  In this paper, we propose a new method for the derivation of a priority
vector from an incomplete pairwise comparisons (PC) matrix. We assume that each
entry of a PC matrix provided by an expert is also evaluated in terms of the
expert's confidence in a particular judgment. Then, from corresponding graph
representations of a given PC matrix, all spanning trees are found. For each
spanning tree, a unique priority vector is obtained with the weight
corresponding to the confidence levels of entries that constitute this tree. At
the end, the final priority vector is obtained through an aggregation of
priority vectors achieved from all spanning trees. Confidence levels are
modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical
examples and comparisons with other methods are also provided. Last, but not
least, we introduce a new formula for an upper bound of the number of spanning
trees, so that a decision maker gains knowledge (in advance) on how
computationally demanding the proposed method is for a given PC matrix.
