Relationships between the deck of cards method and the proximity measures approach

Abstract In this paper, we propose a theoretical comparison of two types of value-based methods within the field of Multiple Criteria Decision Making/Aiding. Both methods make use of qualitative information to produce a value on an interval scale for each alternative, assessed on a set of criteria, for ranking or classification purposes. The two methods are known in the literature as the deck of cards and the one based on ordinal proximity measures. The deck of cards method allows managing the intensities of preferences in a qualitative way by making pairwise comparisons to produce a value for each alternative, while the ordinal proximity measures method allows managing the proximities between the terms of ordered qualitative scales in a pure ordinal way and produces a value for each alternative. This paper provides the mathematical background on the concept of closeness between objects of a linear order, which is common to both methods and the way of assigning values or scores to the terms of ordered qualitative scales. It is presented a proof that, under certain circumstances, these two methods are equivalent. An illustrative example shows how to build an interval scale with the two methods.