*2.2. Ranking*

We evaluated the decision matrix (Table A2) by several multiple MADM methods. MADM refers to making preference decisions by evaluating and prioritizing alternatives on multiple attributes [22,23]. Distinct components of the MADM are (i) the decision matrix, which comprises the alternatives and the attributes, and (ii) attribute weights: the priorities of attributes are expressed quantitatively according to the MADM theory—they quantify the relative importance of each of the attributes [22,23,53]. The attribute weights

are typical of three types [53]: (a) objective weights—based on the decision matrix utilizing mathematical models without considering the decision maker's preferences (e.g., mean weighing, standard deviation method, entropy, etc.), (b) subjective weights, based on the preference derived from the evaluations of the experts (from their previous experience) or designers (constraints of design), or both, and (c) integrated weights, as the name suggests, both objective and subjective weighting are combined to determine the weights. We adopted objective and subjective attribute weights in this investigation.

We evaluated the weights by assigning equal weights (1/3) for each of the attributes based on the understanding of these materials and their intended application. We identified twelve MADM methods to evaluate the data matrix and rank the alloys, including the simple additive weighting (SAW) [22,23,53–55], range of value method (ROVM) [56,57], additive ratio assessment method (ARAS) [58–60], combined compromise solution (CoCoSo) [61–63], operational competitiveness ratio (OCRA) [64–66], simple multi-attribute rating technique (SMART) [22,53,67,68], weighted Euclidean distance-based approach (WEDBA) [23,69,70], multi-attributive border approximation area comparison (MABAC) [71,72], multi-objective optimization on the basis of ratio analysis (MOORA) [73,74], technique of order preference by similarity to ideal solution (TOPSIS) [22,53,75,76], multi-criteria optimization and compromise solution (VIKOR)—the Serbian name is VIse Kriterijumska Optimizacija Kompromisno Resenje—method [77–79], and measurement of alternatives and ranking according to compromise solution (MARCOS) [80,81]. Each MADM approach comprises a unique mathematical aggregation procedure to rank the alternatives. The MADMs identified were diverse. Applying such distinct aggregation procedures is likely to generate a robust set of ranks of the alternatives. The ranks produced by each method, as would be expected, are likely to deviate from one another; nevertheless, the correlation among the various techniques is expected to strengthen the reliability of the results. The modus operandi was soft coded in Microsoft Excel, as formulated in the respective references of MADMs.

#### *2.3. Analyses*

The ranks obtained by various MADMs were correlated. We evaluated Spearman's correlation coefficients [82,83] among the ranks obtained from the 12 MADMs. We consolidated the ranks from various MADMs by estimating their mean and by principal component analysis (PCA). PCA, a multivariate technique, reduces the dimensionality of a dataset consisting of several interrelated variables by transforming to a new set of variables termed the principal components (PCs), which are uncorrelated and are ordered so that the first few PCs (typically one or two) retain most of the variation present in the original data [28,29]. The score plot presents a visual representation of the rank evaluation. The analyses were carried out using the commercial software Minitab® 20.
