A fuzzy multiple linear regression model based on meteorological factors for air quality index forecast

Air quality index (AQI) is an indicator usually issued on a daily basis to inform the public how good or bad air quality recently is or how it will become over the next few days, which is of utmost importance in our life. To provide a more practicable way for AQI prediction, so that residents can clear about air conditions and make further plans, five imperative meteorological indicators are elaborately selected. Accordingly, taking these indicators as independent variables, a fuzzy multiple linear regression model with Gaussian fuzzy coefficients is proposed and reformulated, based on the linearity of Gaussian fuzzy numbers and Tanaka’s minimum fuzziness criterion. Subsequently, historical data in Shanghai from March 2016 to February 2018 are extracted from the government database and divided into two parts, where the first half is statistically analyzed and used for formulating four seasonal fuzzy linear regression models in views of the special climate environment of Shanghai, and the second half is used for prediction to validate the performance of the proposed model. Furthermore, considering that there is beyond dispute that triangular fuzzy number is more prevalent and crucial in the field of fuzzy studies for years, plenty of comparisons between the models based on the two types of fuzzy numbers are carried out by means of the three measures including the membership degree, the fuzziness and the credibility. The results demonstrate the powerful effectiveness and efficiency of the fuzzy linear regression models for AQI prediction, and the superiority of Gaussian fuzzy numbers over triangular fuzzy numbers in presenting the relationships between the meteorological factors and AQI.