Sharif University of Technology Scientia Iranica 1026-3098 26 2 2019 04 01 Bonferroni harmonic mean operators based on two-dimensional uncertain linguistic information and their applications in land utilization ratio evaluation 975 995 20447 10.24200/sci.2018.20447 EN P. Liu School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, China. W. Liu School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, China. Journal Article 2017 01 16 The Bonferroni mean (BM) has the advantages that it can capture the interrelationship among the input arguments, and the Harmonic mean is a conservative average lying between the max and min operators. The 2-dimension uncertain linguistic variables add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information. In this paper, in order to combine the advantages of them, we first propose the 2-dimensional uncertain linguistic weighted Bonferroni mean (2DULWBM) operator. However, it cannot consider the case when the given arguments are too high or too low. So we further proposed the 2-dimensional uncertain linguistic improved weighted Bonferroni harmonic mean (2DULIWBHM) operator, which combine the 2DULWBM with Harmonic Mean. Furthermore, we study some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision making (MAGDM) problems under 2-dimension uncertain linguistic environment based on the proposed operators. Finally, an illustrative example is given to testify the validity of the developed method by comparing with the other existing methods. https://scientiairanica.sharif.edu/article_20447_862f45c4168a6126fe59a89625829759.pdf