Grey-based PROMETHEE II with application to evaluation of source water protection strategies

An approach to handling uncertainty in Multiple Criteria Decision Analysis (MCDA) using grey numbers is proposed. The grey-based PROMETHEE II methodology is designed to represent and analyze decision problems under uncertainty, which are characterized by limited input data and uncertain preferences of Decision Makers (DMs). To begin with, the basic structure of a grey decision system is developed, including definitions, notation, and detailed calculation procedures. By integrating continuous grey numbers with linguistic expressions, each DM’s uncertain preference according to multiple criteria can be expressed. The new methodology takes account of both quantitative and qualitative data, first aggregating the DMs’ individual judgements on the performance of alternatives according to each criterion, and then integrating the criteria in order to determine the relative preference of any two alternatives. These preferences are then incorporated into the PROMETHEE II method to generate a complete ranking of alternatives. The methodology is illustrated using a case study in which source water protection strategies are ranked for Waterloo Region, Ontario, Canada.