## 7 Sensitivity Analysis  
The weights of criteria may continuously fluctuate throughout the entire project ranking process, potentially impacting the final rankings. Conducting sensitivity analysis facilitates a better understanding of the significance and priority of each criterion, ensuring that crucial factors are adequately considered during the project ranking process. In the case of selecting earthquake search and rescue robots, it is imperative to perform sensitivity analysis to assess their robustness and reliability. This analysis aids in comprehending potential outcomes under different circumstances and facilitates necessary measures to ensure that selected earthquake search and rescue robots remain competent in any situation. In this paper, the perturbation method is adopted to conduct sensitivity analysis on index weight; that is, after the index weight in the decision is slightly perturbed, the change of scheme ordering under the same decision framework is observed. Assuming that the weight of the initial index \(C_{j}\) is \(\omega_{j}\), the index weight after disturbance changes to \(\omega^{\prime}_{j}=t\omega_{j}\), where \(0<\omega^{\prime}_{j}<1\) and \(0<t<1/\omega_{j}\). Simultaneously, the weights of other indexes undergo adjustments as \(\omega^{\prime}_{k}=d\omega_{k}\), \(k\
eq j,k=1,2,\cdots,m\). The adjusted weights satisfy the following conditions. \[\omega^{\prime}_{j}+\sum_{k\
eq j,k=1}^{m}\omega^{\prime}_{k}=1 \tag{13}\]  
Equation (13) can be transformed into \(d=(1-t\omega_{j})/(1-\omega_{j})\). Therefore, for each index weight \(\omega_{j}\), when different \(t\) is taken, \(m\) index weights can be disturbed, and \(m\) groups of index weights after disturbance can also be obtained. According to the variation of Equation (13), different values of \(t\) correspond to distinct index weight \(\omega_{j}\). The four criteria weights are individually perturbed, resulting in the derivation of four new criteria weights. It is important to note that when adjusting the  
Figure 6: Performance graphic of three types of earthquake search and rescue robots: (**a**) Improved radar chart; (**b**) Evaluation results. weight of an individual criterion, it is necessary to normalize all criteria weights to maintain consistency in the weighted scheme. The detailed data can be found in Table 9.  
The impact of weight changes on the sample grades can be observed in Figure 7. Sample A is evaluated as the third grade, and Sample B is evaluated as the second grade when the weight of the Survivability criterion decreases from its initial value of 0.208 in Figure 7a to 0.179 or below or when the weight of the Mobility criterion increases from its initial value of 0.257 in Figure 7b to 0.297 or above, or when the weight of Detection perception ability criterion decreases from its initial value of 0.269 in Figure 7c to 0.19 or below, or when the weight of Communication control ability criterion increases from its initial value of 0.266 in Figure 7d to 0.294 or above. Sample C consistently maintains a leading position in the performance evaluation of earthquake search and rescue robots, demonstrating its resilience against changes in other criterion weights. This finding suggests that the performance evaluation system for these robots is relatively insensitive to variations in criterion weights, indicating a certain level of  
Figure 7: Findings of weight sensitivity analysis: (**a**) Sensitivity findings regarding the criterion of “Survivability”; (**b**) Sensitivity findings regarding the criterion of “Mobility”; (**c**) Sensitivity findings regarding the criterion of “Detection perception ability”; (**d**) Sensitivity findings regarding the criterion of “Communication control ability”.