Some Bonferroni mean operators with 2-tuple linguistic information and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems with 2-tuple linguistic information. Motivated by the ideal of Bonferroni mean and geometric Bonferroni mean, we develop two aggregation techniques called the 2-tuple linguistic Bonferroni mean (2TLBM) operator and the 2-tuple linguistic geometric Bonferroni mean (2TLGBM) operator for aggregating the 2-tuple linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the 2-tuple linguistic weighted Bonferroni mean (2TLWBM) operator and the 2-tuple linguistic weighted geometric Bonferroni mean (2TLWGBM) operator, based on which we develop two procedure for multiple attribute decision making under the 2-tuple linguistic environments. Finally, a practical example with comprehensive evaluating modeling of brand extension is given to verify the developed approach and to demonstrate its practicality and effectiveness.