Modelling Short‐Scale Variability and Uncertainty During Mineral Resource Estimation Using a Novel Fuzzy Estimation Technique

For mineral resource assessment, techniques based on fuzzy logic are attractive because they are capable of incorporating uncertainty associated with measured variables and can also quantify the uncertainty of the estimated grade, tonnage etc. The fuzzy grade estimation model is independent of the distribution of data, avoiding assumptions and constraints made during advanced geostatistical simulation, e.g., the turning bands method. Initially, fuzzy modelling classifies the data using all the component variables in the data set. We adopt a novel approach by taking into account the spatial irregularity of mineralisation patterns using the Gustafson–Kessel classification algorithm. The uncertainty at the point of estimation was derived through antecedent memberships in the input space (i.e., spatial coordinates) and transformed onto the output space (i.e., grades) through consequent membership at the point of estimation. Rather than probabilistic confidence intervals, this uncertainty was expressed in terms of fuzzy memberships, which indicated the occurrence of mixtures of different mineralogical phases at the point of estimation. Data from different sources (other than grades) could also be utilised during estimation. Application of the proposed technique on a real data set gave results that were comparable to those obtained from a turning bands simulation.