## 2 Related Work  
In the literature, several approximations for the establishment of the initial path in WSNs can be found. Our proposed classification for strategies related to the scope of this work is as follows: (1) those using fuzzy decisions, (2) those using hierarchy processes, and (3) those using other specific routing techniques. The use of fuzzy decisions in routing protocols has received growing interest in recent years. One of the classic applications is to select the cluster head (CH) node in a cluster-based network topology, using multiple criteria in the assignment of that role mainly to increase the network lifetime. In this area, we have decision schemes such as the fuzzy technique for order of preference by similarity to ideal solution (Fuzzy-TOPSIS) [12]; LEACH fuzzy clustering (LEACH-FC) [13]; data gathering protocol in unequal clustered WSNs utilizing fuzzy decisions (DGUCF) [14]; multiple-attribute decision making (MADM) [15] using criteria such as residual energy, distance from the base station, and number of neighbors; energy-efficient distributed clustering algorithm based on fuzzy scheme (EEDCF) [16] to overcome uneven load on the network and select CH using the fuzzy Takagi-Sugeno-Kang (TSK) model; adaptive network based on fuzzy inference system (ANFIS) [17] which employs a fuzzy neural network; or using the density of nodes [18] jointly with the Mamdani method of fuzzy inference for selecting the CH. Another typical application for fuzzy decisions is the selection of an efficient routing path using multihop links (node-by-node hops), such as in the relay node selection scheme based on fuzzy inference algorithms (RNSFIA) [19]. In RNSFIA, a fuzzy inference algorithm is used to select the relay node, where the criteria used for the decision are distance between nodes, priority on residual energy, and degree of communication. Compared to MODLEACH [20], RNSFIA has a higher throughput and network lifetime. Another example for efficient routing with fuzzy decisions is multi-criteria decision making (MCDM) [21], where weights and criteria such as hop count, packet transmission frequency, and residual energy are used. A second block of strategies (hierarchy processes) is based on multiple comparisons under different criteria. Examples include the analytical hierarchy process (AHP) [22], which selects the relay node in body area networks (WBANs) using weights among several candidate nodes; AHP MCDM [23], which uses a two-phase clustering scheme that includes finding the location of the nodes by using sink position and criteria such as the number of neighbors, centrality, and residual energy; or the analytical network process (ANP) [24] based on MCDM which selects the best CH node using criteria such as initial and residual energy, energy consumption rate, average energy of the network, and distance of a node from CH. Others (e.g., [25]) consider both ANP and AHP using a fuzzy scheme for solving the CH selection in a cluster network. In the UWSN area, various methods are considered to achieve energy efficiency. We have used input parameters such as hop count, distance to the sink, and number of neighbors using the FAHP MCDM strategy and obtained better results compared to some of the existing research techniques. FAHP is almost identical to AHP except for the conversion of verbal appreciation into the numeric scale. AHP indicates the relative importance of criteria in MCDM, being preferable in qualitative judgments, and cannot accept fuzzy numbers as input. Thus, fuzzy AHP (FAHP) was introduced because AHP lacks the benefits of managing vagueness in judgment. For example, a decision maker cannot make exact judgment between number 4 and 6 instead of using exactly the number 5. However, fuzzy numbers are the way to integrate such imprecision, giving benefits for FAHP compared to AHP schemes. The last family of routing techniques considered here is out of the scope of the two cited before. Usually, a specific solution is proposed for the path's creation through the network.