On consistency and ranking of alternatives in uncertain AHP

This paper introduces uncertainty theory to deal with non-deterministic factors in ranking alternatives. The uncertain variable method (UVM) and the definition of consistency for uncertainty comparison matrices are proposed. A simple yet pragmatic approach for testing whether or not an uncertainty comparison matrix is consistent is put forward. In cases where an uncertainty comparison matrix is inconsistent, an algorithm is used to generate consistent matrix. And then the consistent uncertainty comparison matrix can derive the uncertainty weights. The final ranking is given by uncertainty weighs if they are acceptable; otherwise we rely on the ranks of expected values of uncertainty weights instead. Three numerical examples including a hierarchical (AHP) decision problem are examined to illustrate the validity and practicality of the proposed methods.