Multi-criteria sorting problem is concerned with placing available alternatives into different classes, where each alternative is defined by multiple criteria and classes are ordered from best to worst.  Classifying countries into risk level groups based on their current economical and political situations, evaluating the credibility of customers of a bank based on their credit histories, and promoting or demoting personnel based on their performances are some examples of this problem.

We present interactive approaches.  The approaches require the decision maker (DM) to progressively evaluate and place several alternatives in preference classes.  Based on the preference information derived from the DM’s placements as well as from dominance relations and the form of the underlying utility function, we try to place other alternatives.  We discuss the linear and quasiconcave utility function cases.