Non-Probabilistic Uncertainty in Subsurface Hydrology and Its Applications: an Overview

While a presumed equality between uncertainty and probability is dominant in subsurface hydrology, in other areas of science and engineering progress in the mathematics of uncertainty is leading the way in providing new types of uncertainty, distinct from probability. In this paper our focus is on one of these, namely fuzzy set theory and fuzzy logic. We start with an overview of fuzzy theory introducing terminology, notation, and concepts relevant to our paper. We continue our discussion with an overview of currently known applications in several areas that include subsurface characterization, groundwater flow and transport modeling, water resources management and optimization, and groundwater health risk assessment and management.