As the cloud computing develops rapidly, more and more cloud services appear. Many enterprises tend to utilize cloud service\nto achieve better flexibility and react faster to market demands. In the cloud service selection, several experts may be invited\nand many attributes (indicators or goals) should be considered. Therefore, the cloud service selection can be regarded as a kind\nof Multiattribute Group Decision Making (MAGDM) problems. This paper develops a new method for solving such MAGDM\nproblems. In this method, the ratings of the alternatives on attributes in individual decision matrices given by each expert are in\nthe form of interval-valued intuitionistic fuzzy sets (IVIFSs) which can flexibly describe the preferences of experts on qualitative\nattributes. First, the weights of experts on each attribute are determined by extending the classical gray relational analysis (GRA)\ninto IVIF environment. Then, based on the collective decision matrix obtained by aggregating the individual matrices, the score\n(profit) matrix, accuracy matrix, and uncertainty (risk) matrix are derived. A multiobjective programming model is constructed\nto determine the attribute weights. Subsequently, the alternatives are ranked by employing the overall scores and uncertainties\nof alternatives. Finally, a cloud service selection problem is provided to illustrate the feasibility and effectiveness of the proposed\nmethods.
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