A Novel SIR·Choquet Method for Multiple Attributes Group Decision-Making with Interval Grey Linguistic

Considering both the fuzziness caused by uncertainties and the greyness caused by inadequate information, the interval grey linguistic (i.e. IGL) variables were proposed and various multiple attributes group decision-making (i.e. MAGDM) methods have been developed. However, few approaches take the decision-maker’s (i.e. DM’s) preference structure and risk attitude into account. In this paper, the classical method named superiority and inferiority ranking (i.e. SIR) method is extended to solve the MAGDM problems in an IGL environment. First, the level of the DM’s risk attitude is taken into account when dealing with the IGL variables, and a novel G-Hamming distance is developed. Then, the Gaussian criterion, which has been mostly selected by users, is employed to describe the DM’s preference structure. Moreover, the Choquet integral is introduced as an appropriate aggregation procedure for the classical SIR method to cope with the interdependent or interactive characteristics among attributes. Finally, the SIR·Choquet method is presented in detail and two numerical examples are given to show the validity and practicality of the proposed method.