Measuring fuzzy domination in fuzzy weighted directed social networks

In social networks, we are viewing the weighted sociogram as having the edge weights which measure the intensity of the relationship with the adjacent nodes. The weights on the arcs are determined by using a web system named Intensity Relationship Analyzer & Presenter. Due to lack of some reliability on the calculated values we use the concept of fuzzy to get the approximate values of the intensity i.e. imprecise edge weights. In this paper we use triangular fuzzy number (TFN) for the imprecise problem of edge weights. Here we use Type-1 fuzzy set to describe “how strong is the relationship between the two adjacent nodes” or “how much node is dependent on other node” by calculating relationship intensity. After calculating the relationship intensity as the edge weights we use a relational power function to represent the relational power of any node in the network. In this paper dominance relations between the nodes are calculated fuzzy edge weights contained in directed sociogram. We use β-measure to calculate fuzzy dominance in weighted directed social network.