How to handle uncertainties in AHP: The Cloud Delphi hierarchical analysis

In practice, many practical problems occur in uncertain environments, especially in situations that involve human subjective evaluation such as that in the analytic hierarchy process (AHP). This paper presents a practical multi-criteria group decision-making method for decision making under uncertainty. To handle the randomness and fuzziness of individual judgments, the normal Cloud model, group decision-making technique, and the Delphi feedback method are adopted. In the proposed Cloud Delphi hierarchical analysis (CDHA), experts are asked to express their judgments using interval numbers. Individual fuzziness and randomness are then mined from the interval-value comparison matrices. Subsequently, the interval-value pairwise comparison matrices are converted into the corresponding Cloud matrices, and the one-iteration Delphi process is executed to diminish individual judgment mistakes. The individual Cloud weight vectors are calculated using the geometric mean technique and are finally weighted to form the group Cloud weight vector. A simple case study that involved reproducing the relative area sizes of six provinces in China shows that the CDHA method can effectively reduce mistakes and improve decision makers’ judgments in situations that require subjective expertise and judgmental inputs. In addition, a practical decision-making problem in which houses are ranked by home buyers shows that the proposed method is effective when applied to complex, large, multidisciplinary problems with considerable uncertainties. 2012 Elsevier Inc. All rights reserved.