Two-dimensional uncertain linguistic generalized normalized weighted geometric Bonferroni mean and its application to multiple-attribute decision making

2-Dimensional Uncertain Linguistic Variables (2DULVs) are powerful tools to express the fuzzy or uncertain information, and the weighted Bonferroni mean can not only take the attribute importance into account, but also capture the interrelationship between the attributes. However, the traditional Bonferroni mean can only deal with the crisp numbers. In this paper, Bonferroni mean was extended to process the 2DULVs. Firstly, we proposed the Normalized Weighted Geometric Bonferroni Mean (NWGBM) operator and the Generalized Normalized Weighted Geometric Bonferroni Mean (GNWGBM) operator, which had the characteristic of reducibility and considered the interrelationships between two attributes. Then, we introduced the computation rules, characteristics, the expected value, and comparison method of the 2DULVs. Further, we developed the 2-Dimensional Uncertain Linguistic Normalized Weighted Geometric Bonferroni Mean (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean (2DULGNWGBM), and explored some properties and discussed some special cases of them. Finally, we developed a new decision making method based on these operators. An example is given to compare the method with the existing methods. (C) 2018 Sharif University of Technology. All rights reserved.