Abstract: In the theory of the rough set,some results were given to deal with possible inconsistencies in preferential attribute decision.However,in practice,different reductions may occur according to this theory.How to choose the best reduction from different ones is still unanswered.In this thesis,with the theory of lattice and order based on dominance relation,the fidelity of a reduction is defined.Then,the similarities of different reductions compared with original data table are obtained.Through this tool one can choose a better reduction of attributes to make a decision.

Key words: lattice-order, dominance relation, reduction of attributes, fidelity