Bonferroni harmonic mean operators based on two-dimensional uncertain linguistic information and their applications in land utilization ratio evaluation

The Bonferroni Mean (BM) enjoys the advantage of capturing the interrelationship among the input arguments, and the harmonic mean is a conservative average lying between the max and min operators. The 2-dimensional uncertain linguistic variables add a subjective evaluation of the reliability of the evaluation results given by decision-makers; therefore, they can express fuzzy information better. In this paper, in order to combine their advantages, the 2-Dimensional Uncertain Linguistic Weighted Bonferroni Mean (2DULWBM) operator is rst proposed. However, it cannot consider the case when the given arguments are too high or too low. Therefore, we further propose the 2-Dimensional Uncertain Linguistic Improved Weighted Bonferroni Harmonic Mean (2DULIWBHM) operator, which combines the 2DULWBM with Harmonic Mean. Furthermore, some desirable properties and their special cases are studied. Further, a new method is developed to deal with some Multi-Attribute Group Decision Making (MAGDM) problems under 2-dimensional uncertain linguistic environment based on the proposed operators. Finally, an illustrative example is given to testify the validity of the developed method by comparing it with the other existing methods.