Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 765640, 19 pages
Research Article

Friendship Dynamics: Modelling Social Relationships through a Fuzzy Agent-Based Simulation

1Grupo de Investigación en Agentes Software: Ingeniería y Aplicaciones (GRASIA), Departamento de Ingeniería del Software e Inteligencia Artificial, Universidad Complutense Madrid, 28040 Madrid, Spain
2Centre for Research in Social Simulation (CRESS), Department of Sociology, University of Surrey, Guildford, Surrey GU2 7XH, UK

Received 11 March 2011; Accepted 9 June 2011

Academic Editor: Guang Zhang

Copyright © 2011 Samer Hassan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Social relationships such as friendship and partner choice are ruled by the proximity principle, which states that the more similar two individuals are, the more likely they will become friends. However, proximity, similarity, and friendship are concepts with blurred edges and imprecise grades of membership. This study shows how to simulate these friendship dynamics in an agent-based model that applies fuzzy sets theory to implement agent attributes, rules, and social relationships, explaining the process in detail. Although in principle it may be thought that the use of fuzzy sets theory makes agent-based modelling more elaborated, in practice it saves the modeller from taking some arbitrary decisions on how to use crisp values for representing properties that are inherently fuzzy. The consequences of applying fuzzy sets and operations to define a fuzzy friendship relationship are compared with a simpler implementation, with crisp values. By integrating agent computational models and fuzzy set theory, this paper provides useful insights into scholars and practitioners to tackle the uncertainty inherent to social relationships in a systematic way.