Uncertainty propagation in environmental decision making using random sets

Significant uncertain information is involved in environmental decision making due to complexities of natural systems, lack of sufficient data, and the interpretation of information that may be in numerical or linguistic forms. Uncertainties can be present in identification of criteria, interactions among criteria, evaluations of alternatives, eliciting weights from experts, and the choice of aggregation operators. Uncertainties arising from performance evaluations of criteria for each alternative and weights can be identified as aleatory (random) and epistemic (informal and lexical) uncertainty. These two types of uncertainty were best respectively represented as probability density function and possibility distribution. A methodology was presented in this paper to propagate these two kinds of uncertainty through aggregation operators. Random set theory is used as a uniform framework to integrate aleatory uncertainty and epistemic uncertainty. Evidence theory is utilized to approximate the probability measure when both probability density functions and possibility distributions are transformed into random sets. This methodology facilitates the incorporation of aleatory and epistemic information into the multicriteria environmental decision makings.