## On the Notion of Category Size in Multiple Criteria Sorting Models

### Authors: Vincent Mousseau, Lu\'is C. Dias and Jos\'e R. Figueira

ABSTRACT

We consider the Multiple Criteria Sorting Problem, that aims at assigning each alternative in a finite set $A$ to one of the predefined categories. We propose a new concept of category size that refers to {\it the proportion by which an evaluation vector corresponding to a realistic alternative is assigned to the category}''.

Sorting problems usually refer to absolute evaluation (the assignment of an alternative does not depend on the others), as opposed to ranking and choice problems in which the very purpose is to compare alternatives against each other. Considering constraints concerning category size lead to define a Constrained Sorting Problem which refers both to absolute and relative evaluation.

After identifying decision situations in which category size is useful for modelling purposes, this paper defines the concept of category size and proposes a way to compute the size of categories, even when the set of alternatives and/or the preference information is/are imprecisely known. We show how this notion can be used in a preference elicitation process. Finally, in order to illustrate the use of this concept, we propose a procedure to infer the values for preference parameters that accounts for specifications (provided by the DM) about the size of categories, in the context of the UTADIS sorting model.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-02.ps.gz