## 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
\begin{array}{ccc}\underline{A}_{11}(FI_{node_{x}}(1))&\underline {A}_{21}(FI_{node_{x}}(1))&\underline{A}_{31}(FI_{node_{x}}(1))\\ \underline{A}_{12}(FI_{node_{x}}(2))&\underline{A}_{22}(FI_{node_{x}}(2))& \underline{A}_{32}(FI_{node_{x}}(2))\\ \underline{A}_{13}(FI_{node_{x}}(3))&\underline{A}_{23}(FI_{node_{x}}(3))& \underline{A}_{33}(FI_{node_{x}}(3))\\ \vdots&\vdots&\vdots\\ \underline{A}_{1n}(FI_{node_{x}}(n))&\underline{A}_{2n}(FI_{node_{x}}(n))& \underline{A}_{3n}(FI_{node_{x}}(n))\end{array} \right] \tag{18}\]  
where \(\underline{A}_{1i}(FI_{node_{x}}(i))\), \(\underline{A}_{2i}(FI_{node_{x}}(i))\) and \(\underline{A}_{3i}(FI_{node_{x}}(i))\) denote \(low\), \(medium\) and \(high\) membership degrees of the \(i\)-th fuzzy input of the message application user \(node_{x}\), respectively. Through synthetically considering the impact of different weights of fuzzy inputs, the fuzzy transformation mapping \(B_{node_{x}}\) from \(U^{\prime}_{node_{x}}\) to \(V_{node_{x}}\) is calculated by  
\[B_{node_{x}} =W_{(}w_{1},w_{2}\cdots w_{n})\circ R_{f} \tag{19}\] \[=b_{node_{x}}(1),\underline{b}_{node_{x}}(2)\cdots b_{node_{x}}(n).\]After assessing the importance of each social attribute of message application users, the FPRDM system comes to assign a high weight value to the attribute feature that performs a relatively vital role in the data transmission process. And on the contrary, a small weight value will be allocated to other general fuzzy inputs. Additionally, the fuzzy mapping from factor set to evaluation set actually is to explore the fuzzy link between social attributes and message routing-forwarding. Hence the value of \(B_{node_{x}}\) could be used as an important basis for fuzzy decision after defuzzification. Information Fusion and Fuzzy Decision-Making for Message Routing-Forwarding in Opportunistic Mobile Social Networks  
On the grounds of the constant and slight change of attribute features of message users in the data transmission process, it must be inaccurate to evaluate the transmission priority of nodes through some exact values of these attribute features at a certain time. This also leads to a large deviation in decision-making on node classification and data transmission. Therefore, through analysing the network routing environments and the distribution of the data related with node movement, the fuzzy inference system can be employed to comprehensively evaluate the transmission relationship between relay nodes and destinations, constructing a relatively complete and efficient message routing-forwarding link. To effectively quantify the whole process of data transmission from source nodes to destinations, this model defines \(CR_{(node_{x})}\) and \(IR_{(node_{x})}\) as the final fuzzy control result and the inference result of fuzzy relationship for \(node_{x}\), respectively, and the two definitions are shown as  
\[\left\{ \begin{aligned} CR_{node_{x}}&=c_{1},c_{2},c_ {3},c_{4}\cdots c_{q}\\ IR_{node_{x}}&=r_{1},r_{2},r_{3},r_{4}\cdots r_{e} \end{aligned} \right. \tag{20}\]  
where \(c_{1},c_{2},c_{3},c_{4}\cdots c_{q}\) represent different fuzzy subsets that the \(node_{x}\) belongs in, and \(r_{1},r_{2},r_{3},r_{4}\cdots r_{e}\) denote \(e\) different fuzzy transformation relationships from factor set \(U_{node_{x}}\) to evaluation set \(V_{node_{x}}\). For more accurately assessing the transmission relationship between nodes, feature vectors \(CR_{node_{x}}\) and \(IR_{node_{x}}\) will be reasonably digitized to specific values \(D_{node_{x}}\) and \(B_{node_{x}}\), respectively. Eventually, the above system of equations (20) could be translated into another form, which is shown as  
\[F_{node_{y}}=FROM(D_{node_{x}},B_{node_{x}}) \tag{21}\]  
where \(FROM\) denotes the process of fuzzy recognition and decision-making for node classification and data transmission, and \(D_{node_{x}}\) and \(B_{node_{x}}\) represent the membership degree of fuzzy control and fuzzy relationship inference, respectively.