the barest minimum with- out actually putting into consideration juice output quality. However, when producing for commercial purpose more consideration should be given to the quality of juice produced from the machine rather than a cost criterion that was given the highest importance in this paper. It could be concluded that the result of the FUZZY TOPSIS method and other similar techniques in the literature is dependent on the quality of decision-makers, the number of decision-makers and weight attached to the different decision criteria among other. 5. Conclusion In many developing nations across the globe, the majority of fruits produced are wasted due to mainly lack of economic facility to process it into juice and other by-products by the rural dwellers where the bulk of the fruits are produced. In this paper, a methodology that combines FST with TOPSIS referred to as FUZZY TOPSIS is presented for selecting the optimal material for economic production of the cashew juice extractor. The applicability of the technique was illustrated with a case of the Augur one of the most critical compo- nents of the cashew juice extractor. The investigation result showed that Galvanised steel is the optimal material for the production of cashew juice extractor Auger. To ascertain the suitability of the FUZZY TOPSIS method, the results obtained from it was compared with FUZZY MOORA and FUZZY SAW technique. The comparative analysis results indicated that the FUZZY TOPSIS method produces completely same result with the FUZZY SAW method and very similar results with the FUZZY MOORA method. However, the result of analysis using the proposed technique and other techniques in the literature is dependent on the quality of decision-makers, the number of decision-makers and weight attached to the dif- ferent decision criteria. It is therefore recommended that excellent decision-makers should be engaged to achieve an optimal result. Although in this paper, the FUZZY TOPSIS method was specifically designed for analysing cashew juice extractor material selection problem, in practice, the approach can be implemented in solving other multi-criteria material selec- tion problems. For future work, the application of other MCDM tools such as ELECTRE, PROMETHEE, and TODIM in conjunction with FST could be exploited for analysing mate- rial selection problem of the cashew juice extractor. Furthermore, sensitivity analysis can be carried out to determine the impact of ranking parameter changes on the optimum solution. FUZZY INFORMATION AND ENGINEERING 17 Disclosure statement No potential conflict of interest was reported by the authors. Notes on contributors I. Emovon is an Associate Professor in the Department of Mechanical Engineering at the Federal Uni- versity of Petroleum Resources, Effurun, Nigeria. He obtained his PhD degree in Maritime Technology from Newcastle University, Newcastle Upon Tyne, United Kingdom. His research interest includes engineering system risk analysis, reliability analysis and multi-criteria decision making in industrial system environment. The author has published several papers in reputable international Journals such Applied Energy, Applied Ocean Research and Ocean Engineering and he is a reviewer to some of these Journals. W. O. Aibuedefe received his B. Eng. Degree from the Department of Mechanical Engineering at the Federal University of Petroleum Resources, Effurun, Nigeria. 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Fuzzy Information and Engineering
– Taylor & Francis
Published: Jan 2, 2020
Keywords: FUZZY TOPSIS; cashew juice extractor; economic production; decision-makers; optimal material