Learning of Fuzzy Cognitive Map models without training data

Abstract

This paper introduces a novel zero-data learning algorithm tailored for Fuzzy Cognitive Map (FCM) models utilized in control applications where we must maintain concepts' activation values within predefined intervals. Our approach allows domain experts to specify these intervals and optionally impose weight constraints, ensuring the algorithm produces feasible models. At the core of our approach lies a mathematical formalism that approximates the smallest feasible activation space for each neural concept, which translates into lower and upper bounds for concepts' activation values. Moreover, a parameterized quasi-nonlinear reasoning rule allows controlling whether or not the network converges to a unique fixed point. The learning goal of our algorithm narrows down to computing a weight matrix minimizing the error between the analytical bounds and the target intervals specified by domain experts. To address such a constrained minimization problem, we employ numerical methods operating with approximate gradients, which provide highly accurate solutions with short execution times. The main contribution of our learning algorithm is that it does not require any training data to compute the network structure. Therefore, by accurately approximating the specified activation intervals, our learning algorithm guarantees that the outputs produced by the FCM model will remain within these intervals regardless of the initial conditions used to start the recurrent reasoning process.