## 3 System Model Design
### Fuzzy Pattern Recognition Process for Node Classification in Opportunistic Mobile Social Networks
#### 3.2.2 Fuzzy Pattern Recognition for Node Classification in Opportunistic Mobile Social Networks
Since the fluctuation ranges of \(D_{node_{x}}\) and \(B_{node_{x}}\) are both from 0 to 1, the FPRDM strategy adopts the \(tanh\) function (shown as Equation (22)) to comprehensively evaluate the transmission value \(TV\), which can be regarded as the final reference to data transmission between relay nodes and destinations. \[ \begin{aligned} TV&=tanh(D_{node_{x}}+B_{node_{x}}) \\ &=\frac{e^{(D_{node_{x}}+B_{node_{x}})}-e^{-(D_{node_{x}}+B_{ node_{x}})}}{e^{(D_{node_{x}}+B_{node_{x}})}+e^{-(D_{node_{x}}+B_{node_{x}})}}. \end{aligned}  \tag{22}\]  
From the above formula, when \((D_{node_{x}}+B_{node_{x}})\) is between 0 and 2, the slope of \(F_{node_{y}}\) is relatively large and the value of \(TV\) fluctuates enormously, which is conducive to clearly distinguish the transmission priority between nodes. On the basis of feedback mechanism, message application users are able to make an accurate decision on message routing and forwarding by comparing the \(TV\) value of the future two-hop nodes during the data transmission process. Theoretically, most of the traditional and classical routing strategies in opportunistic mobile social networks commonly seeks the next-hop node only from its neighbors and then forward data packets, which is likely to cause the interruption or instability of data transmission. Consequently, we investigate a routing feedback mechanism approach, concentrating on not only the next-hop nodes but also the third-hop nodes, which facilitates the construction of a continuous and stable link in the data transmission process. To be specific, as shown in Figure 3, \(node_{A}\), \(node_{B}\) and \(node_{C}\) are in the online community 1 at the current moment. Additionally, \(node_{D}\) and \(node_{E}\) are in the online community 2, while \(node_{F}\), \(node_{G}\), \(node_{H}\) and \(node_{I}\) are in the online community 3. \(node_{A}\) and \(node_{G}\) are respectively the source node and destination. Moreover, the black point represents the relay node, while the red one denotes an irrelevant node in opportunistic social networks. The number of mobile nodes in a community represents the corresponding node density. Each message application user calculates its own \(TV\) according to the attribute characteristics of the destinations provided by the source \(node_{A}\). As a message carrier, \(node_{A}\) comes to collect and compare the \(TV\) values of its future two-hop message users. As shown in Figure 3, because \(TV_{I}>TV_{E}\) and \(TV_{E}>TV_{C}\), the source node \(node_{A}\) only transmits data packets to \(node_{C}\), and then sends data packets to \(node_{E}\) and \(node_{I}\). Finally, these data packets will be forwarded to the destination \(node_{G}\). According to the different node density and membership degree within each online community, the proposed scheme comes to adopt different strategies to implement message routing and forwarding. The duplicate controlling model is adopted among the mobile nodes in the same community. Moreover, due to a low node density within the online community 2, \(node_{C}\) transmits messages to \(node_{E}\) via the mechanism of copying messages, which is able to avoid the loss of data packets. On the contrary, the node density in community 3 is relatively high, hence \(node_{E}\) employs the method of direct forwarding to transmit messages to \(node_{I}\), and more importantly, preventing the flooding of data packets in the online community.