We present a new method (called UTAGMS) for multiple criteria ranking using strongly and weakly established weak preference relations which result from an ordinal regression. The preference information supplied by the decision maker is a set of pairwise compar isons of reference alternatives. The preference model built via ordinal regression is a set of general additive value functions. The method provides two final rankings: a strong ranking identifying “sure” preference statements, and a weak ranking identifying “possi ble” preference statements. In order to build these two rankings, the method takes into account all value functions compatible with the preference information. The UTAGMS method is intended to be used interactively, with progressive statement of pairwise com parisons. Moreover, the method can support the decision maker also when his/her pref erence statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTAGMS software. Some extensions of the method are also presented.