Computer support in building-up a consistent preference matrix

Abstract

A method of a computer support for an expert who is creating a matrix of pairwise preferences in a decision making problem is described. The final preference matrix should be antisymmetric and consistent. While it is easy to control the antisymmetricity of the entries, the consistency of the inserted values, on the other hand, is far from obvious. The suggested computer support is based on the idea that the consistent hull of the previously inserted entries is maintained in the computer, and in every step the human expert gets the information whether the intended preference value can be chosen independently of the previous inputs. If the opposite case, then computer recommends the unique consistent value. Still, the expert can decide differently according to his/her own opinion. Then the optimal consistent approximation of all previous entries including the last input is computed and maintained for further steps. The computer support uses the optimal approximation algorithm due to the authors. The new method is illustrated by examples.