Cloud Hierarchical Analysis

摘要

The Analytic Hierarchy Process proposed by Thomas L. Saaty has been well developed and widely applied. There are also many doubts about AHP including the 9-scale ratio measurement in making the comparison. To deal with the vagueness of people's judgment, many researchers employ the fuzzy ratios in place of exact ratios. But except the fuzziness in people's subjective sense, there also exists uncertainty and randomness. The Cloud model, which can effectively integrate the fuzziness and randomness of linguistic judgment in a unified way, is used to express the ratios in the comparison matrix. Then the geometric mean method is employed to calculate the Cloud weights for each positive reciprocal Cloud matrix, and these weights are combined in the usual manner to determine the final Cloud scores for the alternatives. We rank the alternatives from highest to lowest by comparing the parameters of the Cloud scores. The examples prove the efficiency of the Cloud Hierarchical Analysis (CHA) proposed in this paper. CHA is the natural development of AHP and FHA.