Predicting air pollution using fuzzy membership grade Kriging

A practical situation often facing us is that fuzzy spatial data are recorded as crisp real-valued numbers, e.g., a PM10 record is 15.1, but we do know that it is an imprecise and vague observation. A new spatial analysis technique – fuzzy membership grade Kriging with semi-statistical membership, proposed by Guo has been developed to address fuzzy spatial data recorded as crisp numbers. In this paper, we will explain fuzzy membership grade Kriging, its root, its theory and its implementations. As an illustration, we will use PM10 data of California, USA. Three sample membership functions are extracted from the data itself: linear, quadratic and hyperbolic tangent and applied to the PM10 data. The predicted membership grades are also transformed back into PM10 concentrations by using inverse functions in order to identify areas being dangerous to human health. Finally, we implement our new fuzzy membership grade Kriging in GIS.