Qualitative Decision Methods for Multi-Attribute Decision Making

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. The preferences over the criteria typically represent the relative importance of the various criteria to the DM, which is typically expressed either in the form of an ordering (e.g., a ranking) over the criteria, or if available, a set of numeric weights on each criterion. Most of the existing quantitative multicriteria decision methods (QnMCDMs) [70, 71] assume that it is possible to (a) completely rank the criteria in order of their importance, and/or (b) precisely quantify the degree of importance of criteria (e.g., as weights). Some formalisms such as Analytic Hierarchy Process (AHP) [75, 4], SMART [7], ELECTRE [6, 16, 43], TOPSIS [32, 27], VIKOR [62] and PROMETHEE [15, 16, 5] elicit relative importance of criteria using a matrix that specifies the pairwise ordering of the criteria, which is then used to generate weights for each criteria by a mathematical transformation [71]. In formal terms, this amounts to assuming that the preferences will always be a weak order [73]. The weak ordering is then typically transformed into a quantitative (numeric) scale, and the transformed importance values are then used to evaluate and compare candidates. However, it is not surprising that generation of weights based on qualitative assessments of pairwise relative importance of criteria often leads to instabil-