Fuzzy Social Network Analysis: Theory and Application in a University Department's Collaboration Network

Social network analysis (SNA) helps us understand the relationships and interactions between individuals, groups, organisations, or other social entities. In SNA, ties are generally binary or weighted based on their strength. Nonetheless, when actors are individuals, the relationships between actors are often imprecise and identifying them with simple scalars leads to information loss. Social relationships are often vague in real life. Despite many classical social network techniques contemplate the use of weighted links, these approaches do not align with the original philosophy of fuzzy logic, which instead aims to preserve the vagueness inherent in human language and real life. Dealing with imprecise ties and introducing fuzziness in the definition of relationships requires an extension of social network analysis to fuzzy numbers instead of crisp values. The mathematical formalisation for this generalisation needs to extend classical centrality indices and operations to fuzzy numbers. For this reason, this paper proposes a generalisation of the so-called Fuzzy Social Network Analysis (FSNA) to the context of imprecise relationships among actors. The article shows the theory and application of real data collected through a fascinating mouse tracking technique to study the fuzzy relationships in a collaboration network among the members of a University department.