Application of fuzzy probability in water quality management of a river system

Water quality management of a river system is addressed in a fuzzy and probabilistic framework. Two types of uncertainty, namely randomness and vagueness, are treated simultaneously in the management problem. A fuzzy-set-based definition that is a more general case of the existing crisp-set-based definition of low water quality is introduced. The event of low water quality at a check-point in the river system is considered as a fuzzy event. The risk of low water quality is then defined as the probability of the fuzzy event of low water quality. Instead of constraining the risk of violation of water quality standard by a finite value of risk through a chance constraint, a fuzzy set of low risk that considers a range of risk levels with appropriate membership values is introduced. Different goals associated with the management problem are expressed as fuzzy sets. The resulting management problem is formulated as a fuzzy multiobjective optimization problem.