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.



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