FUZZY LOGIC

In classical set theory, the membership of a set is defined as true or false (1 or 0) whereas in fuzzy-set theory the membership of a set is defined on a continuous scale from full membership

to full non-membership (e.g. from prospective to non-prospective). The values of fuzzy membership can be chosen based on subjective judgment of an expert. Therefore in prospectivity mapping we first re-scale all the input data into a common scale from 0 to 1 and the combine these various evidence maps using so called fuzzy operators (Fuzzy Overlay tool) in different combinations.

A ROC curve is a plot of the sensitivity (true positive rate: TP / (TP + FN)) on the y-axis compared to 1-specificity (false positive rate: FP / (FP + TN)) on the x-axis. The area under a ROC curve (AUC) can be used as a measure of the accuracy of a diagnostic test and can also be used to measure the performance of a spatial predictive model, as in this paper. The AUC values vary from 0 to 1, with an AUC value of 1 indicating that the result is perfectly accurate having a sensitivity value of 1 and a 1-specificity value of 0. A totally random model would result in an AUC value of 0.5 and the curve would follow the chance diagonal.

References:

Bonham-Carter, G.F., 1994. Geographic Information Systems for Geoscientists - Modelling with GIS. Computer Methods in the Geosciences 13. Pergamon, Oxford, 398 p.

Korhonen, K,. 2018. Python tool to evaluate prospectivity models in ArcSDM 5 using receiver operating characteristic curve analysis. Geological Survey of Finland, Open access report, XX/2018, 12 p. Electronic publication. Available at https://hakku.gtk.fi/fi/reports.

Nykänen, V., Lahti, I., Niiranen, T., Korhonen, K., 2015. Receiver operating characteristics (ROC) as validation tool for prospectivity models - A magmatic Ni-Cu case study from the Central Lapland Greenstone Belt, Northern Finland. Ore Geology Reviews 71, 853−860.

Nykänen, V., Groves, D.I., Ojala, V.J., Eilu P. and Gardoll, S.J. 2008. Reconnaissance-scale conceptual fuzzy-logic prospectivity modelling for iron oxide copper - gold deposits in the northern Fennoscandian Shield, Finland. Australian Journal of Earth Sciences 55 (1), 25−38.

Zadeh, L.A., 1965. Fuzzy sets. Institute of Electric and Electronic Engineering, Information and Control 8, 338-353.