A fuzzy risk approach for seasonal water quality management of a river system

Abstract

A fuzzy optimization model is developed for the seasonal water quality management of river systems. The model addresses the uncertainty in a water quality system in a fuzzy probability framework. The occurrence of low water quality is treated as a fuzzy event. Randomness associated with the water quality indicator is linked to this fuzzy event using the concept of probability of a fuzzy event. In most water quality management models the risk level for violation of a water quality standard is constrained by a preassigned value through a chance constraint. In the fuzzy risk approach a range of risk levels is specified by considering a fuzzy set of low risk, instead of using a chance constraint. Thus the two levels of uncertainty, one associated with low water quality and the other with low risk, are quantified and incorporated in the management model. The model takes into account the seasonal variations of river flow to specify seasonal fraction removal levels for the pollutants. Fuzzy sets of low water quality are considered in each season. The membership functions of these fuzzy sets represent the degree of low water quality associated with the discrete states of water quality in a season. The fuzzy risk of low water quality in a season at a checkpoint in the river system is expressed in terms of the degree of low water quality and the steady state probabilities associated with discrete river flows. Considering the fuzzy goals of the pollution control agency and dischargers, and the crisp constraints, the water quality management problem is formulated as a fuzzy optimization model. The model solution gives seasonal fraction removal levels for the pollutants. Application of the fuzzy optimization model is illustrated with a hypothetical river system.