## 5 Experimental Study and Discussion
### Sorting Results and Comparison  
Table 12 shows the global similarity between \(c_{n}\) and \(nc\) under different aggregation functions, including ACI, AO (average operator), and OWA (ordered weighted averaging), where the attribute weights in OWA are determined by the BWM and calculated by Model (14). According to the decision maker, the preferred solution to the new coming case (\(nc\)) should be \(c_{2}\succ c_{3}\succ\succ c_{1}\succ c_{4}\). From Table 12, the preference ranking of solutions to the new coming case by ACI and OWA is \(c_{2}\succ c_{3}\succ c_{1}\succ\succ c_{4}\). However, AO produces a preference ranking \(c_{3}\succ c_{2}\succ c_{1}\succ\succ c_{4}\), which is inconsistent with the preference derived from the decision maker's attitude. This is because the attribute importance varies significantly, and the AO does not consider this. Both ACI and OWA consider the attribute importance, thus producing reasonable ranking results. In particular, the preference ranking from ACI \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{a_{4}}\) & \(\mathbf{a_{5}}\) \\ \hline \(c_{1}\) & 1 & 1 & 0 & 1 & 0.17 \\ \(c_{2}\) & 1 & 1 & 0 & 1 & 0.91 \\ \(c_{3}\) & 1 & 1 & 1 & 0 & 1 \\ \(c_{4}\) & 0 & 1 & 0 & 0 & 0.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Local similarity between \(c_{i}\) and \(nc\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Attitudinal Choquet** & **Average Operator** & **Ordered Weighted** \\  & **Integral (ACI)** & **(AO)** & **Averaging (OWA)** \\ \hline \(c_{1}\) & 0.7709 & 0.6340 & 0.5035 \\ \(c_{2}\) & 0.9455 & 0.7820 & 0.8008 \\ \(c_{3}\) & 0.9373 & 0.8000 & 0.6746 \\ \(c_{4}\) & 0.2752 & 0.2620 & 0.1711 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Global similarity under different aggregation functions. is closer to the decision maker's cognition. However, regarding the magnitude of global similarity given by \(\mathrm{ACI}\), \(c_{2}\) (with a similarity of 0.9455) has only a 0.87% advantage over \(c_{3}\) (with a similarity of 0.9373). Thus, when solving \(nc\), \(c_{3}\), in addition to the first choice \(c_{2}\), is worth considering. Perhaps the combination of \(c_{2}\) and \(c_{3}\) will produce a better solution for \(nc\). This is because \(\mathrm{ACI}\) considers the decision maker's attitude in addition to the interaction between attributes, thus helping the decision maker to make higher-quality decisions. Notably, decision makers must possess professional knowledge and decision making ability when determining the value of \(\lambda\) in \(\mathrm{ACI}\). In \(\mathrm{CBR}\) embedded with \(\mathrm{ACI}\), the judgment of \(\lambda\) can yield a more accurate case retrieval result, whereas wrong judgment may lead to an unreasonable result. \(\mathrm{CBR}\) is an experience-based approach to knowledge-intensive problem solving. The case base of the \(\mathrm{CBR}\) system contains cases that are considered to have been successfully solved. However, in case representation, one type of empirical knowledge, namely the attitude or preference of decision makers, is difficult to describe and model. The key to the success of \(\mathrm{CBR}\) is to retrieve the most appropriate cases to solve a new coming case. Therefore, case retrieval is the core process of \(\mathrm{CBR}\) cycle. [PERSON] et al. (2022) [28] adopted the \(\mathrm{AO}\) method to calculate the global similarity and obtained high retrieval accuracy. In this study, we synthesize other important but often ignored factors in similarity calculation, including attribute weight, interaction between attributes, and attitude of decision makers, to further improve the accuracy of case retrieval while inheriting the reliability and validity of the method proposed in [28]. Note that in the above experiment, the preference ranking obtained by using \(\mathrm{AO}\) violates the preference associated with the decision maker's attitude.