An interval fuzzy model for magnetic monitoring: estimation of a pollution index

In this contribution, a methodology is reported in order to build an interval fuzzy model for the pollution index PLI (a composite index using relevant heavy metal concentration) with magnetic parameters as input variables. In general, modelling based on fuzzy set theory is designed to mimic how the human brain tends to classify imprecise information or data. The “interval fuzzy model” reported here, based on fuzzy logic and arithmetic of fuzzy numbers, calculates an “estimation interval” and seems to be an adequate mathematical tool for this nonlinear problem. For this model, fuzzy c-means clustering is used to partition data, hence the membership functions and rules are built. In addition, interval arithmetic is used to obtain the fuzzy intervals. The studied sets are different examples of pollution by different anthropogenic sources, in two different study areas: (a) soil samples collected in Antarctica and (b) road-deposited sediments collected in Argentina. The datasets comprise magnetic and chemical variables, and for both cases, relevant variables were selected: magnetic concentration-dependent variables, magnetic features-dependent variables and one chemical variable. The model output gives an estimation interval; its width depends on the data density, for the measured values. The results show not only satisfactory agreement between the estimation interval and data, but also provide valued information from the rules analysis that allows understanding the magnetic behaviour of the studied variables under different conditions.