Abstract
The geometric Bonferroni mean (GBM) is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the GBM, in this paper, we develop the optimized weighted geometric Bonferroni mean (OWGBM) and the generalized optimized weighted geometric Bonferroni mean (GOWGBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments. Furthermore, we develop the intuitionistic fuzzy optimized weighted geometric Bonferroni mean (IFOWGBM) and the generalized intuitionistic fuzzy optimized weighted geometric Bonferroni mean (GIFOWGBM), and study their desirable properties such as idempotency, commutativity, monotonicity and boundedness. Finally, based on the IFOWGBM and GIFOWGBM, we present an approach to multi-criteria decision making and illustrate it with a practical example.