Abstract

This paper presents a learning algorithm designed to address the inverse simulation problems in Quasi-Nonlinear Fuzzy Cognitive Maps (qFCMs). The algorithm determines the initial conditions for qFCM models that produce the desired outputs specified by the modeler. The contribution rests on three main components, which aim to generate feasible and accurate solutions. Firstly, we employ a quasi-nonlinear reasoning rule designed to ensure that the qFCM model will always converge to multiple fixed points that depend on the initial conditions. By steering clear of unique fixed-point attractors, the proposed learning algorithm mitigates the risk of encountering unsolvable inverse simulation scenarios. Secondly, we provide the modeler with mathematically determined, yet comprehensive insights into the feasible activation space for each neural concept. These spaces represent intervals that outline the activation values that can be reached by the neuronal concepts, which allow the modeler to select realistic targets. Lastly, we formulate the inverse learning problem for qFCM models as an optimization task resolved with the aid of numerical optimizers that approximate the Jacobian and Hessian. Empirical studies illustrate the effectiveness of our proposal to produce accurate inverse solutions for real-world scenarios and synthetically generated models.