Non-adaptability measures in the pseudo-questionnaires context

Abstract

Measuring the degree of non-adaptability of a partition to a criterion, represented by a reference partition, is an essential step in pseudo-questionnaires theory. In this work we characterize axiomatically the measure of non-adaptability in a general context. We base it on pre-orders on the set of all the possible experiences (complete or incomplete partitions). The construction of this measure is crucial for practical applications. It can be done in a natural way starting from the atoms of the partitions and constructing the non-adaptability measure by a process of successive aggregations made by suitable aggregation operators.