Fuzzy tonnage-average grade model based on extension principle

Due to the nature of the geological and mining activities, different input parameters in the grade estimation and mineral resource evaluation are always tainted with uncertainties. It is possible to investigate the uncertainties related to the measurements and parameters of the variogram model using the fuzzy kriging method instead of the kriging method. The fuzzy kriging theory has already been the subject of relatively various research studies but the main weak point in such studies is that the results of the fuzzy estimations are not used in decision-making and planning. A very common, but key, tool of decision-making for mining engineers is the tonnage-average grade models. Under conditions where measurements or/and variogram model parameters are tainted with uncertainties, the tonnage-average grade model will be uncertain as well. Therefore, it is necessary to use the fuzzy tonnage-grade model instead of the crisp ones, and the next analysis steps and decision-makings are done accordingly. In this paper, the computational principles of the fuzzy tonnage-average grade curve and a case study regarding its usage are presented.