A Qualitative Reasoning Approach to Measure Consensus

This chapter introduces a mathematical framework on the basis of the absolute order-of-magnitude qualitative model. This framework allows to develop a methodology to assess the consensus found among different evaluators who use ordinal scales in group decision-making and evaluation processes. The concept of entropy is introduced in this context and the algebraic structure induced in the set of qualitative descriptions given by evaluators is studied. We prove that it is a weak partial semilattice structure that in some conditions takes the form of a distributive lattice. The definition of the entropy of a qualitatively-described system enables us, on one hand, to measure the amount of information provided by each evaluator and, on the other hand, to consider a degree of consensus among the evaluation committee. The methodology presented is able of managing situations where the assessment given by experts involves different levels of precision. In addition, when there is no consensus within the group decision, an automatic process measures the effort necessary to reach said consensus.