Probabilistic Fuzzy Cognitive Map

In this paper, we present the probabilistic fuzzy cognitive map (PFCM) which is a novel extension of FCM theory. Each concept in PFCM is extended to a fuzzy event that models not only the fuzzy degree but also the fuzzy probability of both the cause and the effect concepts. PFCM enhances the capability of conventional FCMs to handle both randomness and fuzziness which are necessary to model the uncertainty involved in inference process of complex causal system. A formalized inference process of PFCMs is presented for adjustments on probability of fuzzy events and for dynamic update of causal weights. This enables PFCM to synthetically analyze the impacts of randomness and fuzziness on causal inference process. The simulation result shows a good match to the above features of PFCM. PFCM, as an initial attempt, provides a heuristic approach to model the uncertainty of complex causal systems and opens a collection of interesting research issues for further research.