Geometric Bonferroni means with their application in multi-criteria decision making

In this paper, we introduce the Bonferroni geometric mean, which is a generalization of the Bonferroni mean and geometric mean and can reflect the correlations of the aggregated arguments. To describe the uncertainty and fuzziness more objectively, intutionistic fuzzy set could be used for considering the membership, non-membership and uncertainty information. To aggregate the Atanassov’s intuitionistic fuzzy information, we further develop the Atanassov’s intuitionistic fuzzy geometric Bonferroni mean describing the interrelationship between arguments, and some properties and special cases of them are also discussed. Moreover, considering the importance of each argument, the weighted Atanassov’s intuitionistic fuzzy geometric Bonferroni mean is proposed and applied to multi-criteria decision making. An example is given to compare the proposed method with the existing ones.