## 6 Discussion  
After the deployment of sensors in an ad hoc UWSN, the submerged nodes have to create paths using multihop technique (from node to node) to route the packets to the gateway node on the surface. In this starting phase, parameters such as delay and throughput are unknown until all the nodes are connected by at least a route that ends in the gateway. In that scenario, among the parameters that can be estimated are distance to the gateway (e.g., using received signal strength indicator (RSSI) in the packet), the number of hops that a node needs to reach the gateway in the partial route created, and the number of neighbors that are in the range of a node. These three parameters have been considered in FAHP to select the next node that belongs to a partial route coming from the gateway to the sea bottom. The FAHP scheme has been used in complex decision problems in which multiple criteria are applied to make the best selection among candidates. The problem of selecting which nodes belong to a route to have a low packet delay or energy wasted in the nodes is an interesting problem that relies on the field of FAHP. In this work, it has been proved as with only those three parameters (distance, hops, and neighbors), the problem is solved in a random topology with efficiency similar to that of other techniques (SPRINT-Fuzzy) in time (E2E delay packet) and energy consumption. Moreover, stability can be demonstrated by the results provided when considering 400 nodes, which is a large size for this type of network. These reasons are coupled with the existence of a random topology in the initial deployment phase and the consideration that FAHP can handle more criteria than those presented here in future work, which makes the presented technique a suitable option for the routing problem in UWSNs. Conceptualization, J.K.P., M.-A.L.-N. and W.H. ; methodology, M.-A.L.-N.; software, M.-A.L.-N., W.H. and A.A.; validation, M.-A.L.-N. and A.A.; formal analysis, M.-A.L.-N.; investigation, J.K.P. and M.-A.L.-N.; resources, M.-A.L.-N.; data curation, M.-A.L.-N.; writing--original draft preparation, J.K.P. and M.-A.L.-N.; writing--review and editing, M.-A.L.-N.; visualization, M.-A.L.-N; supervision, M.-A.L.-N. and A.A.; project administration, M.-A.L.-N; funding acquisition, M.-A.L.-N. All authors have read and agreed to the published version of the manuscript. This research was funded in part by the Spanish Ministry of Science and Innovation through the project \"NAUTILUS: Swarms of underwater autonomous vehicles guided by artificial intelligence: its time has come\" (Grant: PID2020-112502 RB/AEI/10.13039/501100011033). Not applicable. Authors express their gratitude to the Institute of Oceanic Engineering Research (IIO, University of Malaga) for its dedication and effort. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No. Nodes**} & \multirow{2}{*}{**Tx Range (km)**} & **Av. Energy Consumption (J)** \\  & & **Sprint** & **FAHP (\%)** \\ \hline
100 & 4 & 21.8 & 36.6 (+67.9\%) \\
100 & 5 & 183.6 & 238.8 (+30.1\%) \\
100 & 6 & 782.3 & 1132.14 (+44.7\%) \\
100 & 7 & 2714.2 & 4060.4 (+49.6\%) \\ \hline
400 & 2 & 0.19 & 0.31 (+63.2\%) \\
400 & 3 & 10 & 17.1 (+71\%) \\
400 & 4 & 173.6 & 292.5 (+68.5\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Statistical comparison for average energy consumption. Applying (11)-(15) to the values in the Tables 13-14, it is possible to calculate the following for every node and criterion: the geometric mean \(\widetilde{\widetilde{g}}\), the fuzzy weights \(\widetilde{w}\), the non-fuzzy weights \(q_{i}\), and the normalized weights \(l_{i}\). The obtained results are presented in Tables 15-16. The last parameter in Tables 15-16 (normalized weights \(l_{i}\)) is employed for calculating the final score of every alternative: the rank (32).