On the derivation of weights from incomplete pairwise comparisons matrices via spanning trees with crisp and fuzzy confidence levels

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