Uncertainty in Fuzzy Membership Functions for a River Water Quality Management Problem

Uncertainty associated with fuzzy membership functions for a water quality management problem is addressed through interval grey numbers. The lower and upper bounds of the membership functions are expressed as interval grey numbers, and the membership functions are modeled as imprecise membership functions. A grey fuzzy optimization model for water quality management of a river system is developed. Application of the optimization model with imprecise membership functions is illustrated with a hypothetical river system.