{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:26:10Z","timestamp":1772252770652,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T00:00:00Z","timestamp":1603324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The accurate prediction of the solar diffuse fraction (DF), sometimes called the diffuse ratio, is an important topic for solar energy research. In the present study, the current state of Diffuse irradiance research is discussed and then three robust, machine learning (ML) models are examined using a large dataset (almost eight years) of hourly readings from Almeria, Spain. The ML models used herein, are a hybrid adaptive network-based fuzzy inference system (ANFIS), a single multi-layer perceptron (MLP) and a hybrid multi-layer perceptron grey wolf optimizer (MLP-GWO). These models were evaluated for their predictive precision, using various solar and DF irradiance data, from Spain. The results were then evaluated using frequently used evaluation criteria, the mean absolute error (MAE), mean error (ME) and the root mean square error (RMSE). The results showed that the MLP-GWO model, followed by the ANFIS model, provided a higher performance in both the training and the testing procedures.<\/jats:p>","DOI":"10.3390\/e22111192","type":"journal-article","created":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T10:27:58Z","timestamp":1603362478000},"page":"1192","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Adaptive Neuro-Fuzzy Inference System and a Multilayer Perceptron Model Trained with Grey Wolf Optimizer for Predicting Solar Diffuse Fraction"],"prefix":"10.3390","volume":"22","author":[{"given":"Randall","family":"Claywell","sequence":"first","affiliation":[{"name":"Kando Kalman Faculty of Electrical Engineering, Obuda University, 1034 Budapest, Hungary"}]},{"given":"Laszlo","family":"Nadai","sequence":"additional","affiliation":[{"name":"Kando Kalman Faculty of Electrical Engineering, Obuda University, 1034 Budapest, Hungary"}]},{"given":"Imre","family":"Felde","sequence":"additional","affiliation":[{"name":"John von Neumann Faculty of Informatics, Obuda University, 1034 Budapest, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7744-7906","authenticated-orcid":false,"given":"Sina","family":"Ardabili","sequence":"additional","affiliation":[{"name":"Kando Kalman Faculty of Electrical Engineering, Obuda University, 1034 Budapest, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4842-0613","authenticated-orcid":false,"given":"Amirhosein","family":"Mosavi","sequence":"additional","affiliation":[{"name":"Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam"},{"name":"Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.apenergy.2011.01.054","article-title":"A study of grid-connected photovoltaic (PV) system in Hong Kong","volume":"90","author":"Li","year":"2012","journal-title":"Appl. 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