From fuzzy information to community detection: an approach to social networks analysis with soft information
Inmaculada Gutiérrez, Daniel Gómez, Javier Castro, Rosa Espínola
TL;DR
The paper addresses the problem of detecting communities in networks when nodes carry soft, linguistically described information rather than crisp attributes. It introduces the multi-dimensional extended fuzzy graph (MEFVFG) framework, built from a crisp network $G=(V,E)$ and a family of fuzzy information vectors, and then couples this representation with fuzzy Sugeno lambda-measures to produce a multi-dimensional, Louvain-based community detection algorithm (Multi-dimensional Fuzzy Sugeno-Louvain). By using defuzzified values from trapezoidal fuzzy sets and Shapley-based aggregation to form synergy matrices, the method produces partitions that reflect both topology and soft evidence, with evaluation via normalized mutual information (NMI) on benchmark models showing high fidelity to reference partitions. The approach generalizes prior work (EFVFG, DUO Louvain) to handle multiple fuzzy information sources and demonstrates the practical viability of incorporating linguistic uncertainty into SNA, potentially improving realism in applications where opinions or tendencies are imperfectly known. Future work points to distance measures for fuzzy sets and real-world deployments to assess robustness and scalability.
Abstract
On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of real-life problems. This work is set on the existence of one (or multiple) soft information sources, independent of the network considered, assuming this extra knowledge is modeled by a vector of fuzzy sets (or a family of vectors). This information may represent, for example, how much some people agree with a specific law, or their position against several politicians. We emphasize the importance of being able to manage the vagueness which usually appears in real life because of the common use of linguistic terms. Then, we propose a constructive method to build fuzzy measures from fuzzy sets. These measures are the basis of a new representation model which combines the information of a network with that of fuzzy sets, specifically when it comes to linguistic terms. We propose a specific application of that model in terms of finding communities in a network with additional soft information. To do so, we propose an efficient algorithm and measure its performance by means of a benchmarking process, obtaining high-quality results.