Multiple-criteria sorting using case-based distance models with an application in water resources management

A case-based distance model to solve sorting problems in multiple-criteria decision analysis (MCDA) is developed, and its application in water resources management is presented. The sorting problem in MCDA is to arrange a set of alternatives into ordered groups. MCDA is introduced as consequence-based preference aggregation, whereby consequence and preference expressions (values and weights) are defined and combined in a sequence of steps. Then, sorting problems are defined, and some properties are explained. Based on weighted Euclidean distance, two case-based distance models are developed for sorting using weights and group thresholds obtained by assessment of a case set provided by a decision maker (DM). This case-based method can elicit the DM's preferences more expeditiously and accurately than direct inquiry. Case-based sorting model I is designed for cardinal criteria, while its extension, i.e., case-based sorting model II, can handle both cardinal and ordinal criteria. Optimization programs are employed to find the most descriptive weights and group thresholds. A case study in which Canadian municipalities are sorted according to water usage is presented.