## 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
Moreover, these related initialization definitions could be formalized as  
\[FS_{node_{x}}(FI_{node_{x}}(i))=MD_{low}(FI_{node_{x}}(i)),MD_{medium}(FI_{ node_{x}}(i)),MD_{high}(FI_{node_{x}}(i)) \tag{3}\]  
where \(MD_{low}(FI_{node_{x}}(i)),MD_{medium}(FI_{node_{x}}(i)),MD_{high}(FI_{node_{x }}(i))\), which respectively correspond to \(low\), \(medium\) and \(high\) fuzzy subsets, are three different grades of membership degrees for the quantization vector \(FI_{node_{x}}(i)\). As shown in Figure 1, for each message application user \(node_{x}\), this system will generate a corresponding quantization vector. In addition, for each level of membership function, the quantization vector \(FI_{node_{x}}(i)\) simultaneously generates \(n\) different corresponding membership degrees. The fuzzy subsets \(\tilde{A}_{low}\), \(\tilde{A}_{medium}\) and \(\tilde{A}_{high}\) are regarded as an evaluation set and the fuzzy inputs are considered as a factor set in the proposed routing strategy, so the mathematical mapping from fuzzy input \(FI_{node_{x}}(i)\) to fuzzy subsets could be defined as  
\[MF(FI_{node_{x}}(i)):R\rightarrow\{\tilde{A}_{low},\tilde{A}_{medium},\tilde{ A}_{high}\} \tag{4}\]  
On the basis of the theory of tripartite method, when \(\forall ei_{x}\in R\), Equation (4) could be expanded as  
\[MF_{\mu\eta}(FI_{node_{x}}(i))= \begin{cases}\tilde{A}_{low}&FI_{node_{x}}(i) \leq\mu\\ \tilde{A}_{medium}&\mu<FI_{node_{x}}(i)<\eta\\ \tilde{A}_{high}&FI_{node_{x}}(i)>\eta\end{cases}  \tag{5}\]  
where \(\mu\) represents a demarcation point between \(low\) and \(medium\) membership degrees, and \(\eta\) is another demarcation point between \(medium\) and \(high\) membership degrees. Furthermore, \(\tilde{A}_{low}\), \(\tilde{A}_{medium}\) and \(\tilde{A}_{high}\) denote the determined \(low\), \(medium\) and \(high\) membership function, respectively. Accordingly, it is essential for us to define three different levels of membership functions \(\tilde{A}_{low}\), \(\tilde{A}_{medium}\) and \(\tilde{A}_{high}\) for the quantization vector \(FI_{node_{x}}(i)\) based on the application of the tripartite method, which shows a general mathematical symmetry. In theory, there exist many membership function references in fuzzy control mathematics, such as trapezoidal distribution and semi-trapezoidal distribution, \(K\)-order parabolic distribution, Cauchy distribution, normal distribution, and Ridge distribution. Naturally, in opportunistic social networks, high-tech mobile device users come to generate a large amount of data when accessing the application platform, including social, mobile, behavioral, physical characteristics and a large amount of text information. Generally, when message application users are in urban areas, relatively developed communication infrastructures contribute to a high-speed and stable network environment. Therefore, the frequent communication among mobile nodes in an online community is likely to generate a great amount of social information. On the contrary, poor and dated communication infrastructures in suburbs or remote areas may result in congested, slow and intermittent communications between mobile users [1], hence there will be less social information about mobile users in this type of network environment. Furthermore, hot issues, novel topics, popular entertainment, and public preferences are the areas that the public is deeply concerned about, even though the distinction in age, occupation, and gender may lead to a slight difference in attention. Through strict data analysis and theoretical proof, the data related to social attributes that come from message application users should be subject to a relatively standard normal distribution [2].