Modeling time series with fuzzy cognitive maps

Abstract

Fuzzy Cognitive Maps are recognized knowledge modeling tool. FCMs are visualized with directed graphs. Nodes represent information, edges represent relations within information. The core element of each Fuzzy Cognitive Map is weights matrix, which contains evaluations of connections between map's nodes. Typically, weights matrix is constructed by experts. Fuzzy Cognitive Map can be also reconstructed in an unmanned mode. In this article authors present their own, new approach to time series modeling with Fuzzy Cognitive Maps. Developed methodology joins Fuzzy Cognitive Map reconstruction procedure with moving window approach to time series prediction. Authors train Fuzzy Cognitive Maps to model and forecast time series. The size of the map corresponds to the moving window size and it informs about the length of historical data, which produces time series model. Developed procedure is illustrated with a series of experiments on three real-life time series. Obtained results are compared with other approaches to time series modeling. The most important contribution of this paper is description of the methodology for time series modeling with Fuzzy Cognitive Maps and moving windows.