Bi-linear adaptive estimation of Fuzzy Cognitive Networks

Abstract

Fuzzy Cognitive Networks (FCNs) have been introduced by the authors as an operational extension of Fuzzy Cognitive Maps (FCMs), initially introduced by Kosko to model complex behavioral systems in various scientific areas. FCNs rely on the admission that the underlying cognitive graph reaches a certain equilibrium point after an initial perturbation. Weight conditions for reaching equilibrium points have been recently derived in [54] along with an algorithm for weight estimation. In this paper, the conditions are extended to take into account not only the weights of the map but also the inclination parameters of the involved sigmoid functions, increasing the structural flexibility of the network. This in turn gives rise to the development of a new adaptive bilinear weight and sigmoid parameter estimation algorithm, which employs appropriate weight projection criteria to assure that the equilibrium is always achieved.