{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:40:13Z","timestamp":1760190013074,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T00:00:00Z","timestamp":1566172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We present a new seasonal forecasting method based on F1-transform (fuzzy transform of order 1) applied on weather datasets. The objective of this research is to improve the performances of the fuzzy transform-based prediction method applied to seasonal time series. The time series\u2019 trend is obtained via polynomial fitting: then, the dataset is partitioned in S seasonal subsets and the direct F1-transform components for each seasonal subset are calculated as well. The inverse F1-transforms are used to predict the value of the weather parameter in the future. We test our method on heat index datasets obtained from daily weather data measured from weather stations of the Campania Region (Italy) during the months of July and August from 2003 to 2017. We compare the results obtained with the statistics Autoregressive Integrated Moving Average (ARIMA), Automatic Design of Artificial Neural Networks (ADANN), and the seasonal F-transform methods, showing that the best results are just given by our approach.<\/jats:p>","DOI":"10.3390\/s19163611","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T11:22:38Z","timestamp":1566213758000},"page":"3611","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Seasonal Time Series Forecasting by F1-Fuzzy Transform"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5690-5384","authenticated-orcid":false,"given":"Ferdinando","family":"Di Martino","sequence":"first","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Centro di Ricerca Interdipartimentale di Ricerca A. Calza Bini, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4303-2884","authenticated-orcid":false,"given":"Salvatore","family":"Sessa","sequence":"additional","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Centro di Ricerca Interdipartimentale di Ricerca A. Calza Bini, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,19]]},"reference":[{"key":"ref_1","unstructured":"Box, G.E.P., Jenkins, G.E.P., and Reinsel, G.C. (2016). Time Series Analysis: Forecasting and Control, John Wiley & Sons. [5th ed.]."},{"key":"ref_2","unstructured":"Chatfield, C. (2003). The Analysis of Time Series: An Introduction, Chapman & Hall\/CRC. [6th ed.]."},{"key":"ref_3","unstructured":"Hymdam, R.J., and Athanasopoulos, G. (2013). Forecasting Principles and Practice, OText Publisher."},{"key":"ref_4","unstructured":"Pankratz, A. (2012). Forecasting with Dynamic Regression Models, John Wiley & Sons."},{"key":"ref_5","unstructured":"Wei, W.W.S. (2006). Time Series Analysis Univariate and Multivariate Methods, Pearson Addison Wesley. [2nd ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1800","DOI":"10.1109\/TNN.2007.896859","article-title":"Quarterly time-series forecasting with neural networks","volume":"18","author":"Zhang","year":"2007","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0169-2070(97)00044-7","article-title":"Forecasting with artificial neural networks: The state of the art","volume":"14","author":"Zhang","year":"1998","journal-title":"Int. J. Forecast."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1111\/1467-9876.00109","article-title":"Time series forecasting with neural networks: A comparative study using the airline data","volume":"47","author":"Faraway","year":"1998","journal-title":"J. R. Stat. Soc. Ser. C Appl. Stat."},{"key":"ref_9","first-page":"41","article-title":"Seasonal time series forecasting: A comparative study of ARIMA and ANN models Afr","volume":"5","author":"Kihoro","year":"2006","journal-title":"J. Sci. Technol. Sci. Eng. Ser."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00521-012-1264-z","article-title":"Time-delay neural networks for time series prediction: An application to the monthly wholesale price of oilseeds in India","volume":"24","author":"Jha","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_11","unstructured":"Ivanovi\u0107, M., and Kurbalija, V. (June, January 30). Time series analysis and possible applications. Proceedings of the 39th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), Opatija, Croatia."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4261","DOI":"10.1016\/j.eswa.2009.11.076","article-title":"Time series forecasting by a seasonal support vector regression model","volume":"37","author":"Pai","year":"2010","journal-title":"Exp. Syst. