Learning-based aggregation of Quasi-Nonlinear Fuzzy Cognitive Maps

Quasi-Nonlinear Fuzzy Cognitive Maps (q-FCMs) are an algorithmic generalization of Fuzzy Cognitive Maps (FCMs) used for modeling and simulation. The key advantages of q-FCMs include their interpretability and hybrid reasoning capabilities where expert knowledge and historical data can be exploited to build the model. Another distinctive feature of neural cognitive mapping is that it allows the aggregation of different models that represent the same problem into a unified neural system. Unfortunately, existing aggregation algorithms focus on producing an aggregated model that resembles the structure of the individual q-FCMs, while neglecting the functional aspect. The ramification of this oversight is that the simulation results produced by the aggregated model often differ significantly from those generated by the individual models. In this paper, we introduce a parameterized learning-based method for aggregating q-FCMs that considers both aspects. Firstly, it ensures that the aggregated model’s weight matrix is reasonably similar to those associated with the individual models, thus maintaining the structural integrity of the aggregation. Secondly, it ensures that the aggregated model’s outputs closely align with those produced by the individual models when operating under the same initial conditions. The core of our aggregation method lies in an analytically derived loss function that is minimized using a gradient-based optimizer which approximates the Jacobian and Hessian while using a limited amount of memory. Extensive simulations on synthetically generated models and a case study with diverse structural properties and complexities demonstrate that our approach significantly outperforms representative state-of-the-art methods.