**1. Introduction**

Air quality is a public and environmental issue that concerns people, whether in terms of global climate change or for health and the quality of life. The Environmental Protection Agency (EPA) regulates six primary air pollutants: Ozone, Particulate matter, Carbon Monoxide, Nitrogen Oxides, Sulfur Dioxide, and Lead [3]. Particulate matter (PM) refers to solid particles and liquid droplets found in air. Many manmade and natural sources produce PM directly, or produce pollutants that react in the atmosphere to form PM [9]. PM2.5 are small particles or particulate matter, that are less than 2.5 micrometers in diameter. PM2.5 can be produced by combustion from motor vehicles (esp. diesel powered buses and trucks), power plants, residential wood burning, forest fires, agricultural burning, and industrial processes [15]. They can also be formed in the air through when gases (air poullutants) and orgnaic compounds are transformed through chemical reactions.

These tiny particles PM2.5 can cause health hazards for people and also for the environment. People with heart diesease and lung problems including asthma, and also the elderly and children, are particularily vulnerable and at high risk when exposed to high levels of PM2.5. Due to the tiny size of these PM2.5 particles, they can penetrate to the deepest parts of the lungs, which is very dangerous to the human health. The California Air Resources Board (CARB) scentifically conducts studies and reports on the impacts of air pollutant exposures on public health, and the studies shows the negative impacts of PM2.5 which is known to cause premature death [2]. Scientific studies has repeatedly found links between particulate matter and many health problems of people who has been exposed to high levels of PM2.5, including asthma, bronchitis, respiratory problems, including shortness of breath and painful breathing, and premature deaths [3].

One must also be aware of the effects of high levels of PM2.5 on the environment as well. Since PM2.5 are tiny, they can be carried by wind and travel great distances, so that it can cause

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problems for areas downwind far from the actual source of air pollution. They have adverse effect on urban areas, agriculture, and the natural envrinonment. High levels of PM2.5 can results in visibility problems, urban haze, and acid rain [3].

The U.S. Environmental Protection Agency has established standards requiring the annual average of the PM2.5 to be not more than 15 micrograms per cubic meter [3]. The State of California monitors and reports on their air pollutants carefully, setting very high standards for their air quality (µg/m3 ). From 1999-2011, there are 113 station locations monitoring PM2.5. The site design originally planned was well spread statistically. See Figure 1. However, in reality, it is too costly in terms of time, finance, and manpower to keep all the 113 sites to be monitoring and recording every single year. Each year, only a part of the 113 sites were actually sampled, and each year at different locations.

**Figure 1.** Complete 113 PM2.5 Observational Sites in the California State

Comparisons of PM2.5 between the years are difficult, due to "missing data" at sample sites [6, 9]. A site that does not have a recorded PM2.5 value is referred to as "missing value", and since there are no patterns so that serious problems would twist the kriging map constructions.

Observing the dataset in Figure 2, the worst (in 1999) only 11 sites (9.73% of 113 sites) were used and at the best (in 2009) 65 sites (57.52% of 113 sites) were used. Over 13 years, 1469 annual arithmatic means (µg/m3 ) should be recorded, but actually, 556 annual arithmatic means (µg/ m3 ) were reported, which occupied 37.85%. Sitewise looking, only one site, Site 2596 (Placer County APCD), was collected data annually and had 13 recored annual arithmatic means (µg/ m3 ), while 16 sites had one annual arithmatic mean (µg/m3 ) only. The comparisons of PM2.5 annual arithmatic means (µg/m3 ) between years for a given site or between sites for a given year, i.e., the investigations of PM2.5 annual arithmatic means (µg/m3 ) patterns will be an

Figure 2. PM2.5 54 Samples Collected in California in 1999 (11 sites) and 2011 (52 sites) **Figure 2.** PM2.5 Samples Collected in California in 1999 (11 sites) and 2011 (52 sites)

Figure 1. Complete 113 PM2.5 47 Observational Sites in the California State

extremely difficult task due to data incompleteness. Therefore it is logical to engage fuzzy theory for treating the "missing" or scarce data. 56 Observing the dataset in Figure 2, the worst (in 1999) only 11 sites (9.73% of 113 sites) were used 57 and at the best (in 2009) 65 sites (57.52% of 113 sites) were used. Over 13 years, 1469 annual arithmatic means (mg/m3 ) should be recorded, but actually, 556 annual arithmatic means (mg/m3 58 ) were

59 reported, which occupied 37.85%. Sitewise looking, only one site, Site 2596 (Placer County APCD),
