Classification of objects into quality categories in the presence of hierarchical decision-making agents

In many practical contexts, it is often required to classify some objects of interest into predetermined unordered quality categories. This operation—referred to as quality classification problem—has received considerable attention in many fields of research, such as Analytical Chemistry, Materials Science, Medicine, Manufacturing, Quality Engineering/Management, Decision Analysis. Assuming that multiple agents perform subjective assignments of categories to the objects of interest, a further problem is that of fusing these assignments into global classifications. To this purpose, the mode and the weighted mode are very practical measures, as long as agents are equi-important or their (different) importance is expressed in the form of a set of weights. Unfortunately, these measures are not appropriate for quality classification problems where the agents’ importance is expressed in the form of a rank ordering (hierarchy). The aim of this article is to present a new method, which addresses the latter quality classification problem in a relatively simple and practical way. The peculiarity of this method is that the different importance of agents determines a different priority in considering their assignments and not a different weight of these assignments. A detailed description of the new method is supported by a realistic example in the Analytical Chemistry field.