Intuitionistic Fuzzy Geometric Bonferroni Means and Their Application in Multicriteria Decision Making

As a useful aggregation technique, the Bonferroni mean (BM) can capture the interrelationship between input arguments and has been a hot research topic recently. Based on the classic BM, many BM operators have been proposed and developed, such as the weighted BM, the generalized BM, the intuitionistic fuzzy BM, and so on. However, these BM operators are all based on the averaging mean, which is one of the basic aggregation approaches and focuses on the group opinion and another basic one is the geometric mean, which gives more importance to the individual opinions. To combine with the geometric mean and the BM, in this paper, we propose the geometric BM, the weighted geometric BM, and the generalized weighted geometric BM. These new geometric BMs can reflect the geometric interrelationship between the individual criterion and other criteria and keep the main advantage of BM. Furthermore, we investigate the geometric BMs under the intuitionistic fuzzy environment, which is more common phenomenon in modern life and develop three intuitionistic fuzzy geometric Bonferroni mean operators, i.e., the intuitionistic fuzzy geometric Bonferroni mean (IFGBM), the intuitionistic fuzzy weighted geometric Bonferroni mean (IFWGBM), and the intuitionistic fuzzy generalized weighted geometric Bonferroni mean (IFGWGBM) and study their desirable properties, such as idempotency, commutativity, monotonicity, and boundedness. Finally, on the basis of the IFWGBM and IFGWGBM operators, we propose an approach to multicriteria decision making under the intuitionistic fuzzy environment, and a practical example is provided to illustrate our results.