Evaluation of the Performance of Fuzzy Logic Applied in Spatial Analysis for Mineral Prospecting

Fuzzy logic, decision making procedure (AHP), and conditional probability were evaluated on the spatial analysis of geological data, to address potential areas for radioactive mineral occurrences in the Poços de Caldas Plateau ( ≅ 750 Km). Spatial inference techniques were applied controlled by a prospecting model based on diagnostic criteria, represented by favorable lithology, structures features and gamma-ray intensity. The diagnostic criteria, favorable lithology and gamma-ray intensity, were converted on fuzzy members through linear functions applied over weights defined from a heuristic manner. In the lithological case linear functions were applied to spatialise the uncertainly associated with the location of the inferred boundaries. Structural features were spatialised through sigmoid functions that constitute the fuzzy members decreasingly ordered as the distance from the features increase. The crossover point of the sigmoid function was defined using the spatial correlation (conditional probability) between the diagnostic criteria and the 48 known radioactive mineral occurrences. Finally the fuzzy evidence was combined through a weighted mean sum where the weights were empirically defined according to the Analytical Hierarchic Process (AHP). The resulting grid was arbitrarily sliced in four classes of potentiality (Null, low, medium and high potential), which express different levels of favorability for radioactive mineral occurrences. The fuzzy scenario was qualitatively and quantitatively compared with previous results obtained by Boolean and Weighted Means based models. The comparison of both procedures showed that the fuzzy scenario accomplished a better performance. A target area of 30.43Km (4.18% of the alkaline complex) encompassed 27 mineral occurrences, whereas each previous model encompassed only 24 in an approximately similar area. The correlation of mineral occurrences in relation to the potential classes for the different scenarios was also assessed. The high and medium potential classes of the fuzzy scenario showed posterior probabilities 12.9 and 5.7 higher than the prior probabilities. These values were, respectively, 12.6 and 4.97 for the same classes defined by the Weighted Means based model. For the potential class of the Boolean model this value was 5.78. These results show that fuzzy set theory enables a better refinement of the data modeling, improving the ability to spatially represent the geological data on continuous surfaces. This improvement can lead to better conclusions during decision making processes. Keyword: spatial analysis, fuzzy logic, GIS and decision making process.