A note on “Incomplete interval fuzzy preference relations and their applications”

• The additive consistency definitions in Xu et al. (2014) are technically incorrect.
• Properties are proposed for consistent interval fuzzy preference relations (IFPRs).
• Errors in Xu et al. (2014) are corrected.
• A new additive consistency definition is put forward for incomplete IFPRs.

In a very recent paper by Xu et al. (2014), an interval-arithmetic-based equation is introduced to define additively consistent interval fuzzy preference relations (IFPRs), and some properties of consistent IFPRs are put forward and used to define additive consistency for incomplete IFPRs. This note shows that such additive consistency definitions are technically wrong, and corrects errors in the definitions and properties of additively consistent IFPRs.