## 4 WASPAS Multi-Objective Assessment
### Implementation of WASPAS Optimization  
To ensure convenience, the weight for the decision matrix is initially determined using the entropy method, a widely used technique in research and decision-making processes. The initial step in the research process involved the calculation of the Normalized Decision Matrix using Equations (1) and (2). In this current work, low value criteria have been followed for all the responses and evaluated by Equation (2). The estimated normalized results are shown in Table S1 (Supplementary File). Pij is calculated using Equation (6). To determine the entropy of the normalized matrix, it is necessary to analyze the distribution of values within the matrix. The entropy of a matrix can be calculated using information theory principles, which quantify the uncertainty or randomness present in the data. For determining the entropy of the normalized matrix, the first calculation of Eij has been performed, where Eij = Pij-In Pij. The results of Pij and Eij are displayed in Table S2 (Supplementary File). Moreover, the results of entropy of the normalized matrix Eij and entropy weight Wj are shown in Table S3 (Supplementary File). The determination of weight is achieved through the utilization of the principle of entropy, as described using Equation (9). The weights for all parameters have been determined, and now these weights (Wj) will be employed to ascertain the rank and identify the optimal input parameter using the Weighted Aggregated Sum Product Assessment (WASPAS) method. In this study, the total relative importance matrices are calculated using the Weighted Sum Model (WSM) method, as described by Equation (3), and values are displayed in Table S4 (Supplementary File). The total relative importance matrices are computed using the Weighted Product Model (WPM) method, as described using Equation (4) and displayed in Table S5 (Supplementary File). For the \(\lambda\) value, when we assign \(\lambda\) = 0 in Equation (5), Qi = Qi(2), exhibiting a resemblance to the concept of WPM. Similarly, when we assign \(\lambda\) = 1 in Equation (5), Qi = Qi(1), which resembles to the concept of WSM (Weighted Sum Model).  
The WASPAS method is a widely used approach in decision-making research. It encompasses several key steps, including the normalization of the decision matrix, the assessment of entropy for the normalized matrix, the determination of relative importance for each criterion, and the utilization of entropy to derive weights for the criteria. These steps collectively contribute to the overall effectiveness and reliability of the WASPAS method in decision-making processes. The weights are subsequently utilized in the WSM and WPM methodologies to derive total relative importance matrices. The Cumulative Relative Relevance Index is computed (Qi = 0.5) using Equation (5) and is shown in Table 7. From Table 7, it is observed that run 9 has the possible optimal input parameters (ap= 0.3 mm; s = 0.05 mm/rev; v = 210 m/min and q = 50 mL/hr) for achieving optimal results. In the seventh run of the experiment, it was observed that the cutting temperature reached its highest point. This increase in temperature was attributed to the combination of the highest speed and lowest flow rate. Consequently, the elevated cutting temperature had a detrimental effect on both the tool and the workpiece surfaces, resulting in rougher surfaces. The highest value of noise was observed in this particular run due to the high friction between the tool tip and workpiece. This increased the cutting force, resulting in higher power consumption during the machining operation. From the ranking of Cumulative Relative Relevance Index, run 7 has the lowest rank, which indicates the worst input parameter during the experiment and can be recommended to avoid this parameter during the hard turning of AISI 52100 steel.