## 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  
In opportunistic mobile social networks, two message application users, which possess a relatively high social similarity between them, are more likely to be in the same online community, and information communication between them is expected to be more frequent. Therefore, a user with a high social similarity to the destination should be a reliable relay node in the data transmission process. Then, the process of pattern recognition for node classification employs fuzzy inference logic to evaluate the social similarity between mobile users, so as to select some suitable relay nodes for message routing and forwarding, and eventually achieves an efficient and sustainable data transmission link. For effectively assessing the pattern recognition results of node classification, we define the membership degree of each quantization vector as \(\underline{\Delta}_{mn}\), in which \(m\) represents different levels of membership subsets and \(n\) denotes different fuzzy input values. Thereupon, each fuzzy subset could be represented by \(n\) different fuzzy inputs, which is mathematically quantified as  
\[\underline{\Delta}_{m}=\left\{ \begin{array}{cc}\bar{A}_{low}&m=1\\ \bar{A}_{medium}&m=2\\ \bar{A}_{high}&m=3\end{array} \right. \tag{9}\]  
\[\underline{\Delta}_{m}(FI_{node_{x}}(i))= (\underline{\Delta}_{m1}(FI_{node_{x}}(i)),\underline{\Delta}_{ m2}(FI_{node_{x}}(i))\cdot\cdot\cdot\cdot\cdot\cdot\underline{\Delta}_{mn}(FI_{node_{x}}(i))) \quad(m=1,2,3) \tag{10}\]  
Figure 2: Three different grades of membership functions quantization vectors. where \(\underline{A}_{nm}(FI_{node_{x}}(i))\) indicates the membership degree of \(FI_{node_{x}}(i)\) from the membership subset \(MD_{m}\). In a traditional fuzzy inference system, the goal of the defuzzifier component is to convert fuzzy membership subsets and membership degrees into an accurate judgment value. As a commonly-used approach to calculate the membership degree in a traditional fuzzy inference system [6], maximum membership principle means the membership degree of each level (low, medium, and high) is equal to the maximum membership of \(n\) quantization vectors from the corresponding level. Consequently, the membership degree \(\underline{A}_{m}(FI_{node_{x}}(i))\) of fuzzy input \(FI_{node_{x}}(i)\) for membership subset \(MD_{m}(FI_{node_{x}}(i))\) could be calculated by  
\[\underline{A}_{m}(FI_{node_{x}}(i))=\bigwedge_{i=1}^{n}\{\underline{A}_{mi}( FI_{node_{x}}(i))\}\ (m=1,2,3). \tag{11}\]  
Generally, there are several paradigms of defuzzification strategies in a fuzzy inference system, such as center of area (CoA) or mean of maximum (MoM) [29]. The maximum membership principle will be regarded as the defuzzification method in the proposed algorithm due to its expansibility. Based on that, the membership degree of fuzzy control result \(D_{node_{x}}\) for pattern recognition of \(node_{x}\) classification could be expressed as the union of three different membership degrees that correspond to three different levels of membership subsets, which is shown as  
\[ \begin{split} D_{node_{x}}&=\bigvee_{m=1}^{3} \big{\{}\bigwedge_{i=1}^{n}\{\underline{A}_{mi}(FI_{node_{x}}(i))\}\big{\}}\\ &=\underline{A}_{low}(FI_{node_{x}}(i))\bigvee\underline{A}_{ medium}(FI_{node_{x}}(i))\bigvee\underline{A}_{high}(FI_{node_{x}}(i)).\end{split}  \tag{12}\]  
After determining the threshold \(K\) accurately, we can compare \(D_{node_{x}}\) with \(K\) to evaluate whether the \(node_{x}\) is a suitable relay node. To be specific, when the value of \(D_{node_{x}}\) is greater than or equal to \(K\), the \(node_{x}\) may be an appropriate next hop; otherwise, the node may not be suitable to participate in the process of message routing and forwarding. Reasonable Weight Allocation and Inference of Fuzzy Relationships Via the Analytic Hierarchy Process  
The main aim of fuzzy pattern recognition is to present a preliminary judgment on node classification.