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Fuzzy Closeness CentralityDefinition
Closeness centrality measures how close a node is to all
other nodes. This definition closely relates to fuzzy concepts:
1) the concept of close is a fuzzy linguistic variable, and the
concept of all other is a fuzzy universal quantifier.
A generalized fuzzy centrality measure is defined as First, there is a path closeness function for a given node v:μ_{close} : (v, u) → [0; 1] which maps possible information flow between a nodepair into a value in the unit interval. Secondly, an aggregation function λ : [0, 1]^{n} → [0, 1], which aggregates these information flows into a single value. Here λ is chosen from the set of andnessdirected operators. Following, the AIWA operator can be plugged in for λ, to get the aggregate measure of closeness to all other nodes, as seen in: When ρ < 0:5 the measure increases the ranking of nodes which have many close nodes, and for ρ > 0:5 ranking is increased for nodes close to all nodes. For ρ = 0:5 the ranking is equal to that of the classic closeness centrality measure. References
