**4. Interpretation and conclusion**

In the results section, the dataset is now calculated and completed. However, it is now up to us to interpret the maps, and decide how to best make use of the calculated dataset, so that it provides us with easy to read information. And we can do this through a change map and 13 health safety maps.

**Figure 5.** Changes in PM2.5 Concentrations in California between 1999 and 2011

As one can clearly see from Figure 5, that PM2.5 concentration has clearly decreased and air quality has improved remarkably over the years. The blue and green colours show negative changes, and orange shows positive changes. Counties such as Los Angeles and Orange show the highest decrease, and other counties such as Lassen, Plumas, Sierra, Inyo, and Imperial show some increase in PM2.5 concentration. However, *a decrease in PM2.5 concentration does not indicate safety in air quality*.

In terms of credibility hypothesis testing, say, with credibility significance level α = 0.25, critical point for the best credibility rejection interval is x0 =14.485. The indictor λ*ij* is defined as

$$
\mathcal{A}\_{\circ} = \begin{cases} 1 & \tilde{\mathbf{x}}\_{\circ} < 14.485 \\ 0 & \text{otherwise} \end{cases},\tag{12}
$$

For comparisons of air quality safety, we generate PM2.5 safety maps with two colours: blue colour if *λij* = 1, orange colour otherwise, in total 13 safety maps. See Figure 6.

2008 2009 2010

2011

**4. Interpretation and conclusion**

**Figure 5.** Changes in PM2.5 Concentrations in California between 1999 and 2011

*ij*

l

health safety maps.

322 Current Air Quality Issues

*indicate safety in air quality*.

colour if *λij*

In the results section, the dataset is now calculated and completed. However, it is now up to us to interpret the maps, and decide how to best make use of the calculated dataset, so that it provides us with easy to read information. And we can do this through a change map and 13

As one can clearly see from Figure 5, that PM2.5 concentration has clearly decreased and air quality has improved remarkably over the years. The blue and green colours show negative changes, and orange shows positive changes. Counties such as Los Angeles and Orange show the highest decrease, and other counties such as Lassen, Plumas, Sierra, Inyo, and Imperial show some increase in PM2.5 concentration. However, *a decrease in PM2.5 concentration does not*

In terms of credibility hypothesis testing, say, with credibility significance level α = 0.25, critical point for the best credibility rejection interval is x0 =14.485. The indictor λ*ij* is defined as

> 1 14.485, 0 othewise *ij*

For comparisons of air quality safety, we generate PM2.5 safety maps with two colours: blue

= 1, orange colour otherwise, in total 13 safety maps. See Figure 6.

% (12)

375

*x*

 <sup>ì</sup> <sup>&</sup>lt; <sup>=</sup> <sup>í</sup> î

375

1999 2000 2001

2002 2003 2004

2005 2006 2007

**Figure 6.** Air Quality PM2.5 Safety areas in California 1999-2011

One can now observe that over the 13 years period 1999-2011, Stanislaus, Merced, Madera, Fresno, Kings, Tulare, Kern, Los Angeles, San Bernardino, Orange, and Riverside counties are the counties with the highest PM2.5 safety problems. These areas have shown to be unsafe for public health safety, and especially for those with lung and heart problems, and for children and the elderly. These places are also sources of environmental and ecological concerns.

In conclusion, facing the difficult problem of "incomplete" PM2.5 data in California from 1999-2011, we used the interpolation and extrapolation smoothing approaches for "filling" those "missing value" sites. For easy computation, the fuzzy exponential membership function is assumed. The treatment is based on an assumption that the smoothing is performed for a given site rather than over different sites for a given year. Such an assumption is emphasizing the fact: the data recorded are PM2.5 concentration annual arithmetic means and they shouldn't change too dramatically over neighbour years. As to neighbour sites impacting, the member‐ ship grade kriging approach is adequate enough for generating smoothed maps. Furthermore, for utilizing credibility hypothesis testing theory, we perform parameter estimation of the fuzzy exponential membership function and in terms of membership ratio criterion for deriving the safety maps under 0.25 credibility significance level. Membership ratio criterion is very similar to likelihood ratio criterion in theoretical development. By comparing those 13 PM2.5 concentration safety maps to 1999-2011 change map, it is quite justifiable to say the safety maps under the credibility hypothesis testing procedure are very intuitive and convenient to the public. Finally, interpreting the 13 safety maps will provide the public with knowledge of air quality in California.
