**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.