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From Fuzzy Information to Community Detection: An Approach to Social Networks Analysis with Soft Information

Author

Listed:
  • Inmaculada Gutiérrez

    (Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, 28040 Madrid, Spain)

  • Daniel Gómez

    (Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, 28040 Madrid, Spain
    Instituto de Evaluación Sanitaria, Universidad Complutense de Madrid, 28040 Madrid, Spain)

  • Javier Castro

    (Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, 28040 Madrid, Spain
    Instituto de Evaluación Sanitaria, Universidad Complutense de Madrid, 28040 Madrid, Spain)

  • Rosa Espínola

    (Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, 28040 Madrid, Spain
    Instituto de Evaluación Sanitaria, Universidad Complutense de Madrid, 28040 Madrid, Spain)

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.

Suggested Citation

  • Inmaculada Gutiérrez & Daniel Gómez & Javier Castro & Rosa Espínola, 2022. "From Fuzzy Information to Community Detection: An Approach to Social Networks Analysis with Soft Information," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4348-:d:977776
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    References listed on IDEAS

    as
    1. Ludo Waltman & Nees Eck, 2013. "A smart local moving algorithm for large-scale modularity-based community detection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(11), pages 1-14, November.
    2. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    3. Daniel Gómez & Javier Castro & Inmaculada Gutiérrez & Rosa Espínola, 2021. "A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection," Mathematics, MDPI, vol. 9(21), pages 1-29, October.
    4. Inmaculada Gutiérrez & Juan Antonio Guevara & Daniel Gómez & Javier Castro & Rosa Espínola, 2021. "Community Detection Problem Based on Polarization Measures: An Application to Twitter: The COVID-19 Case in Spain," Mathematics, MDPI, vol. 9(4), pages 1-27, February.
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