A novel multi-attribute decision-making framework based on Z-RIM: an illustrative example of cloud service selection

In the multi-attribute decision-making (MADM) problems, decision makers refer to the extreme attribute values in general when evaluating the alternatives. However, in the real world, the ideal solution may lie in somewhere between the extreme values. The recently proposed reference ideal method (RIM) is able to solve the problem rightly. This study aims at developing a novel MADM framework combining best–worst method (BWM), maximizing deviation method (MDM), and RIM under Z-number environment. In this framework, Z-number is used to depict the inherent uncertainty and reliability of information in the decision makers’ judgments. And BWM and MDM are combined to determine the comprehensive attribute weights, in which BWM is utilized to obtain the subjective weights, while MDM is utilized to obtain the objective weights. In addition, Z-RIM is proposed by extending the traditional RIM under Z-number environment, which is employed for ranking the alternatives. An illustrative example of cloud service selection problem is implemented to illustrate the proposed framework. By comparison analysis, we demonstrate that Z-RIM can not only avoid rank reversal problem, but also generate reasonable results during the MADM processes.