A high percentage of information that propagates through a social network is sourced from different exogenous sources. E.g., individuals may form their opinions about products based on their own experience or reading a product review, and then share that with their social network. This sharing then diffuses through the network, evolving as a combination of both network and external effects. Besides, different individuals (nodes in a social network) have different degrees of exposition to their external sources, as well. Modeling this influence of external sources is important in order to understand the diffusion process and predict future content sharing patterns. Recognizing this fusion of intrinsic (network) effect and exogenous (external) effect, this paper develops a novel fuzzy relative willingness (FRW) model. Leveraging a fuzzy set approach provides a way to handle the uncertainties arising within the human concept of willingness. We demonstrate that FRW is able to accurately identify both top-k most content producers and diffusion effect based on external influence. We also demonstrate that the fuzzy set theory provides a compelling framework to model uncertainties pertaining to the influence as well as the susceptibility of individuals for both network and exogenous effects.

Community detection in a social network is a well-known problem that has been studied in computer science since early 2000. The algorithms available in the literature mainly follow two strategies, one, which allows a node to be a part of multiple communities with equal membership, and the second considers a disjoint partition of the whole network where a node belongs to only one community. In this paper, we proposed a novel community detection algorithm which identifies fuzzy-rough communities where a node can be a part of many groups with different memberships of their association. The algorithm runs on a new framework of social network representation based on fuzzy granular theory. A new index viz. normalized fuzzy mutual information, to quantify the goodness of detected communities is used. Experimental results on benchmark data show the superiority of the proposed algorithm compared to other well known methods, particularly when the network contains overlapping communities.