## 3 The Air Quality Fuzzy Comprehensive Evaluation (AQFCE) Paradigm
### Evaluation Module of the AQFCE  
Based on the comprehensive consideration about the limitations of AQI and current air pollution, an improved air quality evaluation model is needed. Air quality is a huge and ambiguous system with a large number of uncertain factors, so fuzzy math is chosen as the solution [30]. Fuzzy math can effectively reduce impacts of a sharp boundary on evaluation results, and the combination of membership degree and factor weight can eliminate subjective factors in classification, providing an objective and comprehensive evaluation. In recent years, although some attempts related to fuzzy math have been made in the field of environmental evaluation [31; 32; 33; 34], these methods are either too complicated or too simple to be popularized in practice. There is seldom targeted and comprehensive research about air quality evaluations too. In fact, a fuzzy math model with deep customization can not only have more accurate and comprehensive evaluation result but can be as practical and convenient as the AQI, which is exactly what the present study focuses on. (1) Factor set  
As the evaluation object, air quality is influenced by various air pollutants such as sulfur oxides, nitrogen oxides, particulate matters and so forth, which are treated as evaluation factors and selected. Based on the international consensus on conventional air pollutants, SO\({}_{2}\), NO\({}_{2}\), CO, O\({}_{3}\), PM\({}_{2.5}\) and PM\({}_{10}\) are chosen for current air quality evaluation, and other pollutants can be added to our model immediately if necessary in future. The factor set composed of six factors is shown as follows:  
\[U=\{u_{1},u_{2},\ldots,u_{6}\}=[\text{SO}_{2},\text{NO}_{2},\text{CO},\text{ O}_{3},\text{PM}_{2.5},\text{PM}_{10}] \tag{3}\]  
(2) Evaluation set  
The evaluation set means the classification of air quality, and it has a corresponding calculation criterion which is similar to that of the AQI. The calculation grid ought to accord with the local situation and the algorithm adopted in the evaluation process. It is really significant because an inappropriate calculation grid will lead to questionable evaluation results, and it is also unsuitable for different algorithms to adopt the same calculation grid. Take China as an example--its calculation grid is in need of revisions for following reasons: Firstly, according to the Annual Bulletin on China's Environmental State of the last eight years [35], there have been tremendous changes in many aspects including industrial structure, pollution source, air quality and pollution control capacity, which means the current calculation grid released in 2012 is no longer applicable for present and future air quality evaluation and management. Secondly, there are too many levels concerned with pollution to distinguish in the current criterion: light pollution, moderate pollution, serious pollution and severe pollution (two sublevels). This is confusing for the general public and, with increasing attention and demand on air quality, a clearer and stricter version is imperative. Thirdly, an air quality report consists of a daily report and hourly report, which ought to be separated and follow diverse concentration limits, but there is incompleteness and misuse in the current criterion (Table 1). Hourly reports of PM\({}_{2.5}\) and PM\({}_{10}\) have to follow their daily concentration limits, respectively, leading to severely overrated particulate pollution. Similarly, hourly reports of SO\({}_{2}\) will result in an overestimated evaluation result when its concentration is higher than 800 ug/m\({}^{3}\) and an underestimation of a daily report of O\({}_{3}\) when the concentration is higher than 800 ug/m\({}^{3}\). These problems are not accepted and need corrections immediately. Finally, criterion should be compatible with a specific algorithm.