Generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral operators for multicriteria decision making

The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (IVIFHGSCI) operators, which consider the importance of the ordered positions and correlations among the arguments with the assumption that the aggregated arguments are interrelated. Furthermore, some of the properties and special cases of these operators are discussed. An approach for multicriteria decision making based on these operators is developed. Finally an illustrative example follows.