## 5 Simulation Results and Discussion
Figure 14: Energy/node/packet for 400 nodes. Figure 15: Energy/node/packet vs. number of nodes. The effect of network size (actually, the network density) on the average number of hops is shown in Figure 17, jointly with the average number of hops of SPRINT protocol taken from [4]. In comparison of two graphs, it is well evident that average number of hops of the proposed fuzzy scheme is lower than the same figure obtained with SPRINT protocol. Figures 17 and 18 show a comparison of the results of the proposed protocol and the same results of the SPRINT protocol. The fuzzy inference scheme finds paths with fewer hops and lower energy consumption. Table 7 shows a comparison in terms of energy consumption between the proposed protocol and both SPRINT and RECRP [6]. forwarding node selection algorithm has been proposed, based on fuzzy inference, for the SPRINT protocol. The objective of the work was to improve the energy efficiency of an UWSN routing protocol, which also helped to reduce the number of hops and, consequently, the end-to-end delay. The contributions of the work are (i) the use of fuzzy inference to select the forwarding node to form the path, (ii) the set of rules that form the logic of the fuzzy inference, and (iii) the effect of the transmission range on the number of hops to reach the gateway and on the average energy consumption. The fuzzy inference has been implemented in MATLAB(r). The input variables to the fuzzy logic algorithm are distance (through RSSI value), number of neighbors, and number of hops. Simulations were carried out to obtain the energy/node/packet and number of hops vs. transmission range and number of nodes. In fact, number of nodes means node density, because the considered scenario has a fixed volume. If the transmission circuit is the main energy consumer, it seems that less hops need more power, due to the transmission power law proportional to the squared distance. However, the simulations show that it is possible to find a path with fewer hops, but still less energy consumption. Moreover, fewer hops mean shorter end-to-end delays. The algorithm improves the efficiency of the USWN in terms of used energy and number of hops, which also reduces the end-to-end delay. Simulations results of the proposed scheme show a more energy efficient performance when compared to other UWSN routing protocols as SPRINT and RECRP. Conceptualization, P.O. and M.-A.L.-N.; methodology, W.H. ; software, J.K.P., M.-A.L.-N., W.H. ; validation, J.K.P., M.-A.L.-N.; formal analysis, J.K.P., M.-A.L.-N.; investigation, J.K.P., M.-A.L.-N., W.H., P.O. ; resources, M.-A.L.-N., P.O. ; data curation, M.-A.L.-N.; writing--original draft preparation, J.K.P. ; writing--review and editing, M.-A.L.-N., P.O. ; visualization, J.K.P. ; supervision, M.-A.L.-N., P.O. ; project administration, M.-A.L.-N., P.O. ; funding acquisition, M.-A.L.-N. All authors have read and agreed to the published version of the manuscript. This research was funded by the University of Malaga (Campus de Excelencia Internacional Andalucia Tech, and Consorico de Bibliocas Universitarias de Andalucia), Malaga, Spain, and the Higher Education Commission of Pakistan through Faculty Development Program from Dawood University of Engineering and Technology, Karachi, Pakistan. Not applicable. The authors declare no conflict of interest.