Normal intuitionistic fuzzy Bonferroni mean operators and their applications to multiple attribute group decision making

Normal intuitionistic fuzzy numbers (NIFNs), which express their membership degree and non-membership degree as normal fuzzy numbers, can better character normal distribution phenomena existing in the real world. In this paper, we investigate the multiple attribute decision making problems with normal intuitionistic fuzzy information. Firstly, we introduce some opera- tional laws, score function and accuracy function of NIFNs. Then, motivated by the ideal of Bonferroni mean, which can capture the interrelationship between input arguments, we develop some normal intuitionistic fuzzy aggregation operators, including the normal intuitionistic fuzzy Bonferroni mean (NIFBM) operator, the normal intuitionistic fuzzy weighted Bonferroni mean (NIFWBM) operator, the normal intuitionistic fuzzy geometric Bonferroni mean (NIFGBM) operator and the normal intuitionis- tic fuzzy geometric weighted Bonferroni mean (NIFGWBM) operator; and discuss some desirable properties of these operators. Furthermore, based on these operators, we propose a new approach for the multiple attribute group decision making under normal intuitionistic fuzzy environment. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed approach.