Imprecise probability for modeling partial ignorance: application to waste load allocation in a river system

Abstract

Water resources systems problem are often characterized by uncertainty due to partial ignorance resulting from missing hydrologic data. Imprecise probability is a branch of advanced probability theory which models partial ignorance. The paper presents mathematical background of the theory of imprecise probability with its application to waste load allocation for river water quality management. The example problem of waste load allocation considers the fuzzy or imprecise goals of Pollution Control Agency (PCA) and dischargers discharging pollutants to river. The risk of low water quality due to the discharge of pollutants is computed with imprecise probability and subsequently minimized using fuzzy multiobjective optimization. Application of the model is illustrated with a hypothetical river system.