Solar Energy Forecasting With Fuzzy Time Series Using High-Order Fuzzy Cognitive Maps

Various studies indicate that Fuzzy Time Series (FTS) methods can obtain high accuracy in a variety of forecasting applciations. However, weighted FTS methods tend to show superiority in contrast to weightless ones. This study exploits the use of Fuzzy Cognitive Map (FCM) technique to generate the rules in the knowledge base for the FTS forecasting method. The proposed hybrid method, named HFCM-FTS, combines High Order Fuzzy Cognitive Maps (HFCM) and High Order Fuzzy Time Series (HOFTS), where the weight matrices associated with the state transitions are learned via the genetic algorithm from the data. The objective of FCM is to find the weight matrices that model the causal relations among the concepts defined in the Universe of Discourse. As a case study, we consider solar energy forecasting with public data for Brazilian solar stations from the year 2012 to 2015. The proposed HFCM-FTS is compared with HOFTS, Weighted High Order FTS (WHOFTS), and Probabilistic Weighted FTS (PWFTS) methods. The experiments also cover the influence of three modeling elements on the accuracy of the presented model including the number of concepts, activation function, and bias. The results show that the HFCM-FTS is able to achieve the best results with a low number of concepts.