Can fuzzy set theory bring complex issues in sizing air quality monitoring network into focus?

This paper presents an objective methodology for determining the optimum number of ambient air quality monitoring stations in a air quality monitoring network that will give maximum information of present air quality. The suggested two fold approach is a combination of fuzzy similarity measures and fuzzy c-mean (FCM) clustering. In the first stage, cosine amplitude—one of the fuzzy similarity measures is used to classify or to regroup monitoring stations for the most critical air pollutant PM10 and NO2 for the defined possibility (α-cut) levels. In the second stage, average values of PM10, NO2, SO2, CO and SPM for the winter months being a worst case scenario are used in FCM clustering. Finally, the optimal number of air quality monitoring locations is selected as those (1) which form single station partition (unique partition) in crisp relational matrix for PM10 and NO2 and (2) have highest membership in fuzzy clustering. The methodology has been demonstrated by applying to case study on Delhi Metro City in India. The air quality data of criteria pollutants was collected for 15 months from the installed 41 stations. The outcome of the study reveals that the city of Delhi needs only 16 monitoring stations which will result into sizable reduction in the capital cost and the recurring expenses in ambient air quality monitoring in Delhi.