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), 2538.

 

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