On the Behavior of Fuzzy Grey Cognitive Maps

Abstract

Fuzzy Cognitive Maps (FCMs) are recurrent neural networks made up of well-defined neurons and causal relations. Fuzzy Grey Cogni-tive Maps (FGCMs) are an extension of FCMs, intended to surpass the intrinsic uncertainties modeling real-world problems by means of Grey theory. Despite the rising number of studies about FGCM-based models , little has been investigated with regard to the convergence of such networks. In this paper, we build a mathematical basis to uncover the behavior FGCM-based models equipped with transfer F-functions. To do so, we propose sufficient conditions for the existence and unicity of fixed-point attractors. Also, the results reported in the literature on the convergence of FGCMs, are compared with ours. Furthermore, we elucidate the reach and depth of our findings, especially and not exclusive to the prediction of FCMs' behavior.