A fuzzy rough-interval linear programming model for booster optimization in water distribution systems

In this article, a fuzzy rough-interval linear programming (FRILP) approach is proposed to deal with the uncertainty expressed by the fuzzy rough set in the optimization of booster cost under uncertainty. The FRILP model was applied to two cases to verify its effectiveness in booster optimization under uncertainty. The optimal upper and lower approximation intervals of the injection mass and booster cost in the fuzzy rough set were obtained and the effects of booster number and location were analysed. The results indicated that with an increase in booster number, the injection mass generally decreased, and booster cost decreased or increased. The nodal chlorine concentration also decreased and was distributed uniformly under a scenario with more boosters. Locating the booster far from the source resulted in more uniform chlorine distribution. The results could help managers design booster schemes with consideration of technical and economic factors comprehensively under uncertainty.