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The recent development of Web 2.0 has provided for an enormous increase in human interactions across all corners of the earth. One manifestation of this is the growth of computer mediated social networks. Many notable Web 2.0 applications such as Facebook, Myspace and LinkedIn are social networks. Social relational networks are becoming an important technology in human behavioral modeling. Our goal here is to enrich the domain of social network modeling by introducing ideas from fuzzy sets and related granular computing technologies. We approach this extension in a number of ways. One is with the introduction of fuzzy graphs representing the networks. This allows a generalization of the types of connection between nodes in a network from simply connected or not to weighted or fuzzy connections. Here the idea of strength of connection becomes important. A second and perhaps more interesting extension is the use of ZadehÂ¿s fuzzy set based paradigm of computing with words to provide a bridge between a human network analystÂ¿s linguistic description of social network concepts and the formal model of the network. Fundamental to this capability is the realization that both formal network models and the paradigm of computing with words are built upon set based technologies. More specifically, the formal representation of a social network is in terms a mathematical set object called a relationship and computing with words uses a set object, fuzzy subsets, to formally represent the semantics of linguistic terms. This common underlying set based technology allows us to take human concepts and formally represent them in terms of network properties. This in term allows an analyst to determine the truth or falsity of observations about a network as well helps in the mining of social relation networks.