## 3 System Model Design
### Fuzzy Pattern Recognition Process for Node Classification in Opportunistic Mobile Social Networks
#### 3.2.1 Information Quantification and Determining Membership Degrees for Fuzzy Input  
In OSNs, nodes with multiple different social attributes in unknown online communities try to communicate with each other, so their social attribute characteristics form a strong basis for position locating and data transmission. In general, node profile contains several important social attributes of message application users. To implement a high-performance data transmission process, the FPRDM model reasonably adopts the node profile of message application users to evaluate the special connection relationship between neighbor nodes and destinations. Specifically, as shown in Figure 1, message application users usually embody multiple different social attributes, such as interests, specialities, physical characteristics, workplaces or residence places. For each attribute of the \(node_{x}\), we define a feature vector as a container that is used to load the related and valuable information, and the feature vector is shown as  
\[fv_{node_{x}}(X)=X_{1},X_{2},X_{3},X_{4}\cdots X_{n} \tag{1}\]  
where \(X_{1},X_{2},X_{3},X_{4}\cdots X_{n}\) represent \(n\) different social attributes of the message application user \(node_{x}\), and \(n\) is the number of social attributes of mobile nodes in the networks. By extension, each of these social attributes can be refined into a smaller eigenvector \(ei_{node_{x}}(X)\). Moreover, when the user \(node_{x}\) contains the same feature value as a destination, the corresponding value of the eigenvector is set to 1, otherwise to 0. For example, if the feature vector of interest is defined as \(ei_{node_{x}}(interest)=\{movie,basketball,music,game,book\}\), and the user \(node_{x}\) likes movie, music and book as well as the destinations, then this feature vector could be rigorously initialized to \(e_{node_{x}}(interest)=\{1,0,1,0,1\}\). For the sake of the identifiability of the FPRDM system, we set the module length of each feature vector as the fuzzy input of this system, which is obtained by  
\[FI_{node_{x}}(i)= \begin{cases}|ei(X_{1})|&i=1\\ |ei(X_{2})|&i=2\\ |ei(X_{3})|&i=3\\ &\dots\dots\\ |ei(X_{n})|&i=n\end{cases}  \tag{2}\]  
in which \(FI_{node_{x}}(i)\), namely the quantization vector, denotes different fuzzy inputs of the FPRDM system. Acquired from message application users in the OSNs, the data information associated with social attributes of mobile users is translated from text into a digital format that can be read, recognized, utilized and processed by this system. Originating from the theory of fuzzy control engineering, the fuzzy inference system is able to transform the piecewise function into some curves, thereby making a vague judgement on the transmission priority of each node in the OSNs. After the process of ambiguity resolution, the specific digital value could be regarded as an accurate assessment foundation for message routing and forwarding decision-making. Refer to the traditional and classical Mamdani fuzzy control system, which is a highly extensible and applicable fuzzy inference model. The FPRDM system model [29] could be established using three continuous components, including Fuzzifier, Fuzzy Inference, and Defuzzifier. Next, a detailed description of the three fuzzy components will be presented in the following sections. As shown in Figure 1, \(FI_{node_{x}(i)}\), a specified queue defined by Equation (2) is regarded as the fuzzy input of fuzzy pattern recognition and decision-making system, and it is also the discourse domain of variable fuzzy subsets in this system model, further we adopt tripartite method to define three different levels of membership subsets (\(low\), \(medium\) and \(high\)).