An Evolutionary Methodology to Eliminate the Limit Cycle Phenomenon in FCM-Based Models

Abstract

This paper presents the dynamic behaviour of a hybrid system comprising Fuzzy Cognitive Maps (FCM) and Genetic Algorithms, and focuses on the behaviour of the former under equilibrium at fixed points or limit cycle. More specifically, the theoretical background of both the equilibrium and limit cycle behaviours is examined and a new methodology for eliminating the limit cycle phenomenon is proposed. An evolutionary algorithm is designed based on the correction of the weight matrix, the origin of which is responsible for the creation of the limit cycle phenomenon. The system traces the presence of a limit cycle or chaotic behaviour and then searches the weight matrix using evolutionary techniques to identify which weight or group of weights are responsible for the cause of the limit cycle. This process continues until the system reaches equilibrium, a state which is necessary for the execution of simulations and the optimisation of various weights to meet a certain hypothetical scenarios in the context of decision-making.