On the Convergence of Input-Output Fuzzy Cognitive Maps

Abstract

Fuzzy cognitive maps are recurrent neural networks, where the neurons have a well-defined meaning. In certain models, some neurons receive outer input, while other neurons produce the output of the system. According to this observation, some neurons are categorized as input neurons and the others are the state neurons and output neurons. The output of the system is provided as a limit of an iteration process, which may converge to an equilibrium point, but limit cycles or chaotic behaviour may also show up. In this paper, we examine the existence and uniqueness of fixed points for two types of input-output fuzzy cognitive maps. Moreover, we use network-based measures like in-degree, out-degree and connectivity, to express conditions for the convergence of the iteration process.