Modelling pairwise comparisons on ratio scales

Many ‘real world’ decision problems have multiple criteria on qualitative domains. Given the expectation that more and more of such problems will be modelled as multiple criteria decision making problems involving scoring on subjective/qualitative domains, then there is a class of significant problems for which the evaluator will require an evaluation framework which handles occurrences of seeming intransitivity and inconsistency. These phenomena are likely to appear in qualitative/subjective domains where the decision-making environment is characterized by ambiguity and vagueness. In this paper we present a model for exploring the implications of pairwise comparisons on ratio scales. This model provides a mathematical explanation for the phenomena of intransitivity and inconsistency that sometimes appear in situations involving scoring on a subjective/qualitative domain. Using this framework we develop methods for generating consistent intervals on ratio scales. We also present a two-stage action learning process for generating consistent points on ratio scales that provides both behavioral and mathematical convergence.