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-valued intuitionistic fuzzy HM (GIIFBM) is proposed and some of its desirable properties and special

more »

... are investigated in detail. Then, an approach to multi-criteria decision making based on weighted GIIFHM (GIIFWHM) is proposed. Numerical example about supplier selection in the supply chain is given to illustrate our method. Key words: Interval-valued intuitionistic fuzzy set (IVIFS), generalized interval-valued intuitionistic fuzzy Heronian mean (GIIFHM), generalized interval-valued intuitionistic fuzzy weighted Heronian mean (GIIFWHM), multi-criteria decision making.