Conditions of two methods for estimating missing preference information

There are two methods, Herrera-Viedma et al. (2007)'s method and Fedrizzi-Giove (2007)'s method, for calculating missing preference information of an incomplete fuzzy preference relation. The underlying concept driving both methods is the additive consistency, and both methods are very similar. To Herrera-Viedma et al.'s method, we point out the shortcoming of one proposition about a sufficient condition of the method, and propose a new proposition, and give a new sufficient and necessary condition which is conveniently used for checking the method if applicable, and an example to validate the checking method, and also propose the only case where Herrera-Viedma et al.'s method is not applicable. To Fedrizzi-Giove's method, we give a wider condition where the method can guarantee the uniqueness of the estimates for the problems than theirs, then give an example to validate the condition, and also propose the only case where this method is not applicable. Based on the above contributions, we propose a new policy for reconstructing incomplete fuzzy preference relations by the two methods.