This paper presents an new definition of acceptably consistent interval complement comparison matrix. An
interval complement comparison matrix with unacceptable consistency can be easily adjusted such that the revised matrix
possesses acceptable consistency. By utilizing a convex combination method, a family of crisp complement comparison
matrices with acceptable consistency can be obtained, whose weights are aggregated to obtain interval weights from an
acceptably consistent interval complement comparison matrix. Based on the possibility degree formula, the ranking of
interval weights can be derived. An algorithm for generating the weights from acceptably consistent interval complement
comparison matrices is proposed. Illustrated examples are presented to show the feasibility and effectiveness of the definition
and algorithm.