A dominance-based decision making approach is proposed for multi-attribute decision problems with imprecise
information both on the attribute weights and the alternatives’ values. Firstly, the definitions of dominance, weak dominance
and potential optimality are given and some nonlinear programming models are built to determine which alternative is
nondominated or potential optimality. Then the relationship between the set of potential optimality alternatives and the
set of nondominated alternatives is discussed, and the index of dominance measuring is presented. The procedures to ranking
and screening the alternatives are given. Finally, the algorithm of variable replacement is used to solve the nonlinear decision
model with different kinds of imprecise information. The calculation of the case study and comparison of the results show
that the proposed method is feasible and effective.