Deriving accurate fuzzy priorities is very important in multi-criteria decision making with vague information. In this paper, appropriate formulas for obtaining fuzzy priorities from additive fuzzy pairwise comparison matrices are introduced. The formulas are based on the proper fuzzy extension of the formulas for obtaining priorities from additive pairwise comparison matrices proposed by Fedrizzi & Brunelli (2010, Soft Comput. 14 , 639–645) satisfying Tanino's characterization. Moreover, a new normalization condition for priorities reachable (unlike other normalization conditions formerly proposed in the literature) also for inconsistent additive pairwise comparison matrices is proposed and extended properly to additive fuzzy pairwise comparison matrices. Furthermore, a new definition of a consistent additive fuzzy pairwise comparison matrix independent of the ordering of objects in the matrix is given, and the consistency requirement is also employed directly into the formulas for obtaining fuzzy priorities. Triangular fuzzy numbers are used for the fuzzy extension in the paper, and a brief discussion on how to easily modify the formulas and the definitions presented in the paper in order to apply on intervals, trapezoidal fuzzy numbers or any other type of fuzzy numbers is provided. The theory is illustrated on numerical examples throughout the paper. [ABSTRACT FROM AUTHOR]