3RD: A Multi-criteria Decision-Making Method Based on Three-Way Rankings

By combining ideas from three-way decision theory, prospect theory, and several families of multi-criteria decision-making (MCDM) methods, including ELECTRE, PROMETHEE, TODIM, and dominance-based rough set analysis (DRSA), we propose a new ranking-based MCDM method called 3RD. With respect to a single criterion, we construct a three-way ranking (i.e., trilevel ranking) of a set of decision alternatives by using an alternative as a reference in the sense of prospect theory and a family of three-way rankings from all alternatives. With respect to a set of criteria, we have multiple families of three-way rankings. By adopting the TODIM procedure, we introduce a ranking function to rank the set of alternatives according to these multiple families of trilevel rankings.