Multiple criteria sorting models and methods. Part II: theoretical results and general issues

Multiple criteria sorting methods assign objects into ordered categories while objects are characterized by a vector of n attributes values. Categories are ordered, and the assignment of the object is monotonic w.r.t. to some underlying order on the attributes scales (criteria). We drew a landscape of these methods in Part I “Survey of the literature” (published in a previous issue of the present journal) and we aim to provide a theoretical view of the field in this second part. We describe a general framework for MCS models and position some existing models in the picture. Issues related to imperfect or insufficient information are then discussed. We also address questions that arise in the final phase of a decision aiding process as, e.g., explaining a recommendation or suggesting efficient ways of improving an object assignment.