2-tuple Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Group Decision Making

Aims: The aim of this paper is to develop the 2-tuple linguistic Bonferroni mean and the weighted 2-tuple linguistic Bonferroni mean.
Study Design: Some desirable properties and special cases of the developed operators are discussed. The geometric Bonferroni mean (GBM) is a generalization of the Bonferroni mean and geometric mean. In this paper, we also investigate the GBM under 2-tuple linguistic environments. We develop the 2-tuple linguistic geometric Bonferroni mean and the weighted 2-tuple linguistic geometric Bonferroni mean. We investigate some fundamental properties and special cases of them.
Place and Duration of Study: The Bonferroni Mean (BM) operator is a traditional mean type aggregation operator, which can capture the expressed interrelationship of the individual arguments and which is only suitable to aggregate crisp data.
Methodology: This paper extends the BM operator to 2-tuple linguistic environments.
Results: Based on these operators, we develop two approaches for multiple attribute group decision making with 2-tuple linguistic information.
Conclusion: Two numerical examples are provided to illustrate the effectiveness and practicality of the proposed approaches.