Cognitive Mapping and Certainty Neuron Fuzzy Cognitive Maps

Cognitive maps (CMs) and fuzzy cognitive maps (FCMs) are well-established techniques that attempt to emulate the cognitive process of human experts on specific domains by creating causal models as signed/weighted directed graphs of concepts and the various causal relationships that exist between the concepts. They are mainly used for decision making and prediction. A number of extensions are proposed to increase their inference and representation capabilities. Certainty neuron fuzzy cognitive maps (CNFCMs) are proposed by the authors. This structure can be considered as a recurrent neural network with certainty neurons to be used that are neurons using a special kind of transfer function of two variables. The new transfer function employs the certainty factor handling function that was used in the MYCIN expert system, and also imposes a decay mechanism. In CMs and most FCMs, the activation level of every concept of the model, in a crisp on/off manner, can take one value among the two allowed values, −1 or 1. CNFCM allows the activation level to be any decimal in the interval [−1,1] increasing the representation capabilities of the model. The equations that are applied at the equilibrium points of the CNFCM are found. Through simulations, the dynamical behavior of CNFCMs is presented and the inference capabilities are illustrated in comparison to that of the classical FCM by means of an example.