I-VFRP: An interval-valued fuzzy robust programming approach for municipal waste-management planning under uncertainty

In this study, an interval-valued fuzzy robust programming (I-VFRP) model has been developed and applied to municipal solid-waste management under uncertainty. The I-VFRP model can explicitly address system uncertainties with multiple presentations, and can directly communicate the waste manager's confidence gradients into the optimization process, facilitating the reflection of weak or strong confidence when subjectively estimating parameter values. Parameters in the I-VFRP model can be represented as either intervals or interval-valued fuzzy sets. Thus, variations of the waste manager's confidence gradients over defining parameters can be effectively handled through interval-valued membership functions, leading to enhanced robustness of the optimization efforts. The results of a theoretical case study indicate that useful solutions for planning municipal solid-waste-management practices can be generated. The waste manager's confidence gradients over various subjective judgments can be directly incorporated into the modeling formulation and solution process. The results also suggest that the proposed methodology can be applied to practical problems that are associated with complex and uncertain information.