An interval-valued fuzzy-stochastic programming approach and its application to municipal solid waste management

In this study, an interval-valued fuzzy-stochastic programming (IVFSP) approach is developed for municipal solid waste (MSW) management under uncertainty. IVFSP can tackle multiple uncertainties presented as intervals as well as possibilistic and probabilistic distributions. The adoption of interval-valued fuzzy sets is capable of reflecting waste managers' confidence levels over subjective judgments, and can thus enhance the system robustness. An infinite α-cuts method is employed for discretizing the interval-valued fuzzy sets in IVFSP. Such a method can communicate all fuzzy information into the optimization process without ignoring valuable uncertain information. Moreover, IVFSP can permit in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised waste-allocation targets are violated. The developed approach is applied to a MSW management problem to demonstrate its applicability. The results indicate that interval solutions associated with different risk levels of constraint violation have been generated. They can help waste managers to identify desired waste-flow-allocation schemes and capacity-expansion plans according to their preference and practical conditions, as well as facilitate in-depth analyses of tradeoffs between economic efficiency and constraint-violation risk.