Analyzing the activity of a person in a chat by combining network analysis and fuzzy logic

Chat-log data that contains information about sender and receiver of the statements sent around in the chat can be readily turned into a directed temporal multi-network representation. In the resulting network, the activity of a chat member can, for example, be operationalized as his degree (number of distinct interaction partners) or his strength (total number of interactions). However, the data itself contains more information that is not readily representable in the network, e.g., the total number of words used by a member or the reaction time to what the members said. As degree and strength, these values can be seen as a way to operationalize the idea of activity of a chat-log member. This paper deals with the question of how the overall activity of a member can be assessed, given multiple and probably opposing criteria by using a fuzzy operator. We then present a new way of visualizing the results and show how to apply it to the network representation of chat-log data. Finally, we discuss how this approach can be used to deal with other conflicting situations, like the different rankings produced by different centrality indices.