The fundamental problem underlying all multi-criteria decision analysis (MCDA) problems is that of dominance between any two alternatives: "Given two alternatives A and B, each described by a set criteria, is A preferred to B with respect to a set of decision maker (DM) preferences over the criteria?". Depending on the application in which MCDA is performed, the alternatives may represent strategies and policies for business, potential locations for setting up new facilities, designs of buildings, etc. The general objective of MCDA is to enable the DM to order all alternatives in order of the stated preferences, and choose the ones that are best, i.e., optimal with respect to the preferences over the criteria. This article presents and summarizes a recently developed MCDA framework that orders the set of alternatives when the relative importance preferences are incomplete, imprecise, or qualitative in nature.
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