Design of fuzzy cognitive maps using neural networks for predicting chaotic time series

As a powerful paradigm for knowledge representation and a simulation mechanism applicable to numerous research and application fields, Fuzzy Cognitive Maps (FCMs) have attracted a great deal of attention from various research communities. However, the traditional FCMs do not provide efficient methods to determine the states of the investigated system and to quantify causalities which are the very foundation of the FCM theory. Therefore in many cases, constructing FCMs for complex causal systems greatly depends on expert knowledge. The manually developed models have a substantial shortcoming due to model subjectivity and difficulties with accessing its reliability. In this paper, we propose a fuzzy neural network to enhance the learning ability of FCMs so that the automatic determination of membership functions and quantification of causalities can be incorporated with the inference mechanism of conventional FCMs. In this manner, FCM models of the investigated systems can be automatically constructed from data, and therefore are independent of the experts. Furthermore, we employ mutual subsethood to define and describe the causalities in FCMs. It provides more explicit interpretation for causalities in FCMs and makes the inference process easier to understand. To validate the performance, the proposed approach is tested in predicting chaotic time series. The simulation studies show the effectiveness of the proposed approach.