This paper presents a new notion of complex cubic interval valued intuitionistic fuzzy set (CCIVIFS) which is an extension from the innovative concept of a cubic interval valued intuitionistic fuzzy set (CIVFS). The novelty of CCIVIFS is to achieve more range of values with the combination of interval-valued membership, interval-valued non-membership and fuzzy membership. We define some basic operations namely complement, union, intersection and notions of α ˜ -internal, b ˜ -internal, α ˜ -external and b ˜ -external complex cubic interval valued intuitionistic fuzzy set are introduced. Also P-union, P-intersection, R-union and R-intersection of α ˜ -internal and b ˜ -external complex cubic IVIF sets are discussed. Furthermore, a group decision-making method is discussed to illustrate the applicability and validity of the proposed approach.
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