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.

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.

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To evaluate the quality of cast aluminum alloys quantitatively and intuitively, quality index and quality map have been used. Quality index and quality map are to quantitatively evaluate the quality of cast aluminum alloys according to yield strength (YS), ultimate tensile strength (UTS), elongation to fracture (Ef), and strain energy density (W). There are some quality indices such as Q, QR, QC, and Q0. The quality maps are generated to intuitively evaluate the quality level based on the quality indices. These quality indices and quality maps show the quality levels according to the pairs of tensile mechanical properties such as UTS and Ef, or YS and Ef, or YS and W. By using these quality maps, it is impossible to directly evaluate the quality levels according to the artificial aging heat treatment condition. We develop multiple quadratic polynomial regression models and quality maps for tensile mechanical properties and quality indices of the cast aluminum alloys according to artificial aging heat treatment condition. The performances of the regression models are evaluated using the mean absolute errors, mean relative errors, and coefficients of determination. The regression models and quality maps could be widely used to evaluate the quality of the cast aluminum alloys according to the aging heat treatment conditions and determine the rational aging heat treatment condition.

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