The aim of this paper is to propose the methods to select reasonable normalization method in TOPSIS and decide best optimal material combined with individual results from TOPSIS with some popular normalization methods. In this paper, to evaluate performance of normalization method, entropy-based and variation coefficient-based performance scores are introduced. To decide final result of materials selection combined with individual results from TOPSIS with different normalization methods, final rank index of alternative material is proposed. To verify the effectiveness of the proposed methods, TOPSIS with some popular normalization methods is applied to select optimal tribological coating material. As a result, it is desirable to select the normalization method with highest entropy-based and variation coefficient-based performance scores. In order to select best optimal material using TOPSIS with some popular normalization methods, the method to decide final result of materials selection is proposed by using final indices of alternative materials. The proposed methods may be widely used to solve the materials selection problems in engineering practice.

Technique for order preference by similarity to ideal solution (TOPSIS) is a well-known multi attribute decision making (MADM) method and it has been widely used in materials selection. However, the main drawback of the traditional TOPSIS is that it has a rank reversal phenomenon. To overcome this drawback, we propose an improved TOPSIS without rank reversal based on linear max-min normalization with absolute maximum and minimum values by modifying normalization formula and ideal solutions. Moreover, to study the impacts of changing attribute weights on relative closeness values of alternatives, we propose a sensitivity analysis method to attribute weights on the relative closeness values of the alternatives. We applied the proposed method to select best absorbent layer material for thin film solar cells (TFSCs). As a result, copper indium gallium diselinide was selected as the best one and the next cadmium telluride from among five materials. When the alternative is added to or removed from the set of original alternatives, the elements of the normalized decision-matrix, PIS, NIS and the relative closeness values don’t change at all, they are always coincide with the corresponding elements of the original ones. The relative closeness values are absolute values irrelevant to the composition of the alternatives in the improved TOPSIS, while the relative closeness values are relative values relevant to the composition of the alternatives in the traditional TOPSIS. Therefore, the proposed TOPSIS overcomes the rank reversal phenomenon, perfectly. It could be actively applied to practical problems for materials selection.

The analytic hierarchy process has been widely used to determine subjective weights of materials selection criteria in materials selection using multi-criteria decision-making. However, the analytic hierarchy process has some drawbacks: it is difficult to construct a pairwise comparison matrix and meet the consistency requirement. First, we propose a new simplest questionnaire to perform the pairwise comparison without confusion, conventionally and easily. Next, we propose an improved modifying method for inconsistent pairwise comparison matrix according to the following principles: (1) the elements of the reconstructed pairwise comparison matrix should be nine-point scales, (2) the number and modifying the amount of the modified elements should be as small as possible and (3) the deviation between the original and reconstructed pairwise comparison matrixes should be as small as possible. The outline of the proposed modifying method is as follows: (1) calculate the consistency ration decrements of all the pairwise comparison matrixes reconstructed by modifying every element of the original pairwise comparison matrix to the lower and upper adjacent nine-point scales and (2) find the element with the maximum consistency ratio decrement and modify it to the lower or upper adjacent scale. To illustrate the effectiveness, we apply the proposed methods to determine the criteria weights for selecting the best phase change material used in a solar domestic hot water system, and apply the proposed modifying method to some examples from the published papers, and compare the performances with some previous methods. The simplest questionnaire and improved modifying method help materials designers and engineers to apply the analytic hierarchy process method in materials design and optimization problems, much more actively.

Analytic hierarchy process (AHP) is a well-known attribute weighting method in multiattribute decision-making. Its major requirement is to satisfy the consistency of pairwise matrix (PM). To solve this problem, we first propose a new consistency improvement method of PM based on consistency ratio (CR) decreasing rate. In this method, we calculate the CR decreasing rates of all the PMs reconstituted by replacing all elements of the PM with the lower and upper neighbouring 9-point scales and find the element with maximum CR decreasing rate, and then modify it to its lower or upper neighbouring scale. Second, we develop third-order approximate polynomial for random consistency index using least square method. It enables to determine the RI value according to the number of attributes without a numerical table. Third, we propose the final PM determining method and final attribute weighting method considered decision makers’ levels based on the CR values of the individual PMs in case several decision makers perform their own pairwise comparisons. We test the performances of the proposed and some previous consistency improvement methods with two numerical examples. The results demonstrate that the proposed method improves the consistency of PM better and faster with smaller amount of modification than that of the previous methods, while it modify the elements of the PM to 9-point scales, necessarily. We apply the proposed method to hip joint prosthesis material selection. The proposed methods may be widely used in practical applications of AHP.

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