## 1 Introduction
As one of the dominant algorithms, flooding-based routing protocols [18] transmit message replications to every node that the carriers encounter, which causes the overspread of data packets and a huge waste of cache spaces. Then, several routing protocols have been proposed to reduce the high overhead through controlling the number of message copies. Moreover, there are many other routing protocols based on message replication [19], direct delivery [20], mobility prediction [21], phase division [22], and probability evaluation [23] that have been utilized in the OSNs. Meanwhile, profile-based routing protocols employ different social attributes of mobile users such as spatial and temporal mobility features, social bonds, social influence, or node similarity, to enhance transmission efficiency in the OSNs, which mainly focus on single or multiple attribute characteristics of message users such as hobbies and interests, selfish behavior, encounter history, or distance and location of node mobility [24; 25; 26]. However, in the social scenarios of opportunistic mobile social networks, there are still many challenges for these routing methods that have not been well addressed: (1) It is challenging to construct an applicable mathematical framework to comprehensively consider the numerous attribute features of mobile users, including long-term stability characteristics and short-term variable characteristics, such as occupation, appearance, location or online community [27]. (2) Because each attribute feature of mobile users plays a different role in the process of message routing and forwarding, how to dynamically allocate a reasonable weight value to them is another key issue to be tackled [28]. To address these open questions, we propose and develop an adaptive routing-forwarding control scheme based on fuzzy pattern recognition and decision-making system (FPRDM) for opportunistic social networks, which mainly consists of four phases: fuzzy recognition for node classification, weight adjustment for social features, fuzzy relationship inference, and fuzzy decision-making process. To be specific, after the social attributes of mobile users are formalized, quantization vectors of these features will be regarded as fuzz input values [29] that are adopted to recognize node classification (relay node or irrelevant node). Then, this approach utilizes the improved analytic hierarchy process (AHP) [30] to allocate a seemly weight value to each fuzzy input, thereby determining the fuzzy mathematical mapping of the social features of mobile users into a transmission priority value. Eventually, the message routing-forwarding process will be performed via a feedback mechanism and a defuzzification component. On the whole, the main contributions of this paper are listed as follows:  
* A fuzzy inference model is proposed to implement the fusion of multiple social information of mobile users, thereby providing a reliable and stable strategy for opportunistic message routing and forwarding. * To synthetically evaluate the impact of each social characteristic on the data transmission process in OSNs, we combine the fuzzy inference logic with the analytic hierarchy process, and more importantly, with exploring the data transmission relationships among mobile users. * On the basis of a feedback mechanism, we are able to build a relatively stable and sustained data transmission connectivity between the source nodes and destinations in opportunistic mobile social network environments. * Ultimately, simulation results demonstrate that this scheme reduces the network delay and the overhead ratio, and enhances the delivery ratio as compared to several other typical or latest routing protocols in the OSNs. As a supplement to routing algorithms in multi-layer social networks, this FPRDM mechanism constructs an effective communication link between nodes in different online communities or the same online community by transforming the social attribute characteristics of nodes into a strong basis for data dissemination.