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10574","DOI":"10.1016\/j.eswa.2011.02.107","article-title":"A hybrid model of self-organizing maps (SOM) and least square support vector machine (LSSVM) for time-series forecasting","volume":"38","author":"Ismail","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.5194\/hess-15-1835-2011","article-title":"River flow time series using least squares support vector machines","volume":"15","author":"Samsudin","year":"2011","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_15","first-page":"6207","article-title":"Least square support vector machines as an alternative method in seasonal time series forecasting","volume":"9","author":"Shabri","year":"2015","journal-title":"Appl. Math. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Suykens, J.A.K., Van Gestel, T., De Brabanter, J., De Moor, B., and Vandewalle, J. (2002). Least Squares Support Vector Machines, World Scientific Publishing Company.","DOI":"10.1142\/5089"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1981","DOI":"10.1016\/j.eswa.2012.10.001","article-title":"Forecasting seasonal time series with computational intelligence: On recent methods and the potential of their combinations","volume":"40","author":"Cortez","year":"2013","journal-title":"Exp. Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1016\/j.fss.2005.11.012","article-title":"Fuzzy transforms: Theory and applications","volume":"157","author":"Perfilieva","year":"2006","journal-title":"Fuzzy Sets Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.fss.2010.11.009","article-title":"Fuzzy transforms method in prediction data analysis","volume":"180","author":"Loia","year":"2011","journal-title":"Fuzzy Sets Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.fss.2018.09.010","article-title":"Forecasting seasonal time series based on fuzzy techniques","volume":"361","author":"Nguyen","year":"2019","journal-title":"Fuzzy Sets Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1007\/978-3-319-52962-2_4","article-title":"Fuzzy Transforms and Seasonal Time Series","volume":"Volume 10147","author":"Petrosino","year":"2017","journal-title":"Proceedings of the Fuzzy Logic and Soft Computing Applications, WILF 2016"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Di Martino, F., and Sessa, S. (2017). Time series seasonal analysis based on fuzzy transforms. Symmetry, 9.","DOI":"10.20944\/preprints201710.0053.v1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.fss.2010.11.002","article-title":"Towards a higher degree f-transform","volume":"180","author":"Perfilieva","year":"2011","journal-title":"Fuzzy Sets Syst."},{"key":"ref_24","first-page":"40","article-title":"Advantages of the MAD\/MEAN ratio over the MAPE","volume":"6","author":"Kolassa","year":"2007","journal-title":"Foresight"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1175\/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2","article-title":"The assessment of sultriness. Part I: A temperature-humidity index based on human physiology and clothing science","volume":"18","author":"Steadman","year":"1987","journal-title":"J. Appl. Meteorol."},{"key":"ref_26","unstructured":"Rothfusz, L.P. (2019, March 16). The Heat Index \u201cEquation\u201d (or, More Than You Ever Wanted to Know About Heat Index), 1990 National Weather Service (NWS) Technical Attachment (SR 90-23), Available online: https:\/\/www.weather.gov\/media\/wrh\/online_publications\/TAs\/ta9024.pdf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S0169-2070(00)00086-8","article-title":"The forecast pro methodology","volume":"16","author":"Goodrich","year":"2000","journal-title":"Int. J. Forecast."},{"key":"ref_28","unstructured":"Peralta, J., Gutierrez, G., and Sanchis, A. (2008, January 12\u201316). ADANN: Automatic Design of Artificial Neural Networks. Proceedings of the GECCO \u201808 10th Annual Conference Companion on Genetic and Evolutionary Computation, Atlanta, GA, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s00521-011-0741-0","article-title":"Time series forecasting by evolving artificial neural networks with genetic algorithms, differential evolution and estimation of distribution algorithm","volume":"22","author":"Donate","year":"2013","journal-title":"Neural Comput. Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3611\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:12:17Z","timestamp":1760188337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,19]]},"references-count":29,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["s19163611"],"URL":"https:\/\/doi.org\/10.3390\/s19163611","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,8,19]]}}}