Design of Type-3 Fuzzy Systems and Ensemble Neural Networks for COVID-19 Time Series Prediction Using a Firefly Algorithm

Abstract

In this work, information on COVID-19 confirmed cases is utilized as a dataset to perform time series predictions. We propose the design of ensemble neural networks (ENNs) and type-3 fuzzy inference systems (FISs) for predicting COVID-19 data. The answers for each ENN module are combined using weights provided by the type-3 FIS, in which the ENN is also designed using the firefly algorithm (FA) optimization technique. The proposed method, called ENNT3FL-FA, is applied to the COVID-19 data for confirmed cases from 12 countries. The COVID-19 data have shown to be a complex time series due to unstable behavior in certain periods of time. For example, it is unknown when a new wave will exist and how it will affect each country due to the increase in cases due to many factors. The proposed method seeks mainly to find the number of modules of the ENN and the best possible parameters, such as lower scale and lower lag of the type-3 FIS. Each module of the ENN produces an individual prediction. Each prediction error is an input for the type-3 FIS; moreover, outputs provide a weight for each prediction, and then the final prediction can be calculated. The type-3 fuzzy weighted average (FWA) integration method is compared with the type-2 FWA to verify its ability to predict future confirmed cases by using two data periods. The achieved results show how the proposed method allows better results for the real prediction of 20 future days for most of the countries used in this study, especially when the number of data points increases. In countries such as Germany, India, Italy, Mexico, Poland, Spain, the United Kingdom, and the United States of America, on average, the proposed ENNT3FL-FA achieves a better performance for the prediction of future days for both data points. The proposed method proves to be more stable with complex time series to predict future information such as the one utilized in this study. Intelligence techniques and their combination in the proposed method are recommended for time series with many data points.

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“…Finally, they suggested a real case study in the United States to validate their problem. Melin et al ( 2022 ) proposed a method called ENNT3FL-FA that combines ensemble neural networks and type-3 fuzzy inference systems to predict COVID-19 data for confirmed cases in 12 countries. The method seeks to find the best possible parameters for each module of the ENN and the type-3 FIS.…”

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“…Meanwhile, Luo et al ventured into the realm of the Internet of Vehicles, analyzing, and forecasting macro-scale big data concerning driving behaviors via adaptive fuzzy cyclic neural networks [30]. In the healthcare sector, Melin et al and Castillo et al demonstrated the application of fuzzy systems to predict the trajectory of confirmed COVID-19 cases, providing crucial insights for pandemic management [31,32]. Collectively, these studies underscore the versatility and robustness of FNNs as a tool for tackling diverse predictive challenges characterized by fuzziness and uncertainty.…”

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“…Improved performance of interval type-3 and general type-2 systems over type-1 fuzzy systems has been illustrated in diverse settings, including industrial applications, e.g., flowmeter fault reporting, product temperature prediction and battery management [12]- [16], and financial and health applications requiring time series predictions [17], [18]. Higher-order fuzzy sets have also been employed to represent group or consensus decisions (e.g., [19]- [21]).…”