Fuzzy Cognitive Map Reconstruction: Dynamics Versus History

This study is concerned with a fundamental issue of time series representation for modeling and prediction with Fuzzy Cognitive Maps. We introduce two distinct time series representation schemes for Fuzzy Cognitive Map design. The first method is based on the temporal relationships, namely time series amplitude, amplitude change, and change of amplitude change (dynamics perspective). The second scheme is based on three consecutive historical observations: present value, past value and before past value (history perspective, 2nd order relationships). Introduced procedures are experimentally verified and compared on several synthetic and real-world time series of various characteristics. The history-oriented time series representation turned out to be more advantageous. Quality of FCM-based time series models and one-step-ahead predictions were measured in terms of Mean Squared Error. We have shown that models designed with history-oriented time series representation generally require less FCM nodes to be of comparable quality to models built on dynamics-oriented time series representation. As a result, with the history-oriented time series representation scheme we are able to construct simpler and better models.