## 2 Description of the Proposed Approach
### Fuzzy Logic Reasoning Selection of Candidate Set
This is essential to ensure  
Figure 6: Schematic diagram of node candidate priority acquisition process using outer layer fuzzy reasoning. that the fuzzy inference process produces logically consistent and semantically accurate outputs. If this relationship is not properly considered, the system may yield misleading evaluations. For instance, if a \"low node energy\" fuzzy set were mistakenly designed with a membership degree that increases with increasing energy, then a node with extremely low energy might be falsely assigned a low membership degree, misleading the system to treat it as a high-energy node and prioritize it for data forwarding--thereby accelerating energy depletion and reducing network lifetime. Therefore, appropriate membership function design is crucial for ensuring the correctness and robustness of the fuzzy inference system. Additionally, the use of different membership functions for the three other fuzzy input variables effectively avoids the feature representation blind spots that may arise from using a single function type. The resulting membership function graphs are shown in Figure 7, Figure 8, Figure 9, and Figure 10, respectively. Second, according to the system design requirements, we set inference rules. Since we have set fuzzy logic inputs for three variables and each fuzzy input has three fuzzy subsets, we can exhaustively list all possible inference rules; however, due to space limitations, only a subset of the fuzzy reasoning rules is shown in Table 2.  
Figure 8: The membership function of the fuzzy subset for the fuzzy input LQI. Figure 10: The membership function of the fuzzy subset for the fuzzy output NodePriority. Figure 9: The membership function of the fuzzy subset for the fuzzy input advance distance (AD). In fact, if we broadly define the three fuzzy subsets of fuzzy input as \"good\", \"medium\", and \"poor\", then the fuzzy inference rules can be broadly categorized as follows:  
1. If all three fuzzy inputs are \"good\", then the fuzzy output is \"vhPriority\";
2. If all three fuzzy inputs are \"poor\", then the fuzzy output is \"vlPriority\";
3. If any two fuzzy inputs are \"good\", the fuzzy output is \"hPriority\";
4. If any two fuzzy inputs are \"medium\", the fuzzy output is \"mPriority\";
5. If any two fuzzy inputs are \"poor\", the fuzzy output is \"lPriority\";
6. If the three fuzzy inputs are, respectively, \"good\", \"medium\", and \"poor\", the fuzzy output is \"mPriority\". Finally, the fuzzy reasoning system progresses to the defuzzification process, where the Centroid defuzzification method is used to obtain the final fuzzy output. Assuming two candidate nodes exist within the forwarding area at the same time, their node state information is [8 8 2] and [8 8 9], respectively, (i.e., using [_REi ADi LQli_] to represent the state information of node i). After processing by our nested fuzzy inference system, the priorities of the two nodes are 6.82 and 8.59, respectively. Therefore, the FLRAF routing protocol tends to choose the latter as the forwarding node, because the former indicates that the node has good remaining energy and a long effective advance distance, but poor link quality, while the latter indicates that the node has excellent link quality, sufficient remaining energy, and long effective advance distance. On the other hand, when conducting fuzzy logic reasoning, different reasoning rules can also be assigned different weights to maximize their compatibility with the designer's specific needs.