Decision making with uncertainty: an example of water treatment approach selection

Decision makers often encounter uncertainty in selecting the best available option. Fuzzy multicriteria decision making aggregates different basic criteria through a hierarchy structure. This aggregation combines fuzzy assessment and priority matrices. When available data are imprecise, the assessment and priority matrices for different hierarchy level criteria are developed from expert judgments. In fuzzy aggregation, uncertainties in the assessment matrix are captured with fuzzy membership functions. The priority matrix is developed through pairwise comparison, in which the relative importance of the criteria is represented in crisp values; thus uncertainties associated with priority assignments are not incorporated in traditional fuzzy aggregation. This paper presents the application of a methodology to incorporate fuzziness in developing a priority matrix for environmental decision making. Fuzzy alpha-cut technique for different confidence intervals has been incorporated. The gradient eigenvector method has been followed to obtain consistency in constructing the priority matrix for different hierarchy level criteria. The max-min paired elimination method for hierarchical aggregation has been used to obtain the final fuzzy set. A case study for drinking water treatment technology evaluation is performed to present the potential environmental application of this approach, leading to the identification of the best treatment technology.