Decision-making can be defined as the process of identifying the optimum solution, especially when multiple and typically conflicting criteria must be considered. Although many Multi-Criteria Decision-Making (MCDM) methods exist, most rely on linear normalization, which may not reflect the nonlinear perception of decision makers regarding changes in criterion values. To address this limitation, this study proposes a novel MCDM method called SINCOS (SINe-COSine). The SINCOS method is based on trigonometric functions: the sine function is used for criteria to be maximized, and the cosine function is used for criteria to be minimized. The performance validation of the method was done through a synthetic case study for which the SINCOS achieved 100% accuracy by successfully reproducing the predefined ranking of eight alternatives. The applicability of the SINCOS method was demonstrated on a real data set to evaluate the environmental sustainability of five countries, i.e., Sweden, Brazil, Germany, India, Canada, Nigeria, China, and the United Arab Emirates. Seven indicators were considered: energy consumption, nuclear and alternative energy, carbon intensity of gross domestic product (GDP), electricity generation from renewable sources, carbon dioxide emissions (CO₂), total natural resource rents, PM2.5 air pollution, and electric power use. The results show that Sweden achieved the highest sustainability score, followed by Brazil, Germany, Canada, India, Nigeria, China, and the United Arab Emirates. The SINCOS method was also compared with some of the highly preferred methods in the literature, namely Multi-Attributive Border Approximation Area Comparison (MABAC), Multi-Attributive Ideal-Real Comparative Analysis (MAIRCA), and Complex Proportional Assessment (COPRAS), using Spearman’s rank correlation and Kendall’s tau coefficient tests. The test results indicated strong agreement among the methods. However, the SINCOS method provides interpretable results by clearly revealing the criteria that have greater influence on the ranking of alternatives, and it uses simple calculations that make it computationally efficient.
Karagul et al. (Thu,) studied this question.