## 4 Results and Discussions
### Experimental Results
Furthermore, the existing strategies have been compared with the proposed mechanism, which will be discussed in the subsequent section. The final values for positional score, OWA (at least half), OWA (as many as possible), OWA (most), and OWA (most preferred first) for books on Data Structure (DS) are shown in Table 6. The tabulated score indicates which method to consider the best for the books concerned. The procedure for calculation of OWA (most preferred first) using positional score is as follows:  
The positional scores (for DS1) are represented as:  
\[C_{k}=\left( \begin{array}{c}1\\ 0\\ 0\\ 0.9375\\ 0\\ 0\\ 0\end{array} \right)\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Rank Position**} & \multicolumn{1}{c}{**Book Code**} & \multicolumn{1}{c}{
\begin{tabular}{c} **Score Obtained Using OWA (Most** \\ **Preferred First) Techniques** \\ \end{tabular} } \\ \hline
1 st & DS.9. & 0.4642 \\ \hline
2 nd & DS.1. & 0.450813 \\ \hline
3 rd & DS.3. & 0.408413 \\ \hline
4 th & DS.10. & 0.406175 \\ \hline
5 th & DS.8. & 0.395025 \\ \hline
6 th & DS.4. & 0.25 \\ \hline
7 th & DS.12. & 0.25 \\ \hline
8 th & DS.15. & 0.25 \\ \hline
9 th & DS.5. & 0.234375 \\ \hline
10 th & DS.14. & 0.234375 \\ \hline
11 th & DS.16. & 0.234375 \\ \hline
12 th & DS.6. & 0.21875 \\ \hline
13 th & DS.13. & 0.21875 \\ \hline
14 th & DS.2. & 0.2142 \\ \hline
15 th & DS.7. & 0.203125 \\ \hline
16 th & DS.11. & 0.203125 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Final scores and ranked list of books on Data Structure using OWA (most preferred first). \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Ranked University**} & \multicolumn{1}{c}{**Weights Assigned**} \\ \hline Univ\_1 & W1 = 0.25 \\ \hline Univ\_2 & W2 = 0.21428 \\ \hline Univ\_3 & W3 = 0.17857 \\ \hline Univ\_4 & W4 = 0.14285 \\ \hline Univ\_5 & W5 = 0.10714 \\ \hline Univ\_6 & W6 = 0.07142 \\ \hline Univ\_7 & W7 = 0.03571 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Weights assigned to universities by using OWA (most preferred first). These values are re-ordered and represented in descending order. Let the order be \(d_{k}\). The re-ordered value shall be represented as:  
\[d_{k}=\left( \begin{array}{c}1\\ 0\\ 0\\ 0.9375\\ 0\\ 0\\ 0\end{array} \right)\]  
From Equations (4) and (5), we get:  
\[\text{OWA (most preferred first)}=\text{OWA}(d_{1},d_{2},\ \ldots\ldots,d_{n})= \sum_{k=1}^{n}(W_{k}C_{k})\]  
Therefore, we obtain OWA \((d_{1},d_{2},\ \ldots\ldots,d_{n})\) as:  
\[=\ [0.25,\ 0.21428,\ 0.17857,\ 0.14285,0.10714,0.07142,0.03571]\ \times\left( \begin{array}{c}1\\ 0\\ 0.9375\\ 0\\ 0\\ 0\end{array} \right)\]  
\[=(0.25\times 1+0.21428\times 0+0.17857\times 0+0.14285\times 0.9375+0.10714 \times 0+0.07142\times 0+0.03571\times 0)\]  
These scores are calculated for all the books, and the scores help in sorting the books, which provides a platform for the ranking of the books for the above method. The final OWA scores with the ranking of the respective books for the linguistic quantifier'most preferred first' are shown in Table 6.  
The OWA (most preferred first) score comes out to be 0.450813 for DS1, as shown in Section 4.2. Similarly, values for all books have been calculated. With the help of the proposed mechanism, the above scores are calculated, which lays a foundation for the ranking of the books by different approaches. The ranking for books on DS for OWA (most preferred first) is given in Table 6. In the same way, we have calculated the ranking by all related methods of all books for different courses. In the comparison section, all of these rankings are considered, but we have not shown those scores to save space and avoid repetition. Thus, there are a total of 158 different books that have been filtered from the huge number of books in the process of recommendation, which eases the complexities of the recommendation process.