Application of Interval Type-2 Fuzzy Linear Programming to Chlorine Injection in a Water Distribution System

In this paper, an interval type-2 fuzzy linear programming (IT2FLP) model was proposed to deal with uncertainty in booster optimization of a water distribution system (WDS). The IT2FLP model was applied to two cases to verify the efficiency of the method on the booster cost optimization under uncertainty. After formulating the IT2FLP model, the injection mass and booster costs in a type-2 fuzzy set (T2FS) can be obtained. The effects of booster number and injection pattern on optimal results and nodal chlorine concentration were compared. The results indicated that the injection mass decreased with an increase of booster number. However, the booster costs may increase or decrease with the increase of booster number, which depends not only on the construction costs related to booster number, but also operation cost related to injection mass. In addition, the nodal average chlorine concentrations in the WDS become more uniform with the increase of booster number under injection pattern 1 as well as injection pattern 2. The results obtained can provide more information for managers to make boosters schemes under uncertainty.