Geometric Bonferroni Mean Operators

The Bonferroni mean has been extensively applied in multicriteria decision-making and support system and developed intuitionistic fuzzy set theory. Based on the second interpretation of the Bonferroni mean, in this paper, we introduce the geometric Bonferroni mean, which is a generalization of the Bonferroni mean and geometric mean and generalized geometric Bonferroni mean, and investigate their properties. To describe the uncertainty and fuzziness more objectively, we further develop the intuitionistic fuzzy geometric Bonferroni mean and the generalized intuitionistic fuzzy geometric Bonferroni mean, which describe the relationship between arguments, and the weighted intuitionistic fuzzy geometric Bonferroni mean and the generalized weighted intuitionistic fuzzy geometric Bonferroni mean, which consider the importance of each argument. Finally, we investigate their properties in detail. (C) 2016 Wiley Periodicals, Inc.