To evaluate the most possible failure state of sensitive equipment when they encounter voltage sags,a lattice order based method was studied.Starting with the physical nature of equipment multi-valued mapping outcome due to voltage sag,a multi-valued mapping based outcome state describing method was proposed.Interval numbers which possess the characteristics of lattice order with the upper and lower probabilities of each outcome state as two endpoints were used to describe equipment state,and then the outcome states of decision-making problem could be lattice ordered.The possibility degree concept was introduced,and the possibility degree matrices were used to compare outcome states which don’t satisfy connectedness axioms and the most possible outcome state could be obtained.Comparing the simulation result with actual testing result showed that the proposed method can objectively reflect equipment failure state and quantitatively determine the most possible state.The method is accurate,less-sample-dependent and be of great engineering application significance.