## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Considered Criteria Number**} & \multicolumn{4}{c}{**The Relative Closeness of the Universities**} \\ \cline{2-5}  & **SU** & **KUT** & **AUT** & **IUST** \\ \hline \(1\) & 0 & 0.55 & 0 & \(1\) \\ \(1\) and 2 & 0 & 0.60 & 0.40 & \(1\) \\ \(1\), 2 and 3 & 0.44 & 0.32 & 0.17 & 0.67 \\ \(1\), 2, 3 and 4 & 0.26 & 0.48 & 0.38 & 0.81 \\ \(1\), 2, 3, 4 and 5  
- According to Table 6, the standard deviation of the values for relative proximity is somewhat greater than 0.1 for rows 6 and 9, almost equal to 0.05 (the minimum value) for rows 2 and 5, and ranges from 0.1 to 0.05 in the remaining cases. Accordingly, it can be claimed that eliminating quality criteria 2 and 5 and adding quality criteria 6 and 9 causes the least change in the relative closeness values for each of the four universities. In other words, of the nine quality criteria considered, these four quality characteristics had the most influence on the superiority of institutions over one another based on the relative closeness coefficient. - The standard deviation of relative proximity values fluctuates in most rows of Table 6 within a relatively small range of 0.1 to 0.05, indicating that there is intense competition among the four universities for the best academic programs. The probability of changing the preferred universities' rankings and domination over the others in subsequent years is very high. According to the data in this table, institutions are highly competitive, and their relative proximity to one another is changing. - The IUST has the lowest and highest values of the standard deviation of the data in each column, respectively, of 0.04 and 0.09, according to Table 6 and simple calculations. For the other universities, the standard deviation is roughly 0.05. It can be inferred that IUST's integrated management for the concurrent control and promotion of the nine quality criteria is reasonably good and that each of the quality criteria has been thoroughly taken into account. Namely, the values assessed for this university's quality criteria are not significantly different, and eliminating each of the quality criteria has no significant impact on this university's superiority over the other three universities. In contrast, some quality standards of AUT are substantially higher than at other universities, while others are significantly lower. - When the data in Tables 4 and 5 are compared, it is clear that IUST is closer to the positive ideal than the other three universities, except for row 4 of Table 6, where SU has the best performance with a relative closeness of 0.52. This demonstrates that the values chosen for criterion 4, the teaching role, at IUST, are high and significant from the perspective of the competent people who submitted the surveys. AUT is in direct competition with IUST, according to rows 1, 3, and 7 of Table 6.  
Because relative comparison occurs in MCDM approaches [30; 49; 56], there is a periodic fluctuation in the results values caused by reducing or increasing one or more criteria. The relative-closeness coefficient is employed in this study for the AHP-TOPSIS approach, which analyses and evaluates four universities. This characteristic of MCDM approaches allows for the application of Fourier series expansion [78] to determine the significance of criteria and evaluate the situation more clearly. However, the Taylor series expansion [79] can also be used to evaluate the obtained results by taking into account related considerations and assumptions. A Fourier series is a periodic function extension in terms of an infinite algebraic sum of sines and cosines functions that form a link between these two types of trigonometric functions. Figure 3 depicts the change in relative-closeness coefficients based on the number of quality criteria for the problem as well as the relative-closeness coefficients, as shown in Table 5, except for its first row. It is worth noting that using only one criterion resulted in fitting curves falling down the horizontal axis.