## 3 The Air Quality Fuzzy Comprehensive Evaluation (AQFCE) Paradigm  
### Preprocessing Module of AQFCE  
Here, for concentration data of air pollutants, missing data and reversal data are defined as abnormal data. Missing data are usually due to routine maintenance of monitoring instrument (zero calibration and criterion calibration), communication failure and power failure [28]. Reversal data mean that the concentration of PM\({}_{2.5}\) which belongs to a part of PM\({}_{10}\) is higher than that of PM\({}_{10}\) in the same sampling site and time. There is no uniform rule on automatic monitoring methods of PM\({}_{2.5}\) and PM\({}_{10}\) internationally, and thus distinct monitoring methods of PM\({}_{2.5}\) and PM\({}_{10}\) could result in this phenomenon especially under higher relative humidity. The integrity and accuracy of data are crucial for air quality evaluation, and abnormal data can lead to questionable and useless results. Nevertheless, there is little attention paid to the abnormal data though they are very common and unavoidable in monitoring data. Therefore, in the preprocessing module, abnormal data processing algorithms are proposed.  
1. For missing data, the deletion method will lose useful information and break the continuity of time series. Interpolation is the most frequently used method, but it is not applicable to data of air pollutant concentration which are highly nonlinear and nonstationary. No matter which interpolation method is selected, its ability of processing such data is limited by the essence of interpolation. Although the interpolation curve is through the known data points, there are problems of bigger errors on unknown data points and the poor capability of extrapolation. In contrast, curve fitting does not go through known data points and approaches the overall trend of data with the minimum error, offering a reasonable solution with better physical meaning. Therefore, for a single pollutant, least square polynomial fitting is recommended to deal with missing data and piecewise fitting is employed during the whole process. The fitting results are acquired based on the least root mean square error and the best determination coefficient and approved by a significant test (95% confidence level).
2. For reversal data of particulate matter, it is necessary to understand the cause [29]. Take China for example--PM\({}_{10}\) was included in the ambient air quality monitoring network far earlier than PM\({}_{2.5}\) and there are differences in monitoring methods. Measurement errors caused by the loss of volatile components in PM\({}_{10}\) when heating samples are unavoidable for the old Tapered Element Oscillating Microbalance (TEOM) and \(\beta\)-ray methods which have been used until now. Comparatively, new tapered element oscillating microbalance with a Filter Dynamic Measurement System (TEOM + FDMS) and \(\beta\)-ray with a Dynamic Heating System (\(\beta\)-ray + DHS), which have the calibration of temperature and humidity as well as the compensation of volatile components, can ensure accurate results of PM\({}_{2.5}\). As a part of PM\({}_{10}\), PM\({}_{2.5}\) accounts for 50%-80% according to Air Quality Guidelines of the WHO and PM\({}_{10}\) is highly related to PM\({}_{2.5}\). Least square linear regression is recommended for reversal data of particulate matter and piecewise regression is adopted in the whole process. Normal and paired PM\({}_{2.5}\) and PM\({}_{10}\) near reversal data are treatedas the independent variable and dependent variable to obtain the regression equation which is then used to correct reversal data. The regression result has a high determination coefficient (>0.8) and is approved by a significance test (95% confidence level).