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Hybrid Simulations

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Fuzzy Cognitive Maps

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Abstract

A Fuzzy Cognitive Map can serve to externalize the mental model of an individual or group. However, mental models do not directly communicate, in the same way as two brains lying on a table cannot interact. While FCMs can be quickly developed, they cannot capture how processes differ over space or across time. These limitations can be addressed either through extensions (Chap. 6) or by combining FCMs with other techniques. In this chapter, we focus on hybrid simulations, which involve combining FCMs with other simulation techniques such as cellular automata, complex networks, or agent-based models (ABMs). Hybrid ABM/FCM simulations are our focal point, as they have received the most attention in the literature. We explain how they can be used to simulate interactions between individuals, provide time estimates, and account for spatial differences. We provide a five-step process to build such models and exemplify it on a case study, supported with Python code. This chapter equips readers with fundamental simulation concepts, exemplifies practical applications that motivate ABM/FCM simulations, and provides a reusable process to create such simulations.

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Notes

  1. 1.

    A Cellular Automaton (CA) consists of a set of cells which are arranged in a regular pattern, such as a grid or hexagonal tiling (for a 2D space). Each cell has a state. States are updated over discrete time steps based on time (e.g., an infected cell dies after 4 steps), probability (e.g., chance of recovering), and neighboring cells (e.g., transmitting an infection). While this approach may not be suitable for social systems since people have varying number of social contacts, it is a popular representation of physical systems where dynamics are based on proximity.

  2. 2.

    It is common to specify the behavior of all agents from one category using the same ruleset. For example, a model can capture the vaccine behavior of all farmers as a function of their profile, perceived utility for a certain action, and the perceived norms from their social network. We may still observe heterogeneous actions, because agents have different profiles (i.e., features) or varied positions within their social network and physical environment [48]. However, the implicit assumption is that agents all apply the same reasoning process given a set of inputs. In reality, individuals may have the same set of features and receive the same information, but they could decide differently by following different rulesets or making different errors—a defining characteristic of being human [6]. Experimental research also shows that the different rules perceived by individuals are more closely aligned with the heterogeneity of behavioral outcome than their features [21].

  3. 3.

    Our earlier discussion on building such models proposed three phases [20]. Based on ten years of experience, we divided some of these phases to provide better guidance to modelers in this book.

  4. 4.

    The use of such deep neural networks for population synthesis in ABMs is an emerging research area, and its application for hybrid ABM/FCM models is an open research question.

  5. 5.

    Several studies are following best practices for replicability by disclosing the FCMs of all individual participants [3, 47], which can thus be reused for simulation purposes.

  6. 6.

    The step-by-step tutorial created by Kim Ha and Kareem Ghumrawi is available at https://cuda-hybrid.github.io/tutorials/index.html.

  7. 7.

    To illustrate the impact of the number of virtual agents onto the stability of simulation outcomes, see Fig. 9 in [26].

  8. 8.

    When using multiple generators in a single study, they must be calibrated to produce similar populations. Otherwise, the variance in the simulation outcomes would not be attributable only to how people connect, but also to the number of people and connections. Generators may not be able to create populations of any desired size due to their mechanisms. For example, some generators can create a larger population by copying and linking multiple instances of a smaller population [5]. In our case, we used 2,412 agents because this population size can be generated both by the small-world generator and the scale-free generator. The other parameter values (11, 0.05) were determined to provide an equivalent number of social ties in both generated networks.

  9. 9.

    National statistics can be a valuable source to jointly initialize demographic factors such as age, gender, race and ethnicity. Several constructs are expressed in other data sources as a function of such demographic factors. Note that sources should provide a representative sample for the target population of the model. Since data sources will impact the simulation outcomes, characteristics and limitations of the data sources (e.g., sample size, use of sample weights) should be disclosed as part of a model’s description.

  10. 10.

    The amount of social pressure necessary to change an individual’s behavior, and the extent to which it changes, are both difficult to observe in reality hence data may not be available. Observational studies may provide upper and/or lower bounds on changes, for example by documenting how an individual adapts to certain situations (e.g., how much more people eat when they are in a group). Unknown parameters can thus be calibrated to ensure that the model’s output falls within a plausible range. If the model is not particularly sensitive to the parameters’ values, a plausible output may be obtained for many parameter values and modelers will have to choose them. A model may also exhibit a phase transition, such that an implausible outcome appears once a certain parameter value is reached, which helps to narrow down possible values (see Fig. 6 in [22]).

  11. 11.

    Models involving probabilities are called stochastic models. Those without any probability (i.e., in which the outcome for a given input is always the same) are deterministic. Stochastic models do not mean that the world operates ‘somewhat randomly’. Rather, they posit that there are unknowns about certain processes, and this variability is represented by probabilities that can be tuned to assess their impact onto simulation outcomes. Achieving a more sophisticated model can be a significant project in itself: in our case, we would need a sub-model that determines whether an individual accepts an advice given their characteristics, the characteristics of the influencing peer, past advice offered, or the nature of the advice. The creation of such sub-model may reveal more (albeit specific) unknowns, thus increasing the number of probabilities used in a model.

  12. 12.

    Mass-market GPUs such as GeForce GTX 1660 or GeForce GTX 1080 provide 1408 and 2560 CUDA cores, respectively. A workstation-grade GPU such as a Quadro RTX A5000 has 8192 cores.

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Miami University, Oxford, OH, USA

    Philippe J. Giabbanelli

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Correspondence to Philippe J. Giabbanelli .

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  1. Department of Computer Science and Software Engineering, Miami University, Oxford, OH, USA

    Philippe J. Giabbanelli

  2. Cognitive Science and Artificial Intelligence, Tilburg University, Tilburg, Noord-Brabant, The Netherlands

    Gonzalo Nápoles

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Giabbanelli, P.J. (2024). Hybrid Simulations. In: Giabbanelli, P.J., Nápoles, G. (eds) Fuzzy Cognitive Maps. Springer, Cham. https://doi.org/10.1007/978-3-031-48963-1_4

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