## 1 Introduction
Furthermore, two studies have outlined the routing protocol design in two stages: the first involves defining the forwarding area, and the second selects a forwarding node from the candidate set using various methods. For instance, game theory can be used to design strategy sets and gain functions or to derive forwarding probability through the Nash equilibrium [27]. Alternatively, forwarding probability can be calculated directly from node location information [28]. However, neither of these studies considered energy management; therefore, the network lifetime cannot be guaranteed. In addition to routing protocols, several studies have also provided valuable methodological inspiration and technical guidance for enhancing real-time adaptive routing and intelligent decision-making strategies in UASNs. For example, studies on high-precision localization using multisensor association in space environments [29], the real-time trajectory planning and tracking control of bionic underwater robots in dynamic environments [30], and the design of a forward-looking sonar system with a lightweight multiscale attention network for environmental perception and intelligent decision making [31] offer important references for developing UASN systems with improved environmental awareness and dynamic adaptability. The research purpose of this paper is to optimize the forwarding process of the three-dimensional (3D) underwater acoustic sensor network (UASN) routing protocol by using a fuzzy reasoning system, and the most important part is to deduce the candidate priority of nodes. The fuzzy logic reasoning system has already made important contributions to the research of opportunistic networks and ad hoc networks [32; 33]. Inspired by these developments, we design a fuzzy logic reasoning adaptive forwarding (FLRAF) routing protocol for 3D UASNs and select the forwarding nodes using the fuzzy logic reasoning tool. We innovatively build a nested fuzzy logic reasoning system to determine node candidate priorities. The inner layer obtains the link quality index (\(LQI\)), while the outer layer determines node candidate priorities. In the process of obtaining \(LQI\), refs. [34; 35] inspires us, but after obtaining the cumulative packet reception rate (\(PRR\)), a series of \(PRR\) values are used for calculating its coefficient of variation to serve as one of the fuzzy input variables, which may lead to a misjuddment of the link quality, because when the network encounters an outlier due to a brief emergency, the use of the coefficient of variation will have a significant impact on the fuzzy output. Therefore, we innovatively use the interquartile range of the cumulative \(PRR\) value as one of the inputs of the link quality assessment task to evaluate the \(LQI\) more comprehensively. Finally, we highlight the key innovations of the proposed FLRAF method. 1. The FLRAF routing protocol redefines the geometric boundary and selection criteria of the new forwarding area. It allows more suitable nodes to participate in the forwarding process and prevents unnecessary forwarding by nodes in unfavorable positions, thus reducing transmission redundancy. In addition, unlike traditional approaches based on pipeline or hemispherical forwarding regions, the conical forwarding area helps maintain the directional consistency of multihop forwarding paths from the source node, minimizing path deviations and thereby reducing the total number of hops required for transmission, which improves forwarding efficiency and ensures higher energy efficiency. 2. The FLRAF routing protocol designs a fuzzy logic reasoning system to improve the accuracy of link quality assessment. The system comprehensively analyzes the smoothed \(PRR\) obtained through exponentially weighted moving average processing (\(EWMA\_SPRR\)), the signal-to-noise ratio (\(SNR\)), and the interquartile range (\(IQR\)) of the \(PRR\) to complete the \(LQI\) assessment task.