The Heronian mean provides an aggregation operator that considers the inter-dependent phenomena among the aggregated arguments. Nevertheless, it seems that the existing literatures only consider the HM for aggregating crisp numbers rather than any other types of arguments. In this paper, the HM under interval-valued intuitionistic fuzzy environments is studied. First, a generalized interval-val...

We investigate and propose two new Bonferroni means, that is, the optimized weighted BM (OWBM) and the generalized optimized weighted BM (GOWBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments and can satisfy the basic properties of the aggregation techniques simultaneously. Further, we propose the intervalvalued intuitionistic fuzzy optimi...

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respec...

The dynamic multi-attribute decision making problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators: dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator and uncertain dynamic intuitionistic fuzzy weighted averaging (UDIFWA) operator are pr...