## 2 Description of the Proposed Approach
### Evaluation of Link Quality Between Nodes  
A fuzzy logic reasoning system is an intelligent system that uses fuzzy logic for reasoning and decision making. Its functions include processing uncertainty, fuzzy information, and complex multidimensional data. The implementation process of fuzzy reasoning usually includes fuzzification, rule-based reasoning, and defuzzification steps. This system is commonly applied in fields such as automatic control, pattern recognition, intelligent transportation systems, and wireless sensor networks. Through precise evaluation and decision making, the efficiency and reliability of the system are improved. In this section, we constructed an inner layer fuzzy logic reasoning system to complete the evaluation task of inter-node link quality, as shown in Figure 4.  
In addition to the \(SNR\) mentioned in Equation (9), the input to the fuzzy inference system also includes two other parameters: the interquartile range (\(IQR\)) of the cumulative \(PRR\) at different time points and the smoothed \(PRR\) obtained through exponentially weighted moving average processing (\(EWMA\_SPR\)). The rationale behind selecting these two parameters is as follows. First, we do not use the coefficient of variation (\(CV\)) of \(PRR\) because it is highly sensitive to fluctuations in link quality at a single time instant, which may lead to misleading results. For instance, a momentary degradation in link quality can cause a significant drop in \(PRR\), thereby introducing substantial variations in the computed \(CV\). In contrast, the \(IQR\) is more robust to transient fluctuations, as it primarily reflects the dispersion of the middle 50% of the data points. This makes \(IQR\) a more stable metric for assessing long-term link quality while filtering out short-term variations. Additionally, we calculate the \(EWMA\_SPR\) because it provides a predictive capability. By assigning exponentially decreasing weights to past observations, the \(EWMA\_SPR\) value enables a smoother estimation of \(PRR\) trends, allowing for a more reliable prediction of future link quality based on historical data. This predictive aspect is particularly beneficial in dynamic  
Figure 4: Schematic diagram of link quality index (LQI) acquisition process using inner layer fuzzy reasoning system. underwater acoustic environments, where link quality can fluctuate due to various factors, such as mobility, multipath effects, and environmental disturbances. \(SNR\) reflects the real-time physical channel quality and serves as a primary indicator of potential signal distortion due to environmental noise. Higher \(SNR\) values generally imply more favorable transmission conditions. However, due to the inherent volatility of underwater channels, relying solely on instantaneous \(SNR\) may lead to unstable decision making. \(IQR\) of \(PRR\) captures the dispersion of \(PRR\) values over a predefined observation window, quantifying the consistency and stability of the link performance. A smaller \(IQR\) implies a more stable link, while a larger \(IQR\) indicates fluctuating reception quality and potential unreliability due to transient disturbances such as mobility or interference. \(EWMA\_SPRR\) introduces a smoothing mechanism that emphasizes recent \(PRR\) trends while still considering historical observations. This exponentially weighted average enhances temporal robustness, mitigating the effects of outliers or sudden dips caused by momentary channel degradation. The fuzzy inference mechanism leverages the degree of membership of these parameters to predefined fuzzy sets (e.g., High \(SNR\), Low \(IQR\), Good \(EWMA\_SPRR\)) and integrates them through fuzzy rules to output an aggregated \(LQI\) value, which reflects both instantaneous and long-term link quality trends. This design aims to reduce susceptibility to short-term fluctuations and provide a more resilient and adaptive link assessment model for routing decisions.