Material selection, driven by wide and often conflicting objectives, is an important, sometimes difficult problem in material engineering. In this context, multi-criteria decision-making (MCDM) methodologies are effective. An approach of MCDM is needed to cater to criteria of material assortment simultaneously. More firms are now concerned about increasing their productivity using mathematical tools. To occupy a gap in the previous literature this research recommends an integrated MCDM and mathematical Bi-objective model for the selection of material. In addition, by using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), the inherent ambiguities of decision-makers in paired evaluations are considered in this research. It goes on to construct a mathematical bi-objective model for determining the best item to purchase.

The entropy perspective is implemented in this paper to evaluate the weight parameters, while the TOPSIS technique is used to determine the best and worst intermediate pipe materials for automotive exhaust system. The intermediate pipes are used to join the components of the exhaust systems. The materials usually used to manufacture intermediate pipe are SUS 436LM, SUS 430, SUS 304, SUS 436L, SUH 409 L, SUS 441 L and SUS 439L. These seven materials are evaluated based on tensile strength (TS), hardness (H), elongation (E), yield strength (YS) and cost (C). A hybrid methodology combining entropy-based criteria weighting, with the TOPSIS for alternative ranking, is pursued to identify the optimal design material for an engineered application in this paper. This study aims to help while filling the information gap in selecting the most suitable material for use in the exhaust intermediate pipes. After that, the authors searched for and considered eight materials and evaluated them on the following five criteria: (1) TS, (2) YS, (3) H, (4) E and (5) C. The first two criteria have been chosen because they can have a lot of influence on the behavior of the exhaust intermediate pipes, on their performance and on the cost. In this structure, the weights of the criteria are calculated objectively through the entropy method in order to have an unbiased assessment. This essentially measures the quantity of information each criterion contribution, indicating the relative importance of these criteria better. Subsequently, the materials were ranked using the TOPSIS method in terms of their relative performance by measuring each material from an ideal solution to determine the best alternative. The results show that SUS 309, SUS 432L and SUS 436 LM are the first three materials that the exhaust intermediate pipe optimal design should consider.

The material matrix of the decision presented in Table 3 was normalized through Equation 5, as shown in Table 5, and the matrix was multiplied with weighting criteria ß_j. The obtained weighted normalized matrix V_ij is presented in Table 6. However, the ideal, worst and best value was ascertained by employing Equation 7. This study is based on the selection of material for the development of intermediate pipe using MCDM, and it involves four basic stages, i.e. method of translation criteria, screening process, method of ranking and search for methods. The selection was done through the TOPSIS method, and the criteria weight was obtained by the entropy method. The result showed that the top three materials are SUS 309, SUS 432L and SUS 436 LM, respectively. For the future work, it is suggested to select more alternatives and criteria. The comparison can also be done by using different MCDM techniques like and Choice Expressing Reality (ELECTRE), Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE).

The results provide important conclusions for material selection in this targeted application, verifying the employment of mutual entropy-TOPSIS methodology for a series of difficult engineering decisions in material engineering concepts that combine superior capacity with better performance as well as cost-efficiency in various engineering design.