{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T02:09:51Z","timestamp":1769047791157,"version":"3.49.0"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Air pollution is a worldwide problem faced by most countries across the world. Prediction of air pollution is crucial in air quality research since it is related to public health effects. The symmetry concept of fuzzy data transformation from a single point (crisp) to a fuzzy number is essential for the forecasting model. Fuzzy time series (FTS) is applied for predicting air pollution; however, it has a limitation caused by utilizing an arbitrary number of intervals. This study involves predicting the daily air pollution index using the FTS Markov chain (FTSMC) model based on a grid method with an optimal number of partitions, which can greatly develop the model accuracy for air pollution. The air pollution index (API) data, which was collected from Klang, Malaysia, is considered in the analysis. The model has been validated using three statistical criteria, which are the root mean (RMSE), the mean absolute percentage error (MAPE), and the Thiels\u2019 U statistic. Also, the model\u2019s validation has been investigated by comparison with some of the famous statistical models. The results of the proposed model demonstrated outperformed the other models. Thus, the proposed model could be a better option in air pollution forecasting that can be useful for managing air quality.<\/jats:p>","DOI":"10.3390\/sym12020293","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Predicting Daily Air Pollution Index Based on Fuzzy Time Series Markov Chain Model"],"prefix":"10.3390","volume":"12","author":[{"given":"Yousif","family":"Alyousifi","sequence":"first","affiliation":[{"name":"Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5791-2815","authenticated-orcid":false,"given":"Mahmod","family":"Othman","sequence":"additional","affiliation":[{"name":"Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rajalingam","family":"Sokkalingam","sequence":"additional","affiliation":[{"name":"Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibrahima","family":"Faye","sequence":"additional","affiliation":[{"name":"Center for Intelligent Signal and Imaging Research &amp; Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1202-2552","authenticated-orcid":false,"given":"Petronio C. L.","family":"Silva","sequence":"additional","affiliation":[{"name":"Instituto Federal do Norte de Minas \u2013 IFNMG, Janu\u00e1ria 39400-149, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, L., Wang, J., Tan, X., and Fang, C. (2020). Analysis of NOx Pollution Characteristics in the Atmospheric Environment in Changchun City. Atmosphere, 11.","DOI":"10.3390\/atmos11010030"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5517","DOI":"10.1016\/j.scitotenv.2011.08.069","article-title":"Forecasting of Daily Air Quality Index in Delhi","volume":"409","author":"Kumar","year":"2001","journal-title":"Sci. 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