**Author details**

Danni Guo\*

1999 2000 2001

2002 2003 2004

2005 2006 2007

2008 2009 2010

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

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

324 Current Air Quality Issues

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Address all correspondence to: d.guo@sanbi.org.za

Statistical Ecology Division, Biodiversity Research, Assessment and Monitoring, South Afri‐ can National Biodiversity Institute, Cape Town, South Africa
