Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making

The Bonferroni mean BM was introduced by Bonferroni six decades ago but has been a hot research topic recently since its usefulness of the aggregation techniques. The desirable characteristic of the BM is its capability to capture the interrelationship between input arguments. However, the classical BM andGBM ignore theweight vector of aggregated arguments, the general weighted BM WBM has not the reducibility, and the revised generalized weighted BM GWBM cannot reflect the interrelationship between the individual criterion and other criteria. To deal with these issues, in this paper, we propose the normalized weighted Bonferroni mean NWBM and the generalized normalized weighted Bonferroni mean GNWBM and study their desirable properties, such as reducibility, idempotency, monotonicity, and boundedness. Furthermore, we investigate the NWBM and GNWBM operators under the intuitionistic fuzzy environment which is more common phenomenon in modern life and develop two new intuitionistic fuzzy aggregation operators based on the NWBM and GNWBM, that is, the intuitionistic fuzzy normalized weighted Bonferroni mean IFNWBM and the generalized intuitionistic fuzzy normalizedweighted Bonferronimean GIFNWBM . Finally, based on the GIFNWBM,we propose an approach to multicriteria decision making under the intuitionistic fuzzy environment, and a practical example is provided to illustrate our results.