Novel Fuzzy Centrality Measures in Vague Social Networks

TL;DR

This paper introduces fuzzy centrality measures for social networks with imprecise, vague relationships, extending traditional analysis by representing ties as fuzzy numbers and applying these to real-world collaboration data.

Contribution

It generalizes fuzzy social network analysis by defining fuzzy ties and extending centrality measures, addressing the limitations of previous crisp or weighted models.

Findings

Fuzzy centrality measures effectively capture vagueness in social ties.

Application to university collaboration data demonstrates practical utility.

Fuzzy analysis reveals nuanced relationship dynamics.

Abstract

Social network analysis (SNA) helps us understand the relationships and interactions between individuals, groups, organizations, or other social entities. In the literature, ties are generally considered binary or weighted based on their strength. Nonetheless, when the actors are individuals, these relationships are often imprecise, and identifying them with simple scalars leads to information loss. Indeed, social relationships are often vague in real life, and although previous research has proposed the use of fuzzy networks, these are typically characterized by crisp ties. The use of weighted links does not align with the original philosophy of fuzzy logic, which instead aims to preserve the vagueness inherent in human language and real life. For this reason, this paper proposes a generalization of the so-called Fuzzy Social Network Analysis (FSNA) to the context of imprecise relationships among actors. Dealing with imprecise ties and introducing fuzziness in the definition of relationships requires an extension of social network analysis, defining ties as fuzzy numbers instead of crisp values and extending classical centrality indices to fuzzy centrality indexes. The article presents 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.