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.

翻译：社交网络分析（SNA）有助于我们理解个体、群体、组织或其他社会实体之间的关系与互动。在现有文献中，连接通常被视为二元的或基于其强度的加权关系。然而，当行动者是个人时，这些关系往往是不精确的，用简单的标量来标识它们会导致信息丢失。事实上，现实生活中的社交关系通常是模糊的，尽管先前的研究提出了使用模糊网络，但这些网络通常以清晰连接为特征。使用加权连接与模糊逻辑的原始理念并不一致，模糊逻辑旨在保留人类语言和现实生活固有的模糊性。因此，本文提出将所谓的模糊社交网络分析（FSNA）推广到行动者之间不精确关系的语境中。处理不精确连接并在关系定义中引入模糊性，需要对社交网络分析进行扩展，将连接定义为模糊数而非清晰值，并将经典中心性指标扩展为模糊中心性指标。本文介绍了通过一种引人入胜的鼠标追踪技术收集的真实数据的理论与应用，以研究某大学系部成员合作网络中的模糊关系。