Dual generalized Bonferroni mean operators based on 2-dimensional uncertain linguistic information and their applications in multi-attribute decision making

The dual generalized Bonferroni mean operator is a further extension of the generalized Bonferroni mean operator which can take the interrelationship of different numbers of attributes into account by changing the embedded parameter. The 2-dimensional uncertain linguistic variable (2DULV) adds a second dimensional uncertain linguistic variable (ULV) to express the reliability of the assessment information in first dimensional information, which is more rational and accurate than the ULV. In this paper, for combining the advantages of them, we propose the dual generalized weighted Bonferroni mean operator for 2DULVs (2DULDGWBM) and the dual generalized weighted Bonferroni geometric mean operator for 2DULVs (2DULDGWBGM). In addition, we explore several particular cases and some rational characters of them. Further, a new approach is introduced to handle multi-attribute decision making problems in the environment of 2DULVs by the proposed operators. Finally, we utilize several illustrative examples to testify the validity and superiority of this new method by comparing with several other methods.