Time Series Forecasting Using Fuzzy Cognitive Maps: A Survey

Among various soft computing approaches for time series forecasting, Fuzzy Cognitive Maps (FCM) have shown remarkable results as a tool to model and analyze the dynamics of complex systems. FCM have similarities to recurrent neural networks and can be classified as a neuro-fuzzy method. In other words, FCMs are a mixture of fuzzy logic, neural network, and expert system aspects, which act as a powerful tool for simulating and studying the dynamic behavior of complex systems. The most interesting features are knowledge interpretability, dynamic characteristics and learning capability. The goal of this survey paper is mainly to present an overview on the most relevant and recent FCM-based time series forecasting models proposed in the literature. In addition, this article considers an introduction on the fundamentals of FCM model and learning methodologies. Also, this survey provides some ideas for future research to enhance the capabilities of FCM in order to cover some challenges in the real-world experiments such as handling non-stationary data and scalability issues. Moreover, equipping FCMs with fast learning algorithms is one of the major concerns in this area.

Introducing Randomized High Order Fuzzy Cognitive Maps as Reservoir Computing Models: A Case Study in Solar Energy and Load Forecasting

Fuzzy Cognitive Maps (FCMs) have emerged as an interpretable signed weighted digraph method consisting of nodes (concepts) and weights which represent the dependencies among the concepts. Although FCMs have attained considerable achievements in various time series prediction applications, designing an FCM model with time-efficient training method is still an open challenge. Thus, this paper introduces a novel univariate time series forecasting technique, which is composed of a group of randomized high order FCM models labeled R-HFCM. The novelty of the proposed R-HFCM model is relevant to merging the concepts of FCM and Echo State Network (ESN) as an efficient and particular family of Reservoir Computing (RC) models, where the least squares algorithm is applied to train the model. From another perspective, the structure of R-HFCM consists of the input layer, reservoir layer, and output layer in which only the output layer is trainable while the weights of each sub-reservoir components are selected randomly and keep constant during the training process. As case studies, this model considers solar energy forecasting with public data for Brazilian solar stations as well as Malaysia dataset, which includes hourly electric load and temperature data of the power supply company of the city of Johor in Malaysia. The experiment also includes the effect of the map size, activation function, the presence of bias and the size of the reservoir on the accuracy of R-HFCM method. The obtained results confirm the outperformance of the proposed R-HFCM model in comparison to the other methods. This study provides evidence that FCM can be a new way to implement a reservoir of dynamics in time series modelling.