A Generalized Fuzzy T-norm Formulation of Fuzzy Modularity for Community Detection in Social Networks
Fuzzy community detection in social networks has caught researchers’ attention because, in most real world networks, the vertices (i.e., people) do not belong to only one community. Our recent work on generalized modularity motivated us to introduce a generalized fuzzy t-norm formulation of fuzzy modularity. We investigated four fuzzy t-norm operators, Product, Drastic, Lukasiewicz and Minimum, and the generalized Yager operator, with five well-known social network data sets. The experiments show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure: (1) the Yager operator can provide a more certain visualization of the number of communities for simple networks; (2) it can find a relatively small-sized community in a flat network; (3) it can detect communities in networks with hierarchical structures; and (4) it can uncover several reasonable covers in a complicated network. These findings lead us to believe that the Yager operator can play a big role in fuzzy community detection. Our future work is to build a theoretical relation between the Yager operator and different types of networks.
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