An interval-valued fuzzy linear programming with infinite α-cuts method for environmental management under uncertainty

In this study, an interval-valued fuzzy linear programming with infinite alpha-cuts (IVFLP-I) method is developed for municipal solid waste (MSW) management under uncertainty. IVFLP-I can not only tackle uncertainties expressed as intervals and interval-valued fuzzy sets, but also take all fuzzy information into account by discretizing infinite alpha-cut levels to the interval-valued fuzzy membership functions. Through adoption of the interval-valued fuzzy sets, IVFLP-I can directly communicate information of waste managers' confidence levels over various subjective judgments into the optimization process. Compared to the existing methods in which only finite alpha-cut levels exist, IVFLP-I would have enhanced the robustness in the optimization efforts. A MSW management problem is studied to illustrate the applicability of the proposed method. Four groups of optimal solutions can be obtained through assigning different intervals of alpha-cut levels. The results indicate that wider intervals of alpha-cut levels could lead to a lower risk level of constraint violation associated with a higher system cost; contrarily, narrower intervals of alpha-cut levels could lead to a lower cost with a higher risk of violating the constraints. The solutions under different intervals of alpha-cut levels can support in-depth analyses of tradeoffs between system costs and constraint-violation risks.