Journal of Global Optimization

, Volume 56, Issue 3, pp 1143-1166

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality

  • Miłosz KadzińskiAffiliated withInstitute of Computing Science, Poznań University of Technology Email author 
  • , Roman SłowińskiAffiliated withInstitute of Computing Science, Poznań University of TechnologySystems Research Institute, Polish Academy of Sciences


In this paper, we present a new preference disaggregation method for multiple criteria sorting problems, called DIS-CARD. Real-life experience indicates the need of considering decision making situations in which a decision maker (DM) specifies a desired number of alternatives to be assigned to single classes or to unions of some classes. These situations require special methods for multiple criteria sorting subject to desired cardinalities of classes. DIS-CARD deals with such a problem, using the ordinal regression approach to construct a model of DM’s preferences from preference information provided in terms of exemplary assignments of some reference alternatives, together with the above desired cardinalities. We develop a mathematical model for incorporating such preference information via mixed integer linear programming (MILP). Then, we adapt the MILP model to two types of preference models: an additive value function and an outranking relation. Illustrative example is solved to illustrate the methodology.


Multiple criteria sorting Preference disaggregation Desired class cardinality Additive value function Outranking relation