A New Balance Degree for Fuzzy Cognitive Maps

In this paper a new balance degree is proposed for better evaluation of the conflicts that exist in the graph of Fuzzy Cognitive Maps (FCMs). FCMs are fuzzy weighted directed graphs with feedback that create models that emulate the behaviour of complex decision processes using fuzzy causal relations. The existence of two causal relations of opposite sign between two nodes makes the graph of the FCM imbalanced. The degree to which the whole digraph of the FCM is balanced or imbalanced is given by the Balance Degree. Various types of Balance Degree exist for signed directed graphs. We proposed a new type of Balance degree that is suitable for FCMs. The new degree is evaluated by exhaustively searching all the paths that are created in the graph and gives an indication of the dynamical behaviour that we should expect from the FCM. This is important because the conclusions that we draw from the FCM are coming from the study of its dynamical behaviour